NATURAL LANGUAGE QUERYING OF HISTORICAL DATABASES 
James Clifford 
Information Systems Area 
Graduate School of Business Administration 
New York University 
New York, NY 
In this paper we examine the connection between two areas of semantics, namely the semantics of 
historical databases and the semantics of natural language querying, and link them together via a 
common view of the semantics of time. Since the target application domain is an historical database, we 
present the essential features of the Historical Relational Database Model (HRDM), an extension to the 
relational model motivated by the desire to incorporate more "real world" semantics into a database at 
the conceptual level. We then present the essential features of QE-III, a formally defined English 
database query language whose semantic and pragmatic theory, based on a Montague-type semantics, 
makes explicit reference to the notion of denotation with respect to a moment of time. We demonstrate 
the use of this language to query an example historical database, and discuss the issues of how to provide 
both a semantic and a pragmatic interpretation for questions within a model-theoretic framework. 
1 INTRODUCTION 
The relational model of data (RM), first proposed in 1970 
(Codd 1970), has by now become the standard for both 
database practitioners and theoreticians alike. In spite 
of this success, however, much recent database re- 
search has focused on ways to extend RM to overcome 
perceived shortcomings. Chief among the criticisms has 
been RM's lack of any "real-world semantics." Among 
the many diverse efforts directed at this deficiency have 
been a number of attempts to extend RM to incorporate 
a temporal dimension at the model level. While such 
efforts as Ben-Zvi (1982), Ariav et al. (1984), Snodgrass 
(1984), Lum et al. (1984), Clifford (1985), Snodgrass and 
Ahn (1985), and Gadia and Vaishnav (1985) have all 
addressed this issue, the Historical Relational Database 
Model (HRDM) ((Clifford 1982a), (Clifford and Warren 
1983), (Clifford 1985), (Clifford and Croker 1987)i) has 
the advantage of being directly parallel to a formal 
theory of natural language. In Section 2 we present an 
overview of HRDM, as it serves as the environment in 
which we wish to explore our query language. In 
particular, HRDM views database attributes as func- 
tions from moments in time to values (in the appropriate 
domain), and the intensional logic IL s provides a mech- 
anism for direct reference to these higher-order objects, 
and for incorporating them into a general temporal 
semantics for the database. We can therefore express 
both static and dynamic queries in the same language, 
by quantifying over variables of the appropriate types. 
In a series of papers culminating in Montague (1973), 
henceforth PTQ, Richard Montague embarked upon a 
program of providing a formal syntax coupled with a 
modeMheoretic semantics for increasingly sophisti- 
cated fragments of English. Section 3 argues that a 
successful formal treatment can be given to a natural 
language querying facility for a historical relational data 
base (HRDB), through the medium of the intensional 
logic IL s. 
We view this work as important for two reasons. 
First, it represents one of the initial attempts to adapt 
the ideas of Montague Semantics (MS) (Montague 1974) 
to a practical problem. (Landsbergen (1981) looks at the 
issue of machine translation within an MS framework.) 
The research that has been done since the PTQ paper 
has primarily looked at extensions or modifications to 
its linguistic or logical theory, or at implementations of 
the theory on the computer. We will attempt to show 
that this theory of language can serve as the formal 
foundation of a useable computer system for querying 
actual databases. 
Second, in addition to approaching the problem of 
NLQ formally, rather than from a purely engineering 
approach, the theory presented provides a novel (but 
see Gunji (1981) for a similar approach developed 
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0362-613X/88/010010-34503.00 
10 Computational Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
EMP EMP-NAME MGR DEPT SAL 
John 
Mike 
Elsie 
Liz 
Rachel 
Peter 
John Linen 
John Linen 
Elsie Toy 
Liz Hardware 
Liz Hardware 
Liz Hardware 
Figure 2-1. Example Relation. 
25K 
17K 
26K 
30K 
29K 
29K 
relation emp 
concurrently with ours) approach to the interpretation 
of queries that involves both a semantic and a pragmatic 
account. This work represents only a first step in this 
direction within a MS framework. The fragment of 
English that we define herein is certainly not adequate 
to express all of the queries that one would want to 
present to an HRDB. It is intended only to lay the 
groundwork for a formal theory of database querying 
that is both extendible and implementable. 
In this paper we present an informal overview of a 
fragment of English for database querying that we call 
QE-III. We discuss the kinds of properties and abilities 
that a database query language in English should pos- 
sess; principal among these are (1) an account of 
question semantics that possesses close analogs in 
database theory, (2) an account of the semantics of 
multiple-WH questions, (3) an account of the semantics 
of time, and (4) a grammar that is conducive to a 
computer implementation. After examining a number of 
partial solutions to these problems, we introduce the 
notion of a formalized pragmatics as an equal partner 
with the syntax and semantics in the specification of the 
QE-III language. We argue that assigning to the prag- 
matic component the task of providing a representation 
for the answer(s) to a question is both appropriate and 
elegant. Finally, we discuss several other recent at- 
tempts at developing a formal theory of questions. 
QE-III is defined as a formal language, with syntax 
paired with semantics, and with a pragmatics defined on 
the two of these; the language as a whole is designed 
with the database application in mind. QE-III is both a 
simplification and an extension of the PTQ semantic 
theory. Within the tradition of Montague Semantics, 
QE-III is a formalized fragment of English allowing 
questions, tenses, and temporal operators. The inclu- 
sion of a formal pragmatics as an interpretive compo- 
nent of QE-III is an interesting extension to the tradi- 
tional conception of a Montague Grammar. Among the 
other extensions to the PTQ fragment embodied in 
QE-III are (1) the inclusion of time-denoting expres- 
sions and temporal operators, (2) an analysis of verb 
meanings into primitive meaning units derived from the 
database schema, and, of course, (3) the inclusion of 
certain forms of direct questions. These extensions, and 
the semantic and pragmatic interpretations with which 
they are provided, are motivated by the ultimate goal of 
database access, but they are equally interesting in their 
own right. The syntactic theory presented is in some 
cases admittedly naive, for we have been primarily 
interested in getting the interpretation right. 
Section 4 provides an overview of the salient features 
of the QE-III by means of a number of example deriva- 
tions and translations. The complete definition of QE- 
III is given in Clifford (1982b) and again in Clifford 
(1987), where it appears with a fuller set of examples. 
We conclude in Section 5 with a discussion of some of 
the limitations of the fragment and of some possibilities 
for further extensions. 
2 THE HISTORICAL RELATIONAL DATABASE MODEL 
Analogous to the relationship between the relational 
model of data and first-order logic (Gallaire and Minker 
1978), we can view an HRDB as a model for IL s 
(Clifford 1982b). The higher-order language IL s (with its 
built-in concept of denotation with respect to an index) 
provides a formal semantics for such data bases in a 
natural way. 
In the standard or "static" relational model, we 
might see a relation such as emp on a scheme 
EMP(EMP-NAME MGR SAL DEPT). A typical query 
of such a relation, say, "What is employee John's 
salary?", would be expressed in the relational algebra 
as 77SA L (OrEMP_NAME=John(emp)). A first-order language 
would express this same query as something like {z I 
3x3y emp(John,x,y,z)} where x,y, and z are individual 
variables and John is an individual constant. To answer 
such a query, a data manipulation language (DML) 
would access the current relation instance emp on 
EMP, such as the one in Figure 2-1. 
More complex queries about the employees in this 
company, such as: (1) "Has John's salary risen?", (2) 
"When was Peter rehired?", (3) "Did Rachel work for 
the toy department last year?", (4) "Has John ever 
earned the same as Peter?", or (5) "Will the average 
salary in the linen department surpass 30K within the 
next 5 years, if current trends continue?" have typically 
not been expressible in any query language, because 
neither the structures nor the operations in the under- 
lying data model provide for them. 
Computational Linguistics, Volume 14, Number 4, December 1988 11 
James Clifford Natural Language Querying of Historical Databases 
In practice, database administrators have had to 
resort to ad-hoc solutions, typically involving program- 
ming in some host language, in order to handle queries 
of this sort. The issue of modeling time in a DBMS has 
recently attracted considerable attention within the da- 
tabase community. The HRDM (and other historical or 
temporal database models) attempts to satisfy the need 
for access to the temporal dimension of information by 
providing a unified and formal theory of database se- 
mantics that includes time. In particular, HRDM and 
QE-III, recognizing the need for maintaining a historical 
record of changing data, and a language (English) that 
makes explicit or implicit reference to the concept of 
time, together provide a theory of database semantics 
capable of interpreting sentences in the language cor- 
rectly, i.e., in a way that corresponds with our intuitive 
understanding of the relation of time to the semantics of 
the real world. 
Consider again the query "Has John's salary risen?" 
Even with time represented explicitly in the database, 
there is no apparent simple relational algebraic formu- 
lation for this query. With the first-order representation 
for John's salary given above, as a first guess we might 
imagine that RISE({z I 3x3y emp(John,x,y,z)}) would 
represent this new query, where RISE is a predicate 
symbol. However, even with the knowledge that John 
has only one salary, say 25K, it clearly makes no sense 
to ask whether 25K "rises." To answer this question, 
more data is needed than the current extension of 
John's salary: the values of John's salary for some other 
point(s) of time (in this specific instance, in the past) are 
needed. The HRDM model presented in Clifford and 
Croker (1987), built upon a formalization of the concept 
of intension, provides a uniform way to view attributes 
(such as SALaries) not as individual dollar amounts, but 
as functions from moments in time to dollar amounts. 
For the purposes of this paper we will present an 
overview of HRDM and discuss some of the issues 
involved. 
Informally speaking, tuples in a relation represent 
facts about some object (entity or relationship) identi- 
fied by the value of the key attribute(s). For example, in 
relation emp on scheme EMP (EMP-NAME MGR 
DEPT SALARY), the attribute EMP-NAME is the key 
attribute, and DEPT, MGR, and SALARY define prop- 
erties of employees. A particular tuple, e.g., <Peter, 
Hardware, Maria 30K> represents facts about the 
employee Peter. A relation in the ordinary, or static, 
relational data model would consist of a set of such 
tuples representing the facts about a set of employees. 
Each tuple would consist of exactly four atomic values, 
one for each of the four attributes in the scheme. 
By contrast, in HRDM a relation would provide 
historical information about the changing values of the 
attributes of the objects denoted by values of the key, in 
this instance about EMPloyees. Each tuple would be a 
complex, three-dimensional object whose size would be 
based upon what we call the lifespan of that particular 
/ /I / /I / /I 
/ /I / /I / /I 
/ / I / / I / / I 
/ / I / / I I I I 
/ / / / / / I I / 
/ / / / / / / /I I/ 
I I / I I / I I I_1/ 
I I / I I / I I I 
I II I I/ I I I 
I I/ I I/ I I/ 
t, uple t, in r 
A1 A2 A3 
/ /I / /I / /I 
/ / I / / I I II 
/ / I / / I I II 
/ / I I I I / /I II 
/ / / I__ I / / / I_1/ 
I I I I IIII I I I 
I I / I I1_1/ I I I 
I I / I I I I I / 
I I / I \] I I I / 
I I/ I I/ I I/ 
~uple t," in r 
Figure 2-2. The History of Two Similar Objects. 
employee, i.e., the times when that employee was of 
interest to the enterprise. Figure 2-2 depicts two tuples 
in the same relation but with different lifespans. 
Time is represented in the HRDM as a set T = { .... 
to, ti .... }, at most countably infinite, over which is 
defined the linear (total) order <T, where ti <w tj means 
ti occurs before (is earlier than) tj. (For the sake of 
clarity we will assume that t i <T tj if and only if i < j.) 
The set T is used as the basis for incorporating the 
temporal dimension into the model. We assume that T is 
isomorphic to the natural numbers, and therefore the 
issue of whether to represent time as intervals or as 
points is simply a matter of convenience. Using the 
natural numbers allows us to restrict our attention to 
closed intervals (a closed interval of T, written \[t l, t 2\] is 
simply the set {t i I t i <= t i <= t2}). 
D = {D 1, D 2 ..... Dno } is the set of value domains, 
where for each i, D i ~ q~. Each value domain Di is 
analogous to the traditional database notion of a domain 
in that it is a set of atomic (non-decomposable) values. 
In HRDM, however, attributes take their values not 
from these simple domains, but rather from more com- 
plex fimctions. U = {A I, A 2 ..... Ana } is a (universal) 
set of attributes. Simplifying somewhat, we define over 
the sets T and D a set of temporal mappings from the set 
T into the set D. This set, TD = {TD~, TD2 ..... TDnd} 
where for each i, TD i = {fi I fi : T --> Di}, is the set of 
all partial functions from T into the value domain D i. 
The domain of each attributes in HRDM is some set 
of partial temporal functions. Since key attributes are 
intended to be time-invariant, they are constrained to 
take a constant valued function (i.e., one which associ- 
ates the same value with every time in its domain) as 
their value. As we shall see, these mappings are the 
counterparts to the notion of individual concepts in the 
intensional logic IL s. 
The notion of a tuple t on scheme R is expanded in 
HRDM to be an ordered pair, t = <v,l>, where 
12 Computatienal Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
1. t.I, the lifespan of tuple t, is a subset of the set T, 
and represents the set of times over which its 
attributes are defined, and 
2. t.v, the value of the tuple, is a mapping such that V 
attributes A E R, t.v(A) is a mapping in t.l --> 
DOM(A) (the value-domain of attribute A). 
2.1 EXAMPLE DATABASE 
In the remainder of the paper we will discuss the 
semantics and pragmatic theory of QE-III, illustrated 
with example database queries to an HRDB. For this 
purpose we now define the relation schemas for a 
historical department store data base based upon an 
example in Chang (1978). 
EMP__.REL (EMP MGR DEPT SAL) 
DEPT REL (DEPT FLOOR) 
ITEM REL (ITEM TYPE) 
SALES REL (DEPT ITEM VOL) 
This concludes our brief overview of HRDM. For 
further details the reader is referred to Clifford (1985) 
and Clifford and Croker (1987). 
3 OVERVIEW OF ENGLISH QUERY LANGUAGE QE-III 
3.1 INTRODUCTION 
HRDM serves to formally incorporate a temporal se- 
mantics into an extended relational database model. In 
order to query a historical database using English, we 
define the semantics of queries expressed in English in 
terms of the semantics of HRDM, by defining a small 
query fragment as a Montague Grammar. The correla- 
tion between the database semantics and this query 
language is made explicit by providing the semantics of 
the query fragment via an indirect translation into the 
intensional logic ILs. ~ The translations provide for a 
completely extensional treatment of verbs (i.e., there 
are no verbs like seek, which can be nonextensional in 
object position in the PTQ treatment). This treatment is 
dictated by the application to a database environment, 
in which existence is tantamount to existence in the 
database (Reiter 1978). Through these translations, 
then, the historical database essentially serves as a 
model for ILs and therefore as the model for a formal 
definition of the interpretation of the English queries. In 
addition to providing a semantic interpretation, which in 
model-theoretic terms is called its denotation, we also 
provide for each expression a pragmatic interpretation 
in a manner to be explained. 
Our goal in this effort has not been to define an 
English database query language that is, in any sense of 
the term, complete. Rather, we have been motivated by 
two complementary goals. First, we have wanted to 
investigate the possibility of a formal, model-theoretic 
query language for historical databases. This led to our 
interest in Montague Semantics and to our second 
goal demonstrating that Montague's theories of natu- 
ral language semantics are applicable to such a practical 
task. Along the way we discovered that it was simpler 
and more natural to define the interpretation of this 
query language in two components, one semantic and 
the other pragmatic. 
Two overrriding principles have guided this work. 
First was that whatever interpretation or meaning our 
theory would give to a natural language database query 
should be as close as possible to the interpretation given 
to database queries in, say, the relational algebra or 
calculus. This meant that the interpretation of a query 
should somehow encompass its answer as represented 
in the underlying data base. Second, the theory should 
make sense computationally. This meant taking into 
account what had already been learned about parsing 
strategies for Montague Grammars (Friedman and War- 
ren (1978), Warren (1979), Landsbergen (1981)), as well 
as what database theory had to say about the semantics 
of the modeled enterprise. These principles motivate 
certain systematic simplifications to the PTQ transla- 
tions from English to logic, wherever these are sug- 
gested by the simplified view of the semantics of the 
enterprise provided by the database model. Moreover, 
since we are not attempting to develop a semantic 
theory of questions for English in general, these simpli- 
fications have been introduced into the translation pro- 
cess as early as possible. We believe that this strategy 
has the dual effect of making some of the PTQ theory a 
little more accessible, and eliminating the need to resort 
to the less computationally attractive technique of in- 
troducing a large number of meaning postulates and 
using logical equivalences to perform the reductions at 
a later stage. 
We have made little attempt to develop a sophisti- 
cated syntax for our fragment. Numerous extensions to 
the syntax of the PTQ fragment have been investigated 
by researchers in the past decade that we have not 
incorporated into our fragment. Since our primary con- 
cern has been "getting the meaning right," we felt that 
a too broad syntactic coverage might obscure our major 
points. For this reason, we have extended the PTQ 
fragment only slightly. The treatment of questions that 
we present is syntactically naive, although in its favor 
we might point out that unlike most work on questions 
in Montague Grammar, QE-III makes a stab at direct 
questions. We believe that the semantic theory of 
questions that we present, and particularly our proposal 
to capture the answer in a pragmatic component, are an 
important contribution to the formalization of the inter- 
pretive component of natural language understanding 
systems. Naturally, the true test of a natural language 
query facility is in how useable it is; certainly the syntax 
of QE-III would have to be extended before anyone 
would think of using it. 
In this section we discuss the major issues underlying 
the definition of QE-III, which fall roughly into two 
broad categories: aspects of the process of database 
querying that we have incorporated into the fragment, 
and modifications and additions to the PTQ fragment 
Computational Linguistics, Volume 14, Number 4, December 1988 13 
James Clifford Natural Language Querying of Historical Databases 
that these, and the database semantics, have occa- 
sioned. As in much of the work that has been done in 
the area of Montague Semantics since Montague's 
death in 1970, we have allowed the PTQ fragment to 
stand pretty much intact as the heart of QE-III. How- 
ever, we have redefined this fragment in terms of the 
language ILs, in order to allow direct reference to 
moments in time. 
3.2 PRELIMINARIES 
3.2.1 INDIVIDUAL CONCEPTS VS. ENTITLES 
Most recent research in the field of Montague Seman- 
tics has incorporated the suggestion, first made in 
Bennett (1974), that Montague's treatment of common 
nouns (CNs) and intransitive verbs (IVs) as denoting 
sets of individual concepts (ICs) is unduly complicated. 
Under Bennett's suggestion, both CNs and IVs denote 
sets of simple individuals, with the result that the entire 
typing scheme of the English categories in these frag- 
ments is considerably simplified. In Section 2 we 
showed that attributes in an HRDB can be identified 
with ICs. Accordingly we have not adopted the Bennett 
type system, but have instead maintained the treatment 
of PTQ. 
3.2.2 VERBS 
Montague's semantic treatment of verbs leaves them 
completely unanalyzed; thus, for example, the English 
verb "walk" translates into the constant "walk'" in IL, 
"love" into "love'", etc. The interpretation of these 
constants is some function in the model for the lan- 
guage, a function about which Montague says nothing 
except to specify its logical type (and in certain cases to 
specify an extensional meaning postulate). Because we 
are using a database as a representation of the logical 
model we are in a position to provide an analysis of 
English verbs that takes into account the meaning of the 
verbs as encoded in the database. This analysis is given 
in terms of the database schema. For example, instead 
of translating the verb "manage" into the unanalyzed 
predicate "manage' ", we take advantage of the data- 
base semantics to incorporate directly into its transla- 
tion the information that its subject must be an IC in the 
role of a MGR, and that its object must be a constant IC 
that is an EMP. We do not change the logical type of the 
translation, i.e., a transitive verb in our fragment de- 
notes the same kind of function as it does in Montague's 
treatment; we simply analyze its meaning in terms of the 
database primitives. This analysis in terms of a small set 
of primitive meaning units is not very different from 
some approaches taken in AI work in natural language 
understanding (e.g., Schank 1972), or from the linguistic 
theory of deep cases (Fillmore 1968). The difference, of 
course, is that our primitives or cases are different, 
motivated by the HRDM and the schema design, and 
are no more absolute than any well-chosen database 
design. 
As an example, the translation of "manage" in our 
fragment is given as: hWhxW(i)(hyAS-l(y(i),x) /% 
EMP.'(i)(y(i))/~ MGR'(i)(x)). This expression is of the 
same logical type as manage' in a PTQ-like treatment, 
and will combine with terms in the same way, but it 
does not leave "managing" unanalyzed. Instead it 
specifies what attribute class(es) its subject and object 
must belong to, and how they must be related. Specif- 
ically, the subject must be an entity (y(i)) that is an 
EMP, the object an IC (x) that is a MGR, and the 
MGR-IC must be ASsociated with the EMPloyees (AS- 
I). In general the translation of any verb in our theory 
will so specify the attribute of its subject (or the 
disjunction of alternatives, if any). The translation of a 
TV will further specify the attribute(s) of its direct 
object, and of a DTV of both its objects. Moreover any 
relationship(s) among these attributes will also be spec- 
ified. 
3.3 THE PROBLEMS OF TENSE AND TIME 
3.3.1 INTERVALS OR STATES? 
David Dowty (1979) presents a discussion of a broad 
spectrum of semantic and syntactic issues relevant to 
the understanding of English, and in particular to pro- 
viding a Montague Semantic analysis of these issues. In 
the final chapter of this book he formalizes many of the 
ideas he has discussed by defining a Montague fragment 
of English that includes such features as temporal 
adverbs, dative-taking verbs, a theory of word forma- 
tion, and a treatment of several compound tense struc- 
tures. In order to provide a semantics for this expansion 
of the PTQ fragment Dowty argues for the necessity of 
several significant extensions to the logic IL: a radically 
different treatment of the phenomenon of tense is one of 
his contributions. Because we are concerned with many 
of the same issues as Dowty--in particular tenses and 
direct temporal references---it seems appropriate to 
discuss his work and to contrast two different solutions 
to some of the same issues. 
A major section of the book is concerned with 
developing a rigorous taxonomy of verbs in English 
based upon several syntactic and semantic criteria. The 
problems with a number of different classification 
schemes that have been proposed over the years are 
discussed, in particular Vendler's scheme (Vendler 
1967), which divides verbs into the four categories of 
statives, activities, accomplishments, and achieve- 
ments. Dowty judges all of these proposals by the two 
criteria of syntactic and semantic uniformity: can all of 
the verbs assigned to a given class appear in the same 
syntactic constructs, and are the same inferences in 
meaning justified for all like-classified verbs? Dowty's 
final taxonomy, offered with many reservations, defines 
eight different verb categories. 
These aspectual verb distinctions, and particularly 
the semantics of the progressive tenses, lead Dowty to 
espouse a theory of interval semantics, earlier proposed 
by Bennett and Partee (1972), wherein truth conditions 
are given relative to an interval, rather than to a 
14 Computational Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
moment, of time. Unlike other proposed changes to 
Montague's PTQ analysis of English, this proposal 
causes major modifications to the most basic semantic 
notion of IL, and indeed of most other temporal logics 
that have been studied (e.g., Rescher and Urquhart 
1971). We are not convinced of the necessity of taking 
this step (indeed, Dowty himself says that "it results in 
a system that is really too powerful for natural language 
semantics" (Dowty 1979), p. 138). Certainly from the 
perspective of database querying, the complications 
that it introduces into the logic seem unnecessary. 
The existence of an actual historical database as the 
heart of our logical model is the major constraint within 
which all of our work must be undertaken. This 
"given," which in essence already takes a stand on the 
semantics of the real world, stands as the major differ- 
ence between Dowty's enterprise and ours. The seman- 
tic theory that we present is a theory of the semantics of 
English when used as a database query language for an 
HRDB, and not when used in ordinary discourse, 
whatever that might be. If these two theories diverge, it 
should be neither surprising nor disturbing, and it 
should be of interest to compare and contrast them. 
It is apparent that an HRDB is a gross abstraction of 
the real world:entities are represented by unique iden- 
tifiers, complex relationships are reduced to simple 
tuples in relations, time is rather crudely represented as 
a set of states of gross, perhaps even somewhat amor- 
phous, granularity. And yet in spite of these limitations 
these databases are found to be useful to a large and 
growing number of people. What kind of constraints 
does the abstraction of real-world semantics embodied 
in the HRDB impose upon our enterprise? Precisely 
this: the historical database embodies a semantics that 
is based upon the notion of truth with respect to a state. 
Every fact in the database is recorded with respect to a 
state that "time stamps" it; this is interpreted as 
asserting that the fact is true at that state. If intervals 
come into play, they can be modeled as sets of time 
points, since time in our database view is discrete. 
The differences that Dowty examines certainly exist; 
they do not, however, seem relevant in most database 
applications. Unlike Dowty, our analysis treats the 
progressive tenses synonymously with their simple 
counterparts: 
Did John earn 30K last week? and Was John earning 
30K last week? 
Does Peter work for the toy department? and Is Peter 
working for the toy department? 
Perhaps it is the case that database applications do not 
lend themselves to handling achievements or accom- 
plishments, but instead record stative information. In 
any case it is difficult to conceive of many real database 
examples where distinctions of the sort that Dowty's 
analysis is concerned with actually make sense. 
Dowty's analysis of the interaction of tenses and 
temporal expressions accords exactly with our own. 
Sentences with such interaction, such as "John worked 
yesterday," cannot be analyzed as resulting from two 
separate temporal operators ("-ed" and "yesterday") 
acting on the proposition that John works, as the 
following example should make clear: 
John worked yesterday 
/ \ 
/ \ 
yesterday John worked 
/ \ 
/ \ 
-ed John works 
John works --~ work'(i)(John) 
-ed ~ ~> hp3il\[\[i I < i\] A p(i0\] 
John worked ~ ~> Ap3il\[\[i \] < i\] A p(il)\](Ai work'(i)(John)) 
3i1\[i I < i\] A work'(il)(John) \] 
yesterday ~ ~> Ap3i2\[yesterday'(i2) A P(i2) \] 
John worked yesterday ~ ~> Ap3i2\[yesterday'(i2) 
A P(i2)\](Ai3il\[\[i I < i\] A work'(il)(John)\] ) 
--~ 3i23il\[yesterday'(i 2)/% \[i I < i2\] A work'(il)(John)\] 
This analysis 2 (or the reverse, which would first apply 
"yesterday" and then "-ed") causes the two time 
operators to compete with each other, placing the event 
in the wrong time frame. For example, the following 
time line is consistent with this logical analysis, but 
inconsistent with the intended meaning of the English: 
I I I 
il i 2 NOW 
I I I 
John works yesterday 
Instead the two temporal operators must be treated as 
operating in conjunction; the English -ed is, in a sense, 
semantically superfluous in the presence of the other 
time indicator. Thus the fragment has rules for applying 
tense operators, and separate rules for applying tense 
operators in conjunction with other temporal adver- 
bials. These rules differ slightly from Dowty's in that we 
treat all temporal operators as operating on entire 
clauses, rather than simply on verb phrases. The next 
section will explore some of the reasons for this deci- 
sion. 
3.3.2 SENTENTIAL VS. VERB-PHRASAL TEMPORAL 
OPERATORS 
Our analysis of tense differs from the PTQ analysis and 
the one in Dowty in the manner in which tense is 
incorporated into an English sentence. In PTQ, the Rule 
$4 combines a term with an IV to form a present-tensed 
sentence: 
John walks $4 
/ \ 
/ \ 
John walk 
The past and future tenses are accommodated in Rule 
S 17, which similarly combines the subject and predicate 
to form a sentence in either of these tenses. 
Computational Linguistics, Volume 14, Number 4, December 1988 15 
James Clifford Natural Language Querying of Historical Databases 
Dowty's analysis is somewhat different. In his frag- 
ment a sentence is always formed first by using $4; if 
the tense is other than present, he introduces this with 
an additional rule that takes the present-tensed sentence 
as input and forms its past-tense coun~terpart, as in the 
following example: 
John walked $39 (Dowty's) 
I I 
John walks $4 
/ \ 
/ \ 
John walk 
Extensions to the PTQ fragment have had to deal with 
this issue of tense and how it interacts with the other 
components of a sentence. We agree with Dowty's 
basic premise that tense is really a property of the 
sentence (actually, clause) as a whole. This is particu- 
larly important when, as in our fragment, there are 
different kinds of sentences: declarative, wh-questions, 
yes-no-questions, and when-questions. For under a 
straightforward extension of the FI'Q treatment the 
number of rules would proliferate, since separate rules 
would be needed for each kind and tense of the sentence 
formed by conjoining a term and a VP. However, under 
Dowty's treatment, the tense rules applied after $4 in 
most cases must undo the syntactic work that it has 
done, viz. the inflection of the verb as third-person 
singular present tense. (Semantically, the treatment is 
the same, i.e., the untensed version denotes exactly 
what the present-tensed version does.) This syntactic 
undoing is both inelegant and computationally unattrac- 
tive. For this reason, we have incorporated into QE-III 
the additional categories of tensed sentences of each 
variety, and have modified $4 so that it creates an 
untensed sentence from a term and an IV. The strings of 
ultimate interest in the fragment, then, are the tensed 
sentences (categories T-t, T-WHQ, T-YNQ, and 
WHENQ). The following example from QE-III illus- 
trates this for a simple declarative sentence. 
John worked (T-t) S105 
I I 
John #work (t) $5 
/ \ 
/ \ 
John #work 
In Section 4, when we discuss further examples of 
tensed sentences, particularly tensed questions and 
when-questions, we will discuss this issue further. 
3.4 QUESTIONS 
3.4.1 INTRODUCTION 
Despite their obvious importance as a tool for gaining 
knowledge of the world, both linguists and philosophers 
have historically considered interrogative sentences the 
poor relation of the declaratives, to which they have 
paid the bulk of their attention. Among linguists there is 
no generally accepted theory about the syntactic gener- 
ation of English questions (Kuno and Robinson 1972, 
Pope 1976), and philosophers and logicians have until 
recentlLy given little attention to the question of ques- 
tions. More recently Engdahl (1986) explored the issue 
of constituent questions in Swedish, and proposed a 
semantic theory of questions similar to those of Ham- 
blin (1973) and Karttunen (1977), which we shall discuss 
in Section 3.6. Groenendijk and Stokhof (1983) address 
the issue of the appropriateness of an answer in differ- 
ent situations, an issue outside the scope of the present 
work. Formal logic from its inception directed its atten- 
tion to languages based upon the notion of formulas, 
abstractions of declarative sentences in natural lan- 
guages. Only recently have logicians begun to investi- 
gate the semantics of questions in any depth and to 
develop formal languages powerful enough to express 
questions in order to carry out these investigations. 
Hintikka (1974) discusses a number of interesting lin- 
guistic and philosophical attempts to provide an analy- 
sis of questions. 
Although Montague, too, focused his attention on a 
formal treatment of the syntax and semantics of declar- 
ative sentences in natural language, the framework of 
using a lambda calculus and the model theory of inten- 
sional logic, developed in PTQ, is rich enough to 
incorporate a view of natural language questions as 
well. In what seems to be his only published remark on 
the issue of questions, he says: "In connection with 
imperatives and interrogatives truth and entailment 
conditions are of course inappropriate, and would be 
replaced by fulfillment conditions and a characteriza- 
tion of the semantic content of a correct answer" 
(Montague 1973). 
Perhaps inspired by this comment, a number of 
researchers have been investigating ways to incorporate 
a formal account of the syntax and semantics of ques- 
tions within the framework of Montague Semantics. 
Hamblin (1973), Karttunen (1977), Bennett (1977, 1979), 
Hausser and Zaefferer (1978), and Belnap (1982) are 
perhaps the most important of these investigations, and 
we will discuss their work in relation to ours in the 
following section. Many of the aspects of our proposal 
have been adapted from or influenced by the work of 
these researchers. 
Others not working within the MS framework have 
also made important contributions to our understanding 
of the issues involved. Approaching this issue from an 
entirely different perspective, researchers in artificial 
intelligence (AI) have over the years developed and 
implemented automatic question-answering theories 
and systems to varying degrees of success. These have 
ranged from some early experimental programs (Green 
et al. 1963) to database querying programs bound to a 
particular database domain (Woods et al. 1972 and 
16 Computational Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
Waltz 1978) to some rather sophisticated DBQ systems 
today that are designed to be general and easily portable 
(Harris 1973, Hendrix et al. 1978). The research behind 
these systems seems to share a goal common to much of 
the work in AI (as distinct from cognitive science), i.e., 
an interest more in getting a system to "work" than in 
developing a formal theory that explains its behavior. 
3.4.2 DATABASE QUESTIONS 
As guidelines to help us judge any proposed theory of 
questions we have adopted a number of self-imposed 
criteria that any solution acceptable to us should meet. 
1. It must fall within the general confines of Montague's 
framework: syntax and semantics defined in parallel, 
with the semantics of a phrase defined composition- 
ally in terms of the semantics of its components. 
2. The interpretation of questions should be closely 
analogous to the interpretation of queries in the 
relational database model. This means that their 
interpretation should be objects in the logical model 
which have direct analogs in the HRDM model 
described in Section 2. 
In the relational database model "a query is a 
computation upon relations to yield other relations" 
(Maier 1983). This is an operational view of a data- 
base query; a denotational semantics view would 
hold that a query denotes a relation that is its answer, 
and would define just how, in fact, the query so 
denoted. In order to provide for the closest possible 
parallel between the interpretation of questions in 
our theory and the query semantics of HRDM, we 
hoped to define the semantics of our English query 
language in just such a way, viz., such that each 
query would denote the relation that is its answer 
with respect to the database. In other words, if a 
query in the relational database context denoted an 
n-ary relation over entities (i.e., a set of n-tuples), we 
felt that its expression as a question in our fragment 
should be defined to denote a function of type 
<en,t>. As we shall see we were able to accomplish 
this easily and naturally not in the semantics, but by 
extending the framework of Montague Semantics to 
include a pragmatic component. 
3. The theory should be computationally tractable. 
Because we are interested in developing a theory for 
natural language query systems that are ultimately 
implementable, this criterion leads us to direct our 
attention to solutions that fall within the general PTQ 
framework. This is because there have been success- 
ful results (Warren 1979 and Landsbergen 1981) 
implementing parsers and semantic interpretation 
routines for fragments defined within this frame- 
work, and we wanted to build upon this work as 
much as possible. While this work does not discuss a 
computer implementation of its results, an extension 
of Warren's PTQ parser (Warren 1979) to the QE-III 
fragment has been implemented by Hasbrouck 
(1982). 
4. Proper treatment must be given to the interaction of 
questions and quantifiers. The PTQ treatment suc- 
cessfully accounts for multiple readings of sentences 
with interacting quantifiers ("A woman loves every 
man.") Our solution should likewise allow for all of 
the readings of questions involving quantified terms 
("Who manages every employee?"). 
5. Y-N questions, wh-questions involving "who" and 
"what," and temporal questions ("when") should 
be provided for. This means that we do not treat 
indirect questions ("Tell me whether ..."), since 
these do not generally arise within the database 
framework and could nevertheless easily be para- 
phrased as direct YNQs. 
6. The theory should account for multiple wh-questions 
(e.g., "Who sells what to whom?") as these seem 
indispensable in a database context. 
The problem of providing a correct analysis of questions 
that involve quantified terms is illustrated by a query 
like "Who manages every employee?" An analysis 
should only be considered adequate if it is able to find 
such a query ambiguous between an interpretation of 
"every" as "all" and also as "each." In PTQ Monta- 
gue provided a solution to the familiar problem of the 
multiple readings of such sentences as "A woman loves 
every man." Under one reading there is a single woman 
who (magnanimously) loves each and every man, while 
under the other reading there is, for each man, some 
woman or other who loves him. A similar problem 
arises with respect to the interaction between ordinary 
and question terms, as in "Who manages every em- 
ployee?" 
Under one reading the questioner wishes to know 
what individual(s) manage all of the employees, where- 
as under the other reading what is wanted is really a set 
of ordered pairs, viz., for each employee, the set of 
individuals who manage him/her. Our interpretation of 
English questions must permit both readings, since 
either one is possible; the problem of disambiguating 
between the two is best left, as in PTQ, to a later stage 
that has access to domain-dependent meaning postu- 
lates. 
In order to get these readings, we propose making a 
change in the standard interpretation of the English 
word "every". It is well known that this work is 
ambiguousmin some cases it means "all" and in others 
"for each". This is precisely the ambiguity in this case, 
and we must provide for both readings. 
The first reading, where "who" has wider scope than 
"every," presents no problems. 
who manages every employee 
/ \ 
/ \ 
who \[it-NOM-0\] manages every employee 
Computational Linguistics, Volume 14, Number 4, December 1988 17 
James Clifford Natural Language Querying of Historical Databases 
\[it-NOM-0\] manages every employee : ==> 
'¢x\[EMP'(i)(x) ---> MGR'(i)(Xo) ./~ manage'(i)(Xo,X)\] 
who ~---:> AP3y\[y(i) = u/~ P(i)(y)\] 
who manages every employee ---> 3y\[y(i) = u 
/~ Vx\[EMP'(i)(x) ---> MGR'(i)(y) A manage'(i)(y,x)\]\] 
The other reading requires the opposite scoping. 
Who manages every employee 
/ \ 
/ \ 
every employee who manages \[it-ACC-O\] 
as well as a different meaning for "every employee." 
The desired reading is accomplished by allowing 
"every" to be ambiguous between its standard meaning 
"for all" and its interrogative meaning of "for each", in 
which it is essentially synonymous with "which". 
With this treatment of "every" we obtain the desired 
second (and more likely) reading. 
who manages \[it-ACC-O\] --> 3y\[y(i) = u/~ MGR'(i)(y) 
A EMP'(i)(Xo) A manage'(i)(y,Xo)\] 
every employee ---> AP=lz\[z(i) = v/~ EMP'(i)(z)/~ P(i)(z)\] 
who manages every employee? 
--> AP3z\[z(i) = v/~ EMP'(i)(z)/~ P(i)(z)\] 
(AiAxo=ly\[y(i) = u/~ MGR'(i)(y) 
/~ EMP'(i)(Xo)/~ manage'(i)(y,xo)\]) 
---> 3z3y\[z(i) = v/~ EMP'(i)(z) 
A y(i) = u A MGR'(i)(y) A manage'(i)(y,z)\] 
which denotes a set of ordered pairs <u,v> such that u 
manages v. 
The problem of multiple wh-questions has a rather 
simple solution if one is willing to restrict one's atten- 
tion to questions that involve only one wh-word; it is 
well known, however, that multiple wh-words require a 
considerably more complex treatment if the semantics 
is to be defined compositionally as in a Montague 
framework it must (Kuno and Robinson 1972). Further- 
more, within the database context a restriction to single 
wh-questions would be too severe a constraint--it 
would limit the language to queries that return relations 
over only a single attribute. 
We will discuss a number of different possible solu- 
tions to this issue of multiple wh-questions and ulti- 
mately adopt one as our solution. We will see, however, 
in the course of this presentation, that there are consid- 
erable technical difficulties in defining the semantics in 
such a way as to get it all to come out right for both 
single and multiple wh-questions. The solution that we 
adopt, involving the addition of a formally specified 
pragmatics for the fragment, does have this property in 
addition to meeting our other criteria; moreover, the 
simplicity of our solution, as contrasted with the con- 
siderable complexity in other proposals for a question 
semantics, e.g., Bennett (1977, 1979) and Hausser and 
Zaefferer (1978), makes it especially attractive. How- 
ever, it is clear that many researchers have found the 
same kinds of difficulties in extending Montague's work 
in the direction of interpreting questions, and that 
further work in this area is needed. We hope that our 
propo,~al to treat the answering of a question as a 
component of a formally specified pragmatics of the 
language, apart from its semantics, is a step in the 
proper direction. 
3.5 THE QE-III THEORY OF QUESTIONS 
3.5.1 INTRODUCTION 
We first present a general view of the substance of our 
theory of the interpretation of questions and then dis- 
cuss how this theory is carried out technically for the 
various types of questions that we consider. Our goal is 
a formal interpretation of questions as the set of their 
correct answers with respect to an index and a model 
(state and database.) This viewpoint is inspired by the 
relational database querying paradigm, wherein a query 
denotes the relation that is its answer in the current 
state of the database. It will be important to keep in 
mind the distinction between objects in a model for IL s 
and objects in the relational database model. In the 
relational model, particularly when dealing with the 
relational algebra, one tends to think of all relations as 
being the same kind of object. One projects and joins 
relations at will, since these relational operators are 
defined generically. However, models for IL s are 
strongly typed: considerations of the domains and 
ranges of functions are of critical importance. Within 
IL~, e.g., a one-place relation of individuals is a function 
from D e to D t (denoted by expression of type <e,t>), a 
two-place relation of individuals a function from D e to 
functions from De to Dt (denoted by expressions of type 
<e,<e,t>>), etc. Thus, under our theory, a question 
such as "Who manages Peter?" is pragmatically inter- 
preted (in a sense to be made clear below) as an object 
of a completely different type from the interpretation of 
a question such as "Who manages whom?" Later on we 
will see that this theory does not fall within the main- 
stream of the logical theories for question semantics 
that have been proposed. 
3.5.2. YES-NO QUESTIONS 
A semantic analysis of yes-no questions (YNQs) that 
meets the criteria set forth in the introduction to this 
section is not difficult to obtain. Since we want to 
interpret YNQs as either "yes" or "no" (or equiva- 
lently T or F, or 1 or 0), they can be defined to denote 
objects in {0,1}. But this is just the denotation set of the 
corresponding declarative sentence that expresses the 
proposition that the YNQ asks. Thus we easily meet our 
criteria by providing that a YNQ denote the same 
proposition as that denoted by the declarative sentence 
from which it was derived. For example, 
3-1. John manages the shoe department. 
would roughly be translated as: manage'(i)(John, shoe 
dept.) 
This formula is true with respect to a state s just in 
case John manages the shoe department in that state. 
Our analysis of the corresponding question "Does John 
18 Computational Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
manage the shoe department?" provides that it is de- 
rived syntactically from "John manages the shoe de- 
partment" and that semantically it denotes the same 
object in the model. The pragmatic interpretation of this 
question is represented by the formula: manage' 
(now)(John, shoe dept.), which in effect "questions" 
the model as to its truth or falsity in the same way that 
a YNQ questions the database for the response "yes" 
or "no." This analysis is provided by the following pair 
of syntactic and semantic rules for our fragment, and by 
the pragmatic rules to be introduced in Section 3.5.6: 
S101. (YNQ Formation) 
<F~01a,<t>,YNQ> and <Fiolb,<t>,YNQ> 
Flola(0) = #AUX0* where 0* is 0 with the "first 
verbs" unmarked. 
Fi0~b(0) = "Is it the case that" 0 
T101. Flola(0 ) and Floib(0) ~--~> 0' 
This = => notation is used in each translation rule that 
is not an instance of the general rule of function appli- 
cation. In this case it indicates that the translation of the 
expression formed by performing the operation FI0ia (or 
Fi0~b) on the input string ~b is exactly the same as the 
translation that has already been assigned to ~b, which 
we denote with the notation &. This semantic account 
works, since we want the interpretation of the yes-no 
question to be the same as the interpretation of the 
declarative sentence from which it is derived. 
In what follows we examine the more difficult prob- 
lem of defining compositionally a model-theoretic se- 
mantics for general wh-questions. 
3.5.3 WH-QUESTIONS 
We first present a semantic solution that does provide 
for a successful interpretation for questions involving 
only one wh-word, e.g., "Who manages Peter?" This 
solution has its simplicity to recommend it, but is 
unfortunately unable to accommodate multiple wh- 
questions. We then examine a number of alternative 
solutions to illustrate some of the many problems in- 
volved in attempting to accommodate these multiple 
questions. 
It is obvious linguistic fact that question words like 
"who," "what," "whom," etc. behave syntactically in 
much the same way as terms like "Peter" or "an 
employee" (e.g., Hamblin 1973). In subject position 
there is virtually no difference. 
Interrogative Declarative 
who manages Peter manages 
the shoe depa~ment the shoe department 
/ \ / \ 
/ \ / \ 
who \[it-0\] manages Peter \[it-0\] manages 
the shoe dept. the shoe dept. 
while in object position there is so-called wh-Q- 
movement: 
/ 
what 
Interrogative Declarative 
What does Peter manages 
Peter manage? the shoe department. 
\[ / \ 
I / \ 
Peter manages what the shoe Peter manages 
\[it-0\] 
/ \ department 
\ 
Peter manages \[it-O\] 
Nonetheless in both cases the question word takes the 
role of a term syntactically. Semantically, however, 
there is a difference. Whereas ordinary terms refer to an 
individual or a set of individuals in the model (actually 
in PTQ to the set of properties of these individuals, but 
this point need not concern us here), question terms 
seem in some way to refer to the set of all possible 
individuals that, when substituted for the individual 
variable in a matrix, makes the resulting formula true. 
This observation leads to the consideration that ques- 
tion words should denote, not sets of properties of sets 
of individuals, but rather functions from sets of proper- 
ties to sets of individuals that have those properties. 
The following table makes this analogy clearer. 
Term Logical Translation Logical Type 
Peter AP3x\[x(i) = Peter A P(i)(x)\] <<s,<<s,e>,t>>,t> 
an employee AP3x\[EMP(i)(x) A P(i)(x)\] 
who APAu3x\[x(i) = u A P(i)(x)\] <<s,<<s,e>,t>>,<e,t>> 
Because of the similarity of these wh-words to ordinary 
terms, both syntactically and semantically, we shall 
refer to them as wh-terms. The schematic essentials of 
the translations of two of the above examples will show 
how this analysis of the semantics of wh-terms provides 
the desired analysis of the wh-question. 
Peter = :> ;tP3x\[x(i) = Peter A P(i)(x)\] 
\[it-NOM-0\] manages the shoe 
department ~ ~> manage'(i)(xo,shoe-dept ) 
Peter manages the shoe department -~-=> 
AP3x\[x(i) = Peter/~ P(i)(x)\](AiAxomanage'(i)(Xo,shoe-dept)) 
3x\[x(i) = Peter/~ manage'(i)(x,shoe-dept) 
who -m-~> APAu3x\[x(i) = u/~ P(i)(x)\] 
who manages the shoe department : :> 
APAu3x\[x(i) = u A P(i)(x)\](AiAxomanage'(i)(Xo,shoe-dept)) 
---> Au3x\[x(i) = u/~ manage'(i)(x,shoe-dept) 
The first example demonstrates the PTQ-like analysis of 
a declarative sentence translating into a formula whose 
interpretation in the model with respect to a given state 
is a truth value. The second example provides an 
analysis of an interrogative sentence containing a single 
wh-term, using an analogous substitution rule. We 
obtain an expression of type <e,t> whose denotation 
with respect to an index is a set of entities, viz., the set 
Computational Linguistics, Volume 14, Number 4, December 1988 19 
James Clifford Natural Language Querying of Historical Databases 
of entities who manage the shoe department in that 
state. 
This analysis, unfortunately, cannot be generalized. 
Although it can also be made to provide the desired 
analysis for single wh-terms in direct or indirect object 
position, it will not allow for multiple wh-questions. To 
see why this is the case, consider what the S and T rules 
for the above analysis might look like:. 
SWH. 
If a is a WH-Term and 05 is a formula, then FWH_ n 
(a,05) is a WIll-?, where FwH_ ~ (a,05) would be 
defined as some sort of substitution of a for the 
first occurrence of xn, and the appropriate pro- 
noun for each subsequent occurrence, as in the 
PTQ substitution rules. 
TwI- I. 
FS_WH_ n (a,05) : :> a'(AiAXn\[05'\]). 
Notice that this rule, unlike the analogous substitution 
rules in the PTQ fragment, cannot be applied recur- 
sively to its output. This is because the PTQ rules are of 
the form P~ + Q~ = ~---> R~ (i.e., an expression of type 
a combines with an expression of type /3 to yield 
another expression of type/3) whereas this rule is of the 
form P~ + Q~ ~ ~--> R v (i.e., the output is of a different 
type from either of the inputs). 
A number of alternatives present themselves at this 
point to allow for an analysis of multiple wh-questions 
within this framework. The first requires that wh-terms 
have different flavors (who0, whol, who2 .... ) depend- 
ing on the meaning of the expression into which they are 
substituted for a free variable. The second requires 
subcategorizing the category term, and substituting all 
terms in for free variables at one time. The third, and 
the one we have adopted, achieves the same semantic 
effect as the Rule T-WH, but in a two-stage process 
involving a separate pragmatic component. We will 
examine each of these ideas in turn. First, however, a 
word about substitution. 
In the PTQ analysis, a term can become a constituent 
part of a sentence either by directly combining with 
some other constituent, or indirectly by means of sub- 
stitution for a free variable that has been so directly 
combined. For example, consider the following two 
PTQ-like derivations of the sentence "John works". 
John works $4 
/ \ / 
/ \ / 
John work John 
/ 
he-0 
John works S14 
I \ 
I \ 
0 he-0 works $4 
/ \ 
\ 
work 
Under the semantic analysis of PTQ it turns out that 
these two derivations receive the same translation, and 
hence the same "meaning." But the substitution rules 
are not gratuitous. They are introduced as a theory to 
account for pronomial co-reference and quantifier scop- 
ing. The following example illustrates how pronomial 
co-refi~rence is handled by means of one of the substi- 
tution rules. 
Arz employee manages and he works S104 
I I 
At~ employee #manage and he #work S14,0 
/ \ 
/ \ 
an employee \[it-NOM-0\] #manage and 
\[it-NOM-0\] #work Sll 
/\ / \ 
/ \ / \ 
a employee \[it-NOM-0\] \[it-NOM-0\] 
#manage #work 
In this derivation, the Substitution Rule S14,0 provides 
for the reading in which the same individual is the 
referent of the terms "an employee" and "he". The 
same problem of accounting for co-reference occurs in 
the consideration of the semantics of questions, as the 
following example illustrates 3. 
3-2. Who manages an employee such that he manages 
him? 
The PTQ theory of co-reference, extended to allow 
substitution of wh-terms, is equally able to capture the 
fact that "who" and "him" are co-referent, as are "an 
employee" and "he". Under our analysis, this sentence 
would be derived as follows: 
Who manages an employee such that he manages him? 
I 
I 
Who #manage an employee such that he manages him? 
/ \ 
/ \ 
who \[it-NOM-0\] #manage an employee such that 
\[it-NOM-0\] manages him. 
This idea of extending the PTQ theory of co-reference 
to the case of interrogatives is not ours. It is used in 
most of the work on question semantics in the Monta- 
gue Grammar tradition (including Karttunen 1977, Ben- 
nett 1977, 1979, and Belnap 1982). It is that theory that 
we have incorporated into our fragment. Because ques- 
tion words in our fragment are always assumed to have 
the entire sentence as their scope (i.e., there are no 
embedded question clauses), and because of the exten- 
sional nature of our theory as dictated by the database, 
question words can always be brought in indirectly by 
means of substitution rules. The difference in our re- 
spective treatments lies in our attempts to formalize the 
meaning given to questions. 
Let us take a look now at why the analysis we have 
presented so far cannot be extended to multiple wh- 
questions. According to that analysis, the derivation of 
20 Computational Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
a question like "Who manages what?" is blocked after 
the first wh-term is brought in. 
BLOCKED! 
/ \ 
/ \ 
who \[it-NOM-0\] manages what 
/ \ 
/ \ 
what \[it-NOM-0\] manages \[it-ACC-1\] 
\[it-NOM-0\] manages \[it-ACC-1\] ~--=> 
manage'(i)(Xo,X 0 (PTQ-rules) 
what =-----> hPhu3x\[x(i) = u/~ P(i)(x)\] 
\[it-NOM-0\] manages what : ~> ApAu3x\[x(i) = u/~ p(i)(x)\] 
---> Au3x\[x(i) = u/~ manage'(i)(Xo,X)\] 
Syntactically the derivation is blocked because the 
proposed Rule S-WH only allows a wh-term to combine 
with a string in the category sentence, and under the 
analysis "\[it-NOM-0\] manages what" is not a sentence. 
More to the point is the semantics. "Who" denotes a 
function from sets of properties to sets of individuals 
(having those properties), and the meaning of "\[it- 
NOM-0\] manages what" is not an appropriate argument 
for such a function. 
But suppose that the "who" that combined with 
formulas to form expressions denoting sets of individu- 
als were a different function from the "who" that 
combined with expressions denoting sets of individuals 
to form expressions denoting sets of ordered pairs of 
individuals, etc.? Suppose, that is, that the English 
"who" were really a syntactic realization of a number 
of different meanings, whoo, whol, etc., as follows: 
who o combines with propositions to form a set of 
individuals, 
who1 combines with sets of individuals to form a set of 
ordered pairs, and in general, 
whoi combines with sets of ordered i-tuples to form sets 
of ordered i+ 1-tuples 
These different functions of the English "who" would 
be captured by their different translations into the logic 
(reflecting their interpretation as different semantic 
functions). 
who-word Translation Type 
who 0 APAu:lx\[x(i) = u/k P(i)(x)\] <<s.<s.e>.t>,<e,t>> 
whol ARAvAw3z\[z(i) = v/x R(i)(z,w)\] <<s,<<s,e>,<e,>>>.<e.<e,t>>> 
With this analysis we could complete the above deriva- 
tion, previously blocked, as follows: 
\[it-NOM-0\] manages what ~ ~-> 
;tu3x\[x(i) = u/k manage'(i)(xo,x)\] 
who (as who-l) ~ ~> ARAvAw3z\[z(i) = v/k R(i)(z,w)\] 
who manages what = => ARAvAw3z\[z(i) = v 
/k R(i)(z,w)\](AiAxoAu3x\[x(i) = u/k manage'(i)(Xo,X)\]) 
---> AvAw3z=lx\[z(i) = v/k x(i) = w 
/k manage'(i)(z,x)\] 
In theory there would be an infinite number of such 
(related) meanings to the word "who," one for each 
natural number n, and we could even give a rule for 
generating these meanings inductively from the single 
meaning of who0. In practice (and computationally), 
since ordinary English (and even "database-ese") al- 
lows for only a small number of terms in only a small 
number of places (subject, direct and indirect objects, 
object of preposition, "list..." requests, etc.) only a 
small number would actually ever be used in any normal 
English question. The S and T rules for this analysis 
would be something like the following: 
SWH.n. 
If a ~ PwH-Term-i and/3 ~ P?67 (i.e./3 denotes a set 
of i I -tuples), then Fwn.n(a, 13) E P?i?, where 
FWH.n(a, /3) is the result of replacing the first 
occurrence of \[it-CASE-n\] in/3 with a, and replac- 
ing all subsequent occurrences of \[it-CASE-n\] in/3 
with he/she/it or him/her/it, respectively, accord- 
ing to the gender of a and the CASE of \[it-CASE- 
n\]. 
TWh-n. 
FWH,n(Ot, /3)~ ~> a'(AiAx,/3') 
Moreover, to account for derived wh-terms like "which 
employee" in "which employee sells shoes?", we could 
extend this analysis to the interrogative determiners 
"which" and "what". This would dictate that which o 
combined with employee to form \[which employee\]o, 
which t with employee to form \[which employee\]l , etc., 
of the appropriate types. 
This analysis, while inelegant, is not really so far- 
fetched. After all, in asking, "Who manages John?" 
"who" is in some way asking for a set of individuals, 
viz., those that manage John. In asking, "Who manages 
whom?" however, rather than asking for a set of 
individuals, "who" is asking in conjunction with 
"whom" for a set of ordered pairs such that the first 
component manages the second component. A theory 
such as the above sketch would claim that English 
allows for these many semantic functions of interroga- 
tive terms to be performed by the same surface words 
like "who". 
We might also point out here a closely related alter- 
native to this approach. Instead of having an infinite 
number of meanings for each wh-term, we could suffice 
with one and allow an infinite number of syntactic and 
semantic rules for performing the substitutions. These 
rules would perform the necessary conversions of the 
meanings, not of the wh-term, but of the sentential form 
into which it is being substituted. Thus, e.g., the 
T-WH-I rule for combining "who" with "\[it-NOM-0\] 
manages whom" would form the following expression 
(where WHO* stands for the translation of "who"): 
Aw\[WHO*\[AiAXo/3*(w)\]\] 
Computational Linguistics, Volume 14, Number 4, December 1988 21 
James Clifford Natural Language Querying of Historical Databases 
For example, combining "who" with "\[it-NOM-0\] 
manages what": 
who = => APAv3y\[y(i) = v A P(i)(y)\] 
\[it-NOM-0\] manages what = ~--> 
Au3x\[x(i) = u A manage'(i)(xo,x)\] 
who manages what = => 
Aw\[APAv3y\[y(i) = v A P(i)(y)\]\](\[AiAXo\[Au::lx\[x(i) = u 
A manage'(i)(xo,x)\](w)\]) 
--, Aw\[APAv3y\[y(i) = v A P(i)(y.)\]\] 
(\[AiAXo\[3X\[x(i) = w A manage'(i)(xo,x)\]\]\]) 
--, AwAv3y=lx\[y(i) = v A x(i) = w A manage'(i)(y,x)\] 
Notice that this rule schema essentially converts the 
one-place relation denoted by one of its arguments 
("\[it-NOM-0\] sells what" in the example) into a formula 
(by function application to the new individual variable 
w) in order to allow the single meaning of "who" to 
apply. Lastly, it A-abstracts this variable w over the 
result in order to obtain a two-place relation. A slightly 
unfortunate result of this rule is that the order of the 
individuals in the relation is exactly opposite from the 
order in which the wh-terms were quantified. 
A second possible approach that would handle mul- 
tiple wh-questions would dispense with this essentially 
inductive treatment of i-place questions and attack the 
problem all at once. Such a theory would derive all 
questions in the same manner, by simultaneously sub- 
stituting all wh-terms into the matrix sentence, keeping 
track of which terms were substituted for which varia- 
bles. For example, the question "Who supplies what to 
which departments such that they sell shoes?" would be 
analyzed as follows: 
"Who supplies what to which departments such that 
they sell shoes?" 
/ N 
/ N 
who:0 \[it-NOM-0\] supplies \[it-ACC-1\] to 
\[it-DAT-2\] 
what: I such that \[it-NOM-2\] sells shoes 
which department:2 
Either of these two basic theories is possible; we have 
rejected them both for a number of reasons. First, the 
use of an infinite number of meanings for wh-terms and 
wh-determiners (or an infinite number of rules schemas 
for their substitution) requires the same technique for 
each of the tense rules, and for each of the tense rules 
with time adverbials, and for each of the when-question 
rules, the rules for when-questions with tenses, for 
when-questions with tenses and time adverbials, etc. In 
other words, accepting a solution that types all ques- 
tions differently depending upon what they ask for 
forces the inclusion of rule schemas for all of the other 
semantic functions that in a simple theory would oper- 
ate only on one type, the type given to sentences. (Later 
we will discuss how the solutions of Bennett (1977, 
1979), Belnap (1982), and of Hausser and Zaefferer 
(1978) entail a similar rippling effect of complexity 
throughout the rest of the semantic theory already 
developed for declarative sentences.) 
For an example of this effect in the theory under 
consideration, consider what the rule for adding past 
tense to a sentence would look like. (Recall our argu- 
ments for the necessity of treating tense as a property of 
the entire sentence.) Such a rule would have to be of the 
form P~ + -ED ~> Q~, where a could be the 
category declarative sentence (type t), 1-term question 
(type <e,t>), 2-term question (type <e,<e,t>>), etc. 
Because of the strict typing system of ILs (and of the 
categorial grammar of the PTQ theory of English syn- 
tax), this would require an infinite number of such rules, 
one for each of the possible input categories. While such 
a scheme is possible, it seems to violate a concern for 
simplicity and elegance. 
An additional problem with a theory dependent upon 
simultaneous substitution is a difficulty of conceiving of 
it in semantic terms. While the translation rules for such 
a theory can probably be described (they would be 
somewhat complicated), they strongly suggest the view 
that the translation rules themselves are the semantics, 
when in fact they are nothing more than syntactic 
operations on strings of logical symbols. (This is a 
common problem for people working with Montague 
Grammars, occasioned by the indirect way that the 
semantics for English is specified. Dowty (1978) refers 
to this problem when he reminds us that "the transla- 
tion is a completely dispensable part of the \[PTQ\] 
theory. The 'real' semantic interpretation of an English 
sentence is the model-theoretic interpretation of its 
translation and nothing but the model-theoretic inter- 
pretation of that translation.") When examined in terms 
of the: semantic space of functions in the model, it is not 
clear what simultaneous substitution in the syntax de- 
notes model theoretically• 
3.5.4 TEMPORAL QUESTIONS 
When-questions are different from any of the questions 
we have considered so far for three reasons. First, they 
ask about an object of a different logical type: all of the 
questions we have considered have been treated as in 
some way referring to sets of n-tuples of individuals (of 
type e); when-questions, on the other hand, refer to 
states (of type s). 
Second, although sentences can and do make refer- 
ence to more than one time ("I know that John was 
here"), multiple when-questions are very infrequent. In 
most situations "when" in English can generally only 
be asked once in a given sentence• "When and when 
• . .?" does not make sense, and questions like "When 
did John come and when did he leave?" are really two 
conjoined questions. 4 We have not accounted for mul- 
tiple when-questions of these sorts in our theory. An 
interpretation for them could be formulated in a manner 
analogously to our treatment of multiple wh-questions, 
but this would require modifying the treatment of time 
(modeled after Montague's) in the semantics. We will 
22 Computational \]Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
have more to say about this in our discussion of 
pragmatics. 
Finally, when combining with wh-terms, "when" 
must be brought in last to have the widest scope, for 
essentially the same reasons that led to the recognition 
that tense had to have widest scope. Moreover, some 
account must be given of how "when" interacts with 
our treatment of tenses, the other major temporal 
indicator in the surface structure of English. The fol- 
lowing example indicates how "when" is introduced 
into a sentence and captures the variable i in all of its 
free occurrences. 
When did John work? 
/ I \ 
/ I \ 
when (PAST) John #work 
John #work ~ EMP.'(i)(John) 
When did John work? ~ ApAil\[\[i ~ < i\] 
/% p(i 0\](AiEMP.'(i)(John)) 
--> Ail\[\[i j < i\] A (AiEMP,'(i)(John)(i0\] 
--> Aij\[\[i I < i\] A EMP,'(i0(John)\] 
Thus the question is interpreted as asking for the set of 
times in the past at which John was an employee. 
3.5.5 PRAGMATICS OR SEMANTICS? 
Most theories of question semantics, including those 
sketched above, and those of a number of other re- 
searchers in the Montague framework to be discussed 
shortly, make significant complications to the semantics 
of other parts of the PTQ analysis in order to incorpo- 
rate these new sentences. Perhaps we are overtaxing 
the semantic component of our language theories, ask- 
ing it to do for us more than it was intended to do. For 
example, most theories of question semantics have 
attempted to include some representation of the answer 
of the question as part of its denotation. Is there not 
something odd in a theory that holds that a question 
denotes its answer, especially if one has tried (or tried 
not) to think of denoting as a formal counterpart to the 
intuitive notion of meaning? Yet in one form or another 
(denoting the set of possible answers (Hamblin 1973), 
the set of correct answers (Karttunen 1977), functions 
from sequences of individuals to propositions (Bennett 
1977, 1979 and Belnap 1982), and our sets of n-tuples of 
individuals) many researchers have been investigating 
ways to accomplish this in a formal semantics. The 
similarity between wh-terms and unbound pronouns 
("Who loves whom?" versus "He loves him") suggest 
another approach, viz., one in which 
1. the semantic component provides that questions 
denote as declarative sentences (with unbound 
pronouns) do, and 
2. the pragmatic component provides that questions 
are interpreted as requests for their answers. 
Pragmatics is the least understood branch of the tripar- 
tite division of the study of language that Morris (1938) 
proposed in his theory of semiotics. This century has 
seen tremendous successes in the development of for- 
mal logical syntax and model-theoretic semantics, but 
very little in the way of formal pragmatics. (Martin 
(1959) is an early attempt in this direction.) Marcis- 
zewski (1971) and more recently Levinson (1983) to- 
gether contain a thorough analysis of the various ap- 
proaches that have been taken to define the scope of 
linguistic pragmatics, from its origin in Morris's defini- 
tion of semiotics (Morris 1938) to the present day. It is 
obvious from these accounts that there has been less 
agreement as to the scope of this branch of the field. 
Morris (1938) originally defined pragmatics as the study 
of"the relation of signs to interpreters." Later, at least 
partly in response to Carnap's proposal that "if in an 
investigation explicit reference is made to the.., user 
of a language, then we assign it to the field of pragmat- 
ics" (Carnap 1947), Morris felt the need to expand upon 
this definition. In Morris (1946), he says that pragmatics 
is "that portion of semiotic which deals with the origins, 
uses, and effects of signs within the behavior in which 
they occur." 
Montague's conception of pragmatics (Montague 
1968, 1970a, and 1973), based upon Bar-Hillel's (Bar- 
Hillel 1954) discussion of indexical expressions, repre- 
sents a departure from the traditional view. Hamblin 
(1973) felt that Montague's incorporation of a pragmatic 
component directly in the syntax and semantics was 
unconventional, and felt the need "to defend pragmat- 
ics from this weakened interpretation .... Pragmatics 
is the study of the use (not just reference) of language of 
all kinds; or, if it is not, we need a new name for the 
study that complements syntax and semantics. Monta- 
gue's 'pragmatics' would be better classed as a special 
part of semantics." Dowty (1978), while admitting that 
"the linguist's use of the term pragmatics is far from 
standardized," adopts the view that it should encom- 
pass direct and indirect speech acts, presuppositions, 
and implicatures, and explicitly rejects Montague's use 
of the term to encompass a treatment of indexical 
expressions. 
What we propose in our theory of questions is that 
the proper place for considering the answer(s) to a 
question is in a separate theory of pragmatics for the 
language. We do not propose a completely general 
theory of pragmatics. But we believe that incorporating 
into our fragment a formal pragmatic component that 
treats the notion of a response to a question is defensi- 
ble as at least one component of a theory of language 
use. In the first place, Montague notwithstanding, it falls 
within the confines of pragmatics as that term is gener- 
ally understood. For whether one speaks of "the use 
and effects" of language (Morris 1946), the "relation of 
signs to their interpreters" (Morris 1938), the notion of 
"speech acts" (Dowty 1978), or the "linguistic means 
for effecting literal purposes" (Kasher 1977), it is clear 
that the notion of responding to a question is encom- 
passed. Our attempt to formalize a pragmatic compo- 
Computational Linguistics, Volume 14, Number 4, December 1988 23 
James Clifford Natural Language Querying of Historical Databases 
nent to QE-III accords well with what Stalnaker (1972) 
sees as the goals of "a formal semiotics no less rigorous 
than present day logical syntax and semantics." Those 
goals, he goes on to say, include an analysis of such 
linguistic acts as "assertions, commands ..... re- 
quests . . . to find necessary and sufficient conditions 
for the successful (or perhaps in some cases normal) 
completion of the act." 
A second argument in favor of this approach comes 
from looking at the way that linguists have described the 
concept of a question. Linguists have traditionally clas- 
sifted sentences into four distinct types: declarative, 
interrogative, imperative, and exclamatory. A glance 
through some standard text or reference books on 
English grammar reveals two separate approaches to 
the rationale behind this scheme. According to one 
school, as in Roberts (1954), it is based upon the 
"different kinds of meaning" a sentence may have. The 
other school, as in Quirk and Greenbaum (1974), con- 
siders that the distinction is based upon such criteria as 
word order in the sentence, presence or absence of a 
subject, the presence of an interjection, etc. Clearly the 
disagreement is over whether to consider this a syntac- 
tic or a semantic distinction. Perhaps in some sense it is 
mainly a pragmatic one, reflecting both the use and 
effects of the utterance. 
Finally, this approach in its technical details is both 
simple and elegant. It removes from semantics the 
burden of providing an account of the response to a 
question, and allows it to do what semantics theories 
have always done best--account for reference. Then, 
just as the semantics of a language is based upon its 
syntax, the pragmatics is based upon both the syntactic 
and semantic analyses (or, in Hamblin's phrase, it 
"complements syntax and semantics"). The simplicity 
with which we can state the pragmatic rules for our 
fragment, which take into account the notion of the 
answer to a question, is based upon this ability to have 
both the syntax and the semantics at hand upon which 
to build a theory of pragmatics. An example should 
make this clear. 
In QE-III, questions denote (a semantic concept)just 
as declarative sentences do. Thus QE-III gives the 
following semantic analyses for "Who manages 
whom?" in the syntactic category wh-question, and for 
"He manages him" in the category declarative sen- 
tence. 
who manages whom? ---> 3x\[x(i) = u 2/% EMP,'(i)(u0 
/% AS-l(ul,x)\] 
he manages him ---> 3x\[x(i) = u 2/% EMP,'(i)(u0 
/% AS-l(Ul,X)\] 
Both are treated as denoting the same object with 
respect to an index, a variable assignment, and a model. 
But they are interpreted differently in the pragmatics. 
Pragmatics in QE-III is a function that, given a deriva- 
tion for an expression of QE-III together with its 
syntactic category and its (semantic) denotation, re- 
turns a (possibly) new object in the same model as its 
pragmatic interpretation. Thus, although we view prag- 
matics as a separate component of a language theory, it 
is closely allied to the semantics--both provide inter- 
pretations of linguistic expressions within the context of 
the same logical model. The formal definition of the 
pragmatic ,component of IL s results in these two sen- 
tences, interpreted pragmatically, denoting what the 
following expressions of IL s denote: 
who manages whom? ---> Au2Aul=lx\[x(i) = u 2 
A EMP.'(i)(u0/% MGR'(i)(x)/% AS-l(ul,x)\] 
he manages him ---> 3x\[x(i) = u 2/~ EMP.'(i)(u0 
A MGR'(i)(x) A AS-l(Ul,X)\] 
The pragmatic interpretation of the question is the set of 
n-tuples that answer it, while of the declarative sentence 
is the same as its denotation. 
3.5.6 THE PRAGMATICS OF QE-III 
The pragmatics that we give here for QE-III is a simple 
theory of the effects of producing an expression in that 
language within the assumed context of a question- 
answering environment. That is, we assume that a user 
of QE-III is using the language to produce some effect 
within this context, and it is this effect which we 
formalize as the pragmatic component of the language 
definition. We could, of course, have defined the prag- 
matics in the same manner as the semantics was de- 
fined, i.e., inductively over the syntax. However, in 
doing so we would have seemed to be giving some 
status or importance to the pragmatic interpretation of 
expressions in every category of QE-III. Because we 
had no real intuition about what the pragmatic interpre- 
tation of, say, the expression "in 1978" represented, we 
decided upon a different form of the definition. Accord- 
ingly, our definition provides a pragmatic interpretation 
for expressions in any of the several sentential catego- 
ries of the language, namely T-YNQ, T-WHQ, 
WHENQ, and T-t. (Section 3.2 contains a discussion 
both of some of the issues involved in our decision to 
present a separate pragmatic component to the formal 
theory of QE-III, as well as some of the considerations 
for the present form of this theory.) 
The following preliminary definitions are needed 
before stating the pragmatic rules. 
1. By/a\ is meant a derivation tree for the meaning- 
ful expression a of QE-III, as informally under- 
stood from our discussion of the syntax. We 
further assume that nodes of derivation trees are 
labeled with ordered triples <A,B,C>, such that 
A is the meaningful expression derived at that 
node, B is its syntactic category, and C is the rule 
of syntax applied at that step in the derivation. 
For simplicity, we shall refer to component A of 
the root of/a\ as a, and to the component B as 
CAT(/a\). 
24 Computational Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
2. The translation rules guarantee that correspond- 
ing to any derivation tree/a\ for a E MEQE_nl 
there is a unique translation into IL s. By T(/a\) 
shall be understood this unique translation, and by 
\[/a\\] M the denotation of/t~\ provided indirectly via 
T(/a\) with respect to the model M. 
3. There are two standard ways of defining a (Tars- 
kian) model-theoretic semantics. One is to define 
the notion of denotation with respect to a model M 
only, in which case formulas, e.g., denote the set 
of their satisfying variable assignments. The 
other, and more usual, procedure is to define the 
denotation with respect to a model M and a 
variable assignment g, in which case a formula 
denotes either True or False. The two notions are, 
for all practical purposes, equivalent. Since for 
the purposes of pragmatics we shall want to 
consider that open formulas denote the set of their 
satisfying variable assignments, we shall in this 
section refer to the notion of denotation with 
respect to a model M only. 
4. If \[/a\\] M is a function whose domain is As(M), the 
set of all possible variable assignments over M, 
and if further V= {v I ..... Vk} is a set of variables 
of IL s, then by IIv(\[/a\\]M ) is understood the re- 
striction of \[/a\\]M to the domain V. Note that if V 
= 0, then IIv(\[/a\\]M is defined to be just \[/a\\]M. 
5. If f is any function with domain As(M), then 
now(f) is the restriction of f to the domain 
AS,,ow(M), where ASnow (M) = {g I g E As(M) and 
g(i) -- F(now)}, that is, that subset of the possible 
variable assignments for M for which the distin- 
guished time variable i is interpreted as denoting 
that state denoted by the constant now. 
6. By FV(/a\) we shall understand the set {il, i2, 
.... in} of indices of the variables (expressions of 
the form \[it-CASE-i\]) occurring free in a. This 
notion will not be defined rigorously here, but 
would be defined inductively over the structure of 
/a\ in the usual manner, with particular attention 
paid to which rules bind occurrences of variables 
(all of the PTQ substitution rules) and which rules 
leave them free (e.g., the rules that introduce 
wh-terms.) This definition would be analogous to 
the definition of the set FV e of variables of type e 
occurring free in a logical expression, in particular 
in the expression T(/a\). It is clear that if FV(/a\) 
= {il ..... in} then FV(T(/a\) = {ui, ..... ui,}. 
However, we emphasize that FV(/a\) is defined 
over the derivation tree of a (i.e., over the syntax 
of QE-III) and make no reference to the (interme- 
diate) translation of this tree into ILs. 
7. Finally, if/3 is a meaningful expression of IL s, and 
if the free variables of type e in/3, FV e (/3) = {Ui, , 
Ui 2 ..... Ui.}, are such that ui,, ui2 ..... ui. are in 
alphabetical order, then LCFvc (/3) is the unique 
expression:hui..., hul/3 formed by first prefixing 
/3 with Aui,, then prefixing hUi2 to the result, and so 
on. 
In order to understand the form of some of the following 
definitions we state the following fact (the proof follows 
directly from the translation rules of QE-III): If/3 is the 
translation of any meaningful expression a of QE-III, 
then the free variables of a are all of type e, except for 
the possible exception of the distinguished variable i of 
type s. 
The rules of pragmatics that we now state constitute 
a definition of the pragmatic function, in a manner 
analogous to the way in which the translation rules 
constitute a translation relation. In particular they con- 
stitute a definition of the function P: P :/QE-III\ --> M 
U {ERROR}, which assigns to any derivation tree of a 
meaningful expression a of QE-III, either an object in 
the model M or the distinguished symbol "ERROR" as 
its pragmatic interpretation. 
P1. If CAT(/a\) ~ {WHENQ, T-WHQ, T-t, 
T-YNQ} 
then P(/a\) = ERROR. 
P2. If CAT(/a\) ~ {WHENQ, T-WHQ, T-t, T- 
YNQ} then P(/a\) = IIFv ° (now (\[/a\\]M)) 
Rule P1 ensures that only sentences have a pragmatic 
interpretation. Rule P2 ensures that all sentences are 
interpreted with respect to the "current" state index, 
and that in the case of questions, the infinite sequences 
of variables that the question denotes is projected down 
to include only the questioned variables. 
It is clear that the set of sequences given by IIFv ° 
(now (\[/a\\]M)) is equivalently represented by the deno- 
tation of the expression LCFv c (hiT(/a\)(now)) of ILs 
with respect to M and g. P2 is therefore alternatively 
defined as: 
P(/a\) = \[LCFv ~ (ZiT(/a\) (now))\]M,g. 
What this alternative definition allows us to do is to 
utilize the semantic notion of denotation to define the 
pragmatic interpretation of sentences in QE-III. For it 
allows us to take a translation T(/a\) of any sentence a 
and determine its pragmatic interpretation as the deno- 
tation of the expression LCFv c (hiT(/a\)(now)) and thus 
evaluate the pragmatic interpretation of a in terms of 
the semantics of IL s by means of this simple syntactic 
transformation on T(/a\). 
3.5.7 CONCLUSIONS 
The QE-III theory defines the denotation of a question 
in exactly the same way as the denotation of the 
corresponding declarative sentence that has pronouns 
in place of the interrogatives, but defines its pragmatic 
interpretation as the set of n-tuples that answer it. We 
have discussed our initial attempts to accomplish this 
result directly, by having wh-terms denote functions 
from sets of properties to sets of individuals that had 
those properties. Technically, we discovered that to 
Computational Linguistics, Volume 14, Number 4, December 1988 25 
James Clifford Natural Language Querying of Historical Databases 
accomplish this directly required a c, onsiderable com- 
plication of the semantics throughout the structure of 
our fragment. And we discovered, as we shall see, that 
others with similar goals had also been forced to intro- 
duce more complexity into their logical model in order 
to accomplish these goals in the semantic component of 
their theory. Finally, we realized thai: by eliminating as 
a goal of the semantics the capturing of the answer(s) of 
questions, we could leave the basic semantic theory of 
PTQ intact, and moreover, we could easily accomplish 
this goal in the pragmatics. 
This concludes our informal discussion of the syntax, 
semantics, and pragmatics of QE-III. We now proceed 
to discuss the theory in relation to :some of the other 
work in the field of Montague Semantics which has 
attempted to extend the PTQ fragment to include a 
theoretical account of the syntax and semantics of 
questions. 
3.6 RELATED WORK 
3.6.1 INTRODUCTION 
Two common threads run through much of the recent 
work on formalizing a theory of questions. The first is 
the idea that all questions should be defined so as to 
denote objects of the same type. Generally, this has 
meant propositions or sets of propositions, but it seems 
that even before the choice of just what questions 
denote was made, this "single semantics" viewpoint 
had been adopted. The other, as we have already 
pointed out, is that some account of the answer(s) to a 
question should be included at least as a component of 
its semantics. When combined with other factors these 
two biases have led to somewhat different results. Thus 
Hamblin (1973) suggests that a question denotes the set 
of all "propositions that count as answers to it"; 
Karttunen (1977), "the set of propositions expressed 
by\[its\] true answers"; Bennett (1977, 1979) and Belnap 
(1982), who worked with Bennett on the theory, "sets 
of open propositions:functions from sequences of indi- 
viduals to propositions." 
3.6.2 KARTTUNEN 
As we have said, Karttunen (1977) presents an analysis 
of the semantics of questions that falls within the single 
semantics tradition. (Hamblin (1973) earlier proposed a 
treatment similar to Karttunen's, but his theory was not 
worked out in as much detail.) In Karttunen's theory, 
for example, the question "Who manages John?" 
would roughly be translated as: Ap3x\[p(i) /% p = Ai 
\[manage'(i)(x)(i),John\]). Semantically, this expression, 
when interpreted with respect to a model and a state, 
denotes the set which contains, for each person x that 
manages John, the proposition that x manages John. 
Such a treatment of the semantics of questions seems 
inappropriate to us for two related reasons. First, it 
seems to confuse propositions with the sentences that 
express them. Whatever a proposition might be in our 
informal use of the term, it is in the formal system 
defined by ILs a function from indices to truth values, or 
equiwdently a set of indices. In order to see why this 
seems; an inappropriate choice for the semantic object 
denoted by a question, consider a model in which the 
constants manage' and love' are interpreted as follows: 
I 1978 ~ {<Mary, John>, <Susan, John>} I 
F(manage') = I 1979 --~ {<Mary, John>, <Bill, John>} I 
I 1980 ~ {<Bill, John>} I 
I 1978 ~ {<Bill, John>, <Susan, John>} I 
F(love') = I 1979 ~ {<Bill, John>} I 
I 1980 ~ t~ I 
Now consider the two queries QI: "Who manages John 
in 1978?", which translates to Ap3x\[manage'(1978) 
(x,John)/% p = Mmanage'(i)(x,John)\]; and Q2: "Who 
loves John in 1978?", which translates to Ap3x\[love' 
(1978)(x,John) /% p = Mlove'(i)(x,John)\]. Given these 
translations, the interpretation of these two queries in 
this model, \[Q1\] and \[Q2\], is: 
\[Q1\] = { {1978,1979}/*Mary manages John */ 
{1978} }/*Susan manages John*/ 
\[Q2\] = { {1978,1979}/*Bill loves John */ 
{1978} }/*Susan loves John */ 
Under this interpretation, both queries, which are ob- 
viously quite distinct, denote exactly the same set of 
propositions in the model, the set containing the prop- 
osition {1978,1979} and the proposition {1978}. Thus 
under this interpretation we cannot distinguish between 
these two questions--they are semantically equivalent 
in the database under this theory. 
The second and related objection is that under this 
interpretation all direct mention of the entities (Mary, 
Susan, John .... ) involved disappears. Instead, the 
theory claims that the question denotes a set that 
contains sets of states (years). What this implies is that 
there is no obvious way of going backwards from these 
objects in the model (the sets of propositions) to some 
useful expression in a language (English) that names 
them. Since in this theory the denotation of questions 
loses the people involved, we have no simple way to 
recover their names and report them to the questioner. 
The theory neglects considering the use and effects of 
the question. Moreover, there seems to be no way even 
to add a pragmatic component to such a theory in order 
to account for a question's answer(s), for on the one 
hand the syntax has no mention of the names of the 
individuals involved, nor on the other hand does the 
denotation involve any individuals at all. In the prag- 
matics of our theory the two queries would instead be 
interpreted, with respect to a given database, as follows 
(where \[Qi\] now means the pragmatic interpretation of 
Qi): \[Q1\] = {Mary,Susan}, and \[Q2\] = {Bill,Susan}. 
With these interpretations we have not lost the 
people involved, and there is an obvious relationship 
between these objects and English expressions for them 
26 Computational Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
("Mary and Susan" and "Bill and Susan"), as well as 
the relations in the database that express the same 
information. 5 
understand it, we provide the following table of the 
types of the variables used. 
Q1 
Mary 
Susan 
Q2 
Bill 
Susan 
Variable symbols Type of variable symbol 
P <e,t> : sets of individuals 
r,s <n,e> : sequences of individuals 
0 <<n,e>,<s,t>> : open propositions 
As noted earlier, Bennett discussed the issue of the 
logic of questions in two separate papers, and collabo- 
rated with Belnap in the development. Their theory is 
presented cumulatively in Bennett (1977, 1979) and 
Belnap (1982). Motivated again by the goal of a single 
semantics, and even more strongly by a desire to 
account for the individuals that answer the question, 
Belnap and Bennett develop a theory that incorporates 
sequences of individuals into the model theory. Thus a 
question like "Whom does John love?" is treated as 
denoting a set of functions from sequences of individu- 
als to propositions. Essentially all and only those se- 
quences that close the open proposition "John loves 
\[it-ACC-0\]" and make it true are included in this 
denotation. What this is tantamount to is incorporating 
the standard (Tarskian) notion of a variable assignment 
into the model theory, instead of leaving it in the meta 
theory of the logic. For technical reasons the entire 
system must be altered to include these sequences, so 
that even sentences are no longer translated into formu- 
las, but rather into expressions denoting sets of such 
sequences. This rippling effect of the complications to 
the semantics is extraordinarily reminiscent of the prob- 
lems we had in formulating a theory with inductive 
wh-terms. 
In order to accomplish this result, the set of types of 
the IL is expanded to include as a basic type n, 
expressions of type n denoting a natural number. Thus 
the natural numbers must be included as objects in the 
model, as well as functions constructed from them. Of 
particular interest in their theory are the functions from 
N to individuals, i.e., sequences. The ripple effect 
necessitates that "all expressions of English \[denote\] 
functions from sequences of individuals to their usual 
extensions" (Bennett 1979). Even sentences are no 
longer translated into formulas, but rather into expres- 
sions of type <<n,e>,t> that denote sets of sequences. 
Unfortunately, the results of this complication to the 
logic and the English translations do not seem to justify 
the cost. Certainly this theory represents a step closer 
to the goal of capturing explicitly in the denotation the 
individuals that answer the question, so it is an improve- 
ment over the proposition proposal. But these individ- 
uals are hidden somewhere inside infinite sequences of 
individuals, with no indication of their position within 
those sequences. 
An example should clarify this point. In order to 
In the Bennett/Belnap theory, an open sentence 
like "John loves him" is translated as: \[As\[love' 
(\['APP(s(1))\])(John')\], which denotes (ignoring inten- 
sions) the set of sequences such that John loves the first 
member of each of them. The corresponding question 
"Whom does John love? ''6 would be: \[AO\[O = 
\[As\[^love'(\[^APP(s(1))\])(John')\]\] A 3r\[VO(r)\]\]\], which 
denotes a set of open propositions. But these again 
involve infinite sequences of individuals, and there is no 
indication of which projection of these sequences rep- 
resents the individuals that John loves. 
This problem of having the individuals that constitute 
the answer embedded in infinite sequences without 
knowing how to project them out is the same one that 
we have in our semantic theory. For our semantics 
translates questions into open formulas, which denote 
the set of variable assignments that satisfy the formula. 
Our relegating to pragmatics the task of projecting these 
variable assignments could also be used to solve this 
problem here. But if this is the case, then what is gained 
by paying the price for the complication to the model 
theory and the translation rules? This use of sequences 
in effect duplicates the variable assignment of their 
Tarskian meta-theory (albeit restricted to the domain 
D e) in the object language and in the logical model with 
no noticeable advantages. 
3.6.3 HAUSSER AND ZAEFFERER 
The proposal of Hausser and Zaefferer (Hausser and 
Zaefferer (1978) and hereafter H-Z) is quite different 
from the other theories we have discussed, and makes a 
number of interesting points. The theory is motivated 
early in the paper by a discussion of the range of 
answers that are possible to any given question, and a 
classification of these possibilities as ranging from 
"minimal" to "redundant". For example, in answer to 
the question "Who dates Mary?" the following list of 
possibilities is cited: 
a. Bill. 
b. Bill does. 
c. Bill does so. 
d. Bill dates her. 
e. Bill dates Mary. 
Answer (e), of course, is just what the propositional 
approach would say that the question denotes (as- 
suming Mary is going steady with Bill.) H-Z goes on to 
say, however, that "the truth value of the answer 
Computational Linguistics, Volume 14, Number 4, December 1988 27 
James Clifford Natural Language Querying of Historical Databases 
expression will depend on the question in the context of 
which it is uttered, except for \[the completely redundant 
answer\]. This shows that redundant answers are not 
very interesting from a semantica point of view since 
their semantic representation is identical to that of 
ordinary declarative sentences. Since both redundant 
and non-redundant answers are possible, and since 
non-redundant answers are generally much more natu- 
ral, we hold that no serious theory of questions and 
answers should restrict itself to a treatment of redun- 
dant answers alone, and that it should be able to handle 
both." 
H-Z then proceeds to develop a theory to account for 
all of these possible answers, by extending the PTQ 
grammar and the logic IL. This theory replaces the 
model theory of IL by what they call a "context- 
model." In essence this model is an IL-model expanded 
to include as model-theoretic objects the entire language 
of IL itself. Minimal answers are then translated into 
expressions that denote formulas when interpreted 
within the context of a preceding question. This is 
accomplished technically by including in the logic a set 
of context variables, and by including an abstraction 
over a context variable in the translation of the non- 
redundant answers. A context variable denotes an 
expression of IL, viz., the question that has set up the 
context. This idea of a context allows H-Z to define a 
semantics not just for questions like "Who dates 
Mary?", but also for each of the answers (a) through (e) 
in such a way that each of them is equivalent in 
extension. 
H-Z's concern with the semantics of the answers to 
the questions, which at first sight seems to be our 
concern, is in fact another issue. For our theory, while 
it takes the answers of questions into account, is 
essentially not a theory of answers but a theory of 
questions. Of course, in the context of a more complete 
and user-friendly question-answering system, the ability 
to keep track formally of the context of the discourse 
and to express the answer in a number of different 
ways, is very attractive. Such a system would need the 
ability to go "backwards" from expressions in the logic 
to expressions in English with the same interpretation; 
Friedman (1981) discusses this issue from the point of 
view of the PTQ fragment. But the development in H-Z 
of the semantics of the questions themselves, although 
motivated from this different concern with the equiva- 
lence of redundant and non-redundant answers, does 
also lead them to an analysis of question semantics 
outside of the single semantics framework. Their anal- 
ysis "lets questions denote different types of sets ac- 
cording to the type of that expression which is the 
critical one in any kind of answer." In other words, 
their semantic analysis of answers is quite similar to our 
pragmatic analysis of questions. The following table 
comparing the types assigned to various kinds of ques- 
tions by their semantics and our pragmatics might help 
to make this analogy clearer. 
Question class Our typing 
yes-rio t 
1 ind~viduM <e,t> 
2 indNidual <e,<e,t>> 
H-Z typing 
<<s,<<s,t>,t>>,t> 
<<s,f(T)>,t> 
<<s,f(T)>,<<s,f(T)>,t>> 
3.6.4 SCHA AND GUNJI 
The work of Scha (1983) on the PHLIQA1 project and 
Gunji (1981), both being developed concurrently with 
the development of QE-III (Clifford 1982b), are remark- 
ably similar in spirit, though not in detail, to the present 
work. The close parallels in the motivation of these 
three works indicate a trend among many researchers 
toward developing a formal foundation for computer 
systems that do natural language processing. 
The major theoretical difference between QE-III and 
that of the PHLIQA1 project of Scha are that we make 
a distinction between the semantics and pragmatics of 
sentences in QE-III, so that the pragmatic interpretation 
of questions in QE-III is closely analogous to Scha's 
semantics for the same question. We continue to believe 
that this separation between the denotation of a sen- 
tence (given by the semantic component of the lan- 
guage) and its interpretation (given by the pragmatic 
component) is a simpler and more easily extendible 
approach to the problem of providing a formal account 
of meaning. 
Much of the motivation for the work reported in 
Gunji (1981), namely to provide a formal pragmatics to 
a language specification by means of the computational 
application of a"superinterpreter" after the completion 
of the syntactic and semantic interpretation, is the same 
as ours. Gunji's superinterpreter, in fact, is quite clearly 
the computational realization of what we have termed 
our pragmatic interpretation. The major difference be- 
tween these two projects is in the scope of their lan- 
guages, which reflect Gunji's focus on conversation 
implicatures and ours on querying historical databases. 
Whereas Gunjrs work covers declarative and impera- 
tive sentences, and true-false questions, QE-III resulted 
from a concentration on wh-questions and an explicit 
treatment of time-denoting expressions. 
This concludes our informal discussion of the goals 
and philosophy behind the definition of the fragment 
QE-III, and its relation to other recent work in the area 
of formal question semantics. The next section provides 
an overview of QE-III through a series of examples and 
discussions illustrating the major features of the lan- 
guage. (The complete definition of the syntax, seman- 
tics, and pragmatics of QE-III can be found in Clifford 
(1987).) 
4 EXAMPLES FROM THE QE-III FRAGMENT 
4.1 INTRODUCTION 
This section presents and discusses examples of the 
syntactic and translation rules of the QE-III fragment. 
As we pointed out in Section 3, the PTQ fragment 
28 Computational Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
stands essentially intact as the core of QE-III. There 
are, however, certain changes to this core. One major 
change is our use of the logic IL s as the intermediate 
translation language; this logic is a modification to 
Montague's IL, and makes explicit the "hidden" ab- 
straction over indices that is a part of the evaluation 
process in Montague's PTQ analysis. With respect to 
IL, the major change is that in IL s, we evaluate any 
expression a with respect to a state s by forming the 
expression \[Aia\](s). 
The other major aspect of QE-III is the inclusion of a 
formal pragmatic component to the language, on an 
equal standing with the syntactic and semantic compo- 
nents. The formalized pragmatic component of QE-III 
was primarily motivated by the desire to simplify the 
provision of an interpretation for questions in a formal 
way. As we showed in Section 3.5.6 the pragmatic 
interpretation of any sentential expression was essen- 
tially the denotation of the expression formed by 
Aabstracting over all of the free individual variables and 
also evaluating with respect to "now." 
In addition to these changes in the underlying logic 
and method of evaluation, the following additional 
modifications have been made to the rules of the PTQ 
fragment. 
1. Rule $4 has been modified to perform the single 
function of combining a term with an IV to form a 
sort of protosentence. It no longer performs the 
verb inflection for third-person singular present 
tense. The entire treatment of tense and time 
adverbials is now performed more systematically 
by rules S101-S106. (The tensing functions of S17 
have therefore been totally eliminated.) 
2. Montague's use of the variables he o and him o 
amounted to a simple technique of case marking in 
order to choose the appropriate personal pronoun 
upon substitution of a term. We have expanded 
this technique somewhat, using variables of the 
form \[it-CASE-i\] where CASE ranges over 
{NOM,DAT,ACC} and i over the natural num- 
bers. 
3. Rule $9 for combining a sentence adverbial 
("Necessarily") with a sentence, has been elimi- 
nated. This is because the only sentence adver- 
bials in QE-III are time adverbials, which are 
brought in together with the tense marker in rules 
S 104-S 106. 
4. It is well know that there are problems with the 
PTQ treatment of conjunction and disjunction of 
terms and IVs (see discussion in Friedman (1979) 
and Bennett (1974)). While Friedman's bracketing 
solution is ultimately more acceptable (both by 
virtue of its generality and, of particular interest, 
its natural correspondence to a LISP implementa- 
tion), we have for simplicity of presentation 
adopted Bennett's simple solution of marking all 
basic verbs with a # marker, which is removed 
when the verb is ultimately tensed. (We choose 
this solution because the points we wish to make 
have only to do with the verbs, and are easily 
understood with this technique. 
For ease of understanding the translations to follow, the 
following table shows the types of the variables used. 
Variable symbols Type of variable symbol 
X, y, Z, X0, XI, . . . 
P, Q, QI, Q2 .... 
P,q, ql, q2 .... i 
il, i 2, . . . 
w 
<s,e> : individual concepts (ICs) 
<s,<<s,e>,t>> : properties of ICs 
<s,t> : propositions 
s : distinguished state variable wrt, 
which all expressions are evaluated 
s : states 
<s,<<s,<<s,e>,t>>,t>> 
:properties of properties of ICs 
4.2 PTQ-LIKE EXAMPLES FROM THE QE-III FRAGMENT 
Before illustrating some of the added features of the 
QE-III database query fragment, we present a simple 
example within the syntactic range of the PTQ fragment 
(up to vocabulary differences) in order to contrast the 
way these two fragments derive and translate it. For 
example, under one analysis, 
4-1. John manages Mary. 
would have the following derivation tree in QE-III: 
John manages Mary S104 
I I 
John #manage Mary $4 / \ 
/ \ 
John #manage Mary $5 
/\ 
/ \ 
#manage Mary 
The syntactic and translation rules illustrated in this 
example are $4 to form an untensed clause from a 
SUBJect and PREDicate, $5 to form a verb phrase from 
a transverb and a direct object, and $104 to form a 
present-tense clause. 
Several points arise with this example. First, we note 
that this analysis tree presents the derivational history 
of non-basic expressions in the language in the obvious 
way. Each node is labeled with a meaningful expression 
in QE-III; in case the expression is non-basic, it is 
further labeled by the syntactic rule by which it was 
constructed, and is given children labeled with the 
expressions from which it was obtained. Montague 
(1970b) provides a more formal definition of analysis 
trees; it should be sufficient to point out that the 
language is defined in such a way that to each analysis 
tree (though not necessarily to each meaningful expres- 
sion) there corresponds a unique translation into the 
intermediate logical language. 
This analysis of Example 4-1 illustrates several de- 
partures from the corresponding PTQ analysis. First, 
we note that the basic verb is prefixed with #, and this 
Computational Linguistics, Volume 14, Number 4, December 1988 29 
James Clifford Natural Language Querying of Historical Databases 
prefix remains even after $4 is applied to combine the 
term "John" with the intransitive verb phrase 
"#manage Mary". Second, Rule SI04 is new. It takes 
an untensed sentence as input and gives a (present) 
tensed sentence as output. Thus we have characterized 
tense as a property not of verbs, but of clauses, al- 
though this property in English is realized by the 
inflection of the main verb of the clause. The impor- 
tance of this characterization will be made clearer when 
we consider the interaction of tense with interrogative 
sentences. 
This method of introducing tense,'~ into a sentence 
obviates the need for undoing the English verb inflec- 
tions that would be required by a method (such as in 
PTQ or in Dowty (1979) that always introduced present 
tense first, subject to possible subsequent modifica- 
tions. Dowty (1979) makes a similar point--though still 
in terms of introducing the tense via a SUBJ + PRED 
rule---but does not incorporate the idea into the frag- 
ment presented there. 
In a number of the PTQ rules Montague makes use of 
the auxiliary notions of the gender of a CN or a T, and 
the third-person singular form of ave, rb. These notions 
are never defined with the same rigor that Montague 
demanded of other characteristics of his logic and 
grammar, presumably because he felt they were obvi- 
ous and uninteresting. As in Bennett (1974) we make 
use of a number of similar auxiliary notions in our rules. 
This example points out two such notions, viz., that of 
the tense of a clause and the case of a variable. In our 
fragment a clause is either untensed or tensed, and 
belongs to a different category (though of the same 
logical type) in either case. A variable introduced into a 
sentence is either uncased, or one of NOM, ACC, or 
DAT. 
The translation of Example 4-1 corresponding to the 
above analysis tree is as follows: 
Mary ~-~-> hP=lx\[P(i)(x) A x(i) = Mary\] 
#manage ~ ~> AWAx\[W(i)(AiAy\[AS-I(y(i),x) 
A EMP,'(i)(y(i)) A MGR'(i)(x)\])\] 
#manage Mary =-----> AWAx\[W(i)(AiAy\[AS-I(y(i),x) 
A EMP,'(i)(y(i)) A MGR'(i)(x)\])\](AiAP=ix\[P(i)(x) 
A x(i) = Mary\]) 
--~ Ax3z\[AS-l(z(i),x) A EMP,'(i)(z(i)) 
A MGR'(i)(x) A z(i) = Mary\] 
John = ~> AP=ly\[P(i)(y) A y(i) = John\] 
John #manage Mary ~ :> AP=ly\[P(i)(y) A y(i) = John\] 
(AiAx=lz\[AS-l(z(i),x) A EMP,'(i)(z(i)) 
A MGR'(i)(x) A z(i) = Mary\]) 
---> =ty\[AS-l(Mary,y) A EMP,'(i)(Mary) 
A MGR'(i)(y) A y(i) = John\] 
John manages Mary ~ ~> =ly\[EMP,'(i)(Mary) 
A MGR'(i)(y) A y(i) = John A AS-I(Mary,y)\] 
The pragmatic interpretation is represented by: 3y 
\[EMP,' (now)(Mary) A MGR' (now)(y) A y(now) = 
John A AS-l(Mary,y)\]. 
Our treatment of proper terms is slightly different 
from the PTQ treatment, in that the translations include 
an individual concept variable whose extension at the 
state i is as,~erted to be the indicated individual. This is 
done because in HRDM all individuals of interest must 
be playing a role in the-database, and roles can only be 
filled by individual concepts. Further, as we discussed 
in Section 13, verbs are treated as objects of the same 
type as in I?TQ, but they are analyzed in terms of the 
database schema. 
4,3 TEMPORAL REFERENCE IN QE-III 
In addition to its indication by means of the tense 
system, temporal reference in English is also indicated 
by certain time adverbials (today, last year .... ) and 
also by prepositional phrases (in 1978, on Monday...). 
Care must be taken in order to analyze properly the 
semantics of sentences that involve an interaction be- 
tween tenses and these other temporal indicators. They 
cannot be applied sequentially as operators to a clause, 
or the semantics will be incorrect. (Dowty (1979) makes 
the same observation.) The following derivation for 
4-2. Peter earned 25K in 1978. 
illustrates this aspect of QE-III. 
Peter earned 25K in 1978 S108 
/ \ 
/ \ 
in 1978 Sl13 Peter #earn 25K $4 
/ \ (derived as in Example 4-1) 
/ \ 
in 1978 
This example illustrates Rule S108, which simulta- 
neously adds a tense (past) and a time adverbial, and 
S113, which forms a temporal prepositional phrase. The 
pragmatic interpretation correctly indicates that there is 
some state in the past that is also in the set of states 1978 
at which the present-tense sentence "Peter earns 25K is 
true": 3i13y\[1978'(ii) A \[il < now\] A EMP,'(il)(Peter) 
A SAL'(il)(y) A y(i 1) = 25K A AS-l(Peter,y)\]. 
If we had introduced the two temporal indicators (the 
tense and "in 1978") separately, in either order, the 
resulting interpretations would be incorrect. 
Peter earned 25K in 1978 
/ \ 
/ \ 
(PAST) Peter #earn 25K in 1978 
/ \ 
/ \ 
in 1978 Peter #earn 25K 
interpreted as: 3i23i1=1y\[\[i2 < now\] A 1978'00 A 
EMP,'(il)(Peter) A SAL'(i~)(y) A y(i0 = 25K A AS- 
l(Peter,y)\]. This places the three times i~, i 2, and now on 
the time line as follows: 
....... I ......... I ..................... 
i2 now 
with i~ anywhere on the time line in 1978. 
30 Computational Linguistics, Volume 14, Number 4, December 1988 
James Clifford Natural Language Querying of Historical Databases 
The reverse order of sequential introduction is also 
incorrect. 
Peter earned 25K in 1978 
/ N 
/ N 
in 1978 Peter earned 25K 
/ N / \ 
(PAST) Peter #earn 25K 
since it is interpreted as: 3i23i13y\[1978'(i2) A \[i I < i2\] A 
EMP,'(il)(Peter) A SAL'(i0(y ) A y(il) = 25K A AS- 
l(Peter,y). Here the two times are located as follows: 
........ I .............. I ..... 
i! i 2, in 1978 
The properties of Peter are asserted to be true in state i~, 
but il may or may not be in 1978, and may or may not be 
in the past (with respect to now.) Only the simultaneous 
introduction of these temporal operators provides the 
correct interpretation. 
Example 4-3 illustrates how tense is treated as a 
property of clauses in compound sentences, and how 
these tenses are independent of one another. It also 
illustrates how relative clauses are maintained in the 
QE-III fragment. 
4-3. Peter manages an employee such that he earned 
30K. 
Under the most likely analysis, this sentence is inter- 
preted in QE-III as: :lw=lxqy=lil\[EMP,'(now)(x(now)) 
A MGR'(now)(w) A w(now) = Peter A AS-l(x(now),w) 
A EMP,'(i0(x(now)) A SAL'(i0(y ) A y(i 0 = 30K A 
1978'(il) A \[i I < now\] A AS-l(x(now),w)\]. 
Example 4-4 illustrates how propositions can be 
treated in almost the same way as time constants for 
denoting sets of states. 
4-4. John worked before Mary worked. 
This sentence is analyzed as asserting that there was 
some state S1 before now at which John worked, and 
that S 1 was also before some other state $2 before now 
at which Mary worked. 
:lil\[\[il <<(AiEEMP,'(i2)(Mary))\] A \[i 2 < now\] 
A \[i I < now\] A EMP,'(i0(John)\]. 
Similarly, we can combine simple time expressions with 
prepositions to form temporal adverbials, as in Example 
4-5. 
4-5. Rachel worked before yesterday. 
which is analyzed as: 3i1\[\[i I << yesterday'(now)\] A \[i l 
< now\] A EMP,'(i 0 (Rachel)\]. Notice that this transla- 
tion places two restrictions upon when the state i I can 
occur in time. 
1. \[i I << yesterday'(now)\] because of "before yes- 
terday," and 
2. \[i I < now\] because of the past tense. Since a time 
before yesterday must be before now (by the 
meaning of "yesterday"), a meaning postulate for 
words such as "yesterday" might well be in order 
here to remove this redundancy and reduce the 
final translation to 3i~\[\[i~ << yesterday'(now)\] A 
EMP,'(il)(Rachel)\]. 
We now proceed to discuss the other additional rules of 
the QE-III fragment. These rules either form expres- 
sions that have particular relevance to the database 
realm (possessives, role specifications, etc.) or form 
interrogative sentences. We will look first at the ques- 
tions; some of the considerations involved in the fram- 
ing of these rules for database querying purposes was 
given in Section 3. 
4.4 QUESTIONS IN QE-III 
Consider the following query: 
4-6. Who managed Rachel? 
translated as 3i13y\[\[i Z < i\] A EMP.'(i0(Rachel) A 
MGR'(im)(y) A y(i0 = u A AS-l(Rachel,y)\]. Recall that 
the pragmatics provides a representation for the answer 
to questions, and that the pragmatic interpretation of 
this query is denoted by the expression Au 3il3y\[\[i I < 
now\] A EMP.'(il)(Rachel) A MGR'(i0(y) A y(i0 = u A 
AS-l(Rachel,y)\] formed by binding all free occurrences 
of the variable i to the constant now, and A-abstracting 
over all of the free individual variables. 
This example illustrates why the tense must be 
considered a property of the entire clause, rather than 
just of the verb phrase, if the semantics of the question 
is to come out right. For suppose instead that we 
derived (4-6) as follows: 
Who managed Rachel? 
/ \ 
/ \ 
who \[it-NOM-0\] managed Rachel 
The translation would then be 3y3il \[y(i) = u A \[i~ < i\] 
A EMP.'(i0(Rachel) A MGR'(i0(y) A AS- l(Rachel,y)\]. 
The problem with this translation is that the manager-IC 
y is not tensed properly. When evaluated, this query 
will return the set of individuals u who are the extension 
of Rachel's manager-IC, not at some time in the past, 
but now. Because "who" has wider scope in this 
derivation, the past-tense operator could not capture 
the free i of the translation of "who". The question, 
under our treatment, is correctly analyzed as "Who 
(past) managed (past) Rachel?}" rather than as "Who 
(now) managed (past) Rachel?" In order to get this 
reading, tenses (and tenses + TmADVerbials) must be 
brought in last over all clauses, including interrogative 
sentences. 
Interrogative terms (WriT's) can also be derived 
from common nouns and the interrogative determiners 
such as "which," as seen in Example 4-7. 
4-7. Who manages which employees? 
which is interpreted as: hUlAU2:ly\[EMP,'(now)(u2) A 
MGR'(now)(y) Ay (now) = u I A AS-l(u2,y)\]. 
Example 4-8 illustrates a three-term interrogative, 
using the three-place verb "#supply" and a rule (a 
simple extension of the two-place case, essentially 
Computational Linguistics, Volume 14, Number 4, December 1988 31 
James Clifford Natural Language Querying of Historical Databases 
taken from Dowty (1979)) for combining such a verb 
with an indirect object to form a two-.place verb. 
4-8. What does who supply to whom? 
The interpretation 7 is AUaAUEAUl\[COMP,'(now)(u3) A 
DEPT,'(now)(u2) A ITEM,'(now)(u0 A REL-3 
(u3,u2,uP\]. 
Example 4-9 illustrates a more complicated question 
that requires, in terms of the database: representation, a 
"join" of two relations. 
4-9. Who works for a department such that it sells 
shoes? 
It is interpreted as Au:lx\[EMP,'(new)(u) ADEPT,' 
(now) (x(now)) A AS-l(u,x) A ITEM,'(now)(Shoes) A 
REL-2(x(now),Shoes)\]. 
Yes-no questions can take two forms in the frag- 
ments 
4-10. Is it the case that Peter earns 30K? 
and 
4-11. Does Peter earn 30K? 
Both of these questions receive the same interpretation: 
3x\[EMP,'(i)(Peter) A SAL'(i)(x) A x(i) =30K A AS-1 
(Peter,x)\]. 
When-questions, very important in a historical data- 
base context, are illustrated by the following example. 
4-12. When did Peter earn 25K? 
interpreted as hil3y\[\[il < now\] A EMP,'(i0(Peter) A 
SAL'(i~)(y) A y(il) -- 25K A AS-l(Peter,y)\]. 
Finally, the next two examples illustrate the interac- 
tion of when and an already-formed term question, and 
the interaction of when with time phrases. 
4-13. When did who manage whom? 
interpreted as Au2AuiAil3x\[\[il < now\] A EiP,'(il)(U l) 
A MGR'(il)(X) A x(il) = u2 A AS-l(Ul,X)\], and 
4-14. When and to whom did company A sell item B 
yesterday? 
interpreted as: AilAu2Aut 3x\[\[il < now\] A yesterday'(i 0 
A DEPT,'(il)(Ul) A x(i 1) = u I A COMP,'(il)(A) A 
ITEM,'(it)(B ) A REL-3(A,B,u0\]. 
This concludes the examples of the kinds of queries 
expressible in the language QE-III, and the semantics 
and pragmatics that the fragment provides for them. We 
now present some of the other additions we have made 
to the PTQ fragment in order to express certain other 
common query constructions. 
4.5 MISCELLANEOUS FEATURES OF QE-III 
The use of possessives is very common in database 
queries, and is easily incorporated into the fragment, as 
in 
4-15. Who is Peter's manager? 
which is interpreted as Au3x\[MGR'(now)(x) A x(now) = 
u A AS-l(Peter,x)\]. An alternative way of phrasing the 
same question uses "of" instead of the possessive 
marker. 
4-16. Who is a manager of Peter'? 
and ultimately receives the same interpretation. Finally, 
specification of the role played by an individual in the 
database can also be accomplished by means of the 
word "as". 
4-1'7. Who has Peter as manager? 
interpreted as Au3z\[MGR'(now)(z) A z(now) = Peter A 
AS-I(u,z)\], or by the simple concatenation of the role 
and a term. 
4-18. Who sells Item 37? 
interpreted as Au\[DEPT,'(now)(u) A ITEM,'(now)(37) 
A REL-2(u,37)\]. 
5 CONCLUSION 
The problem of modeling the semantics of time is one 
which is beginning to be explored by researchers in a 
number of different areas of computer science. We 
believe that formal logic can make an important contri- 
bution to our understanding and specification of the 
properties of time that we can incorporate into our 
models and systems. Using the logic IL s and the frame- 
work of MS, we have presented in this paper an 
overview of the HRDM, which is a formalization of the 
concept of a historical database. HRDM provides for 
the modeling of historical information in a DBMS, for 
the specification of constraints on the way that infor- 
mation can change over time, and for a query language 
for accessing that information with specific reference to 
its temporal dimension. 
To complement the relational query language of 
HRDM (Clifford and Croker 1987), we have in this 
paper described a formal English database query lan- 
guage, QE-III, which is defined in a MS framework. 
QE-III incorporates a formal syntax, semantics, and 
pragmatics to account for an interpretation of questions 
that accord with the interpretation of HRDM, including 
an account of multiple-wh questions, a semantics and 
pragmatics of time, and a grammar that is conducive to 
a computer implementation. In addition to its formal 
syntax and parallel semantics, QE-III is provided with a 
formal pragmatics that provides a representation for the 
answer(s) to a question as a function of its syntax and 
semantics. We believe that this approach, and the whole 
area of formal pragmatics as a component of language 
theory, is a fertile area for further research. 
ACKNOWLEDGEMENTS 
This paper is based upon research done while I was a graduate student 
in computer science at SUNY Stony Brook. I would like to thank my 
advisor David Warren for introducing me to, and schooling me in, the 
complexities of Montague Semantics, and also Professor Joyce Fried- 
man for encouraging me to conduct this research. I would also like to 
thank the referees for their many useful and constructive comments 
on an earlier draft of this paper. 
NOTES 
1. See Clifford (1987) for the definition of ILs, and adiscussion ofhow 
(and why) it differs from Montague's IL. 
2. In all translation examples we follow Partee in using a double 
arrow "~ ~--->" to indicate the immediate result of applying a 
translation rule of the fragment, and a single arrow "--->" to indicate 
the result of any of a number of logical simplifications (principally 
A-reduction). 
3. The "such that" construction for heading relative clauses is a 
syntactic holdover from the PTQ fragment, which, because our 
concern is primarily semantic, we have not attempted to replace 
with a more sophisticated treatment. For a treatment of more usual 
English relative clauses, the reader is referred to Cooper (1979). 
4. Although David Warren suggests considering the following sort of 
exchange: 
\[SHE\]: "There are several Fire Island ferries each day." 
\[HE\]: "Oh, really! When do they arrive and when do they leave?" 
It is natural to interpret this as a request for the set of ordered pairs 
<t~,t2> representing the arrival and departure times of particular 
ferry runs. Other sorts of multiple when-questions that ask for a 
range ("Between when and when...") seem to be of this same 
type. 
5. Tichy (1978) makes many of the same points that we make here 
regarding the proposition idea. 
6. Actually their syntax does not cover direct questions, and so this 
is really their treatment of "John loves him" in the category of 
Basic Question; it seems clear, however, that they intend the 
semantics of the corresponding direct question to be the same. 
7. REL-3 indicates that there is a tri-ary relationship among the 
indicated three individuals. 

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