A Computational Semantics for Natural Language 
Lewis G. Creary and Carl J. Pollard 
Hewlett-Packard Laboratories 
1501 Page Mill Road 
Palo Alto, CA 94304, USA 
Abstract 
In the new Head-driven Phrase Structure Grammar 
(HPSG) language processing system that is currently under 
development at Hewlett-Packard Laboratories, the 
Montagovian semantics of the earlier GPSG system (see 
\[Gawron et al. 19821) is replaced by a radically different 
approach with a number of distinct advantages. In place 
of the lambda calculus and standard first-order logic, our 
medium of conceptual representation is a new logical for- 
realism called NFLT (Neo-Fregean Language of Thought); 
compositional semantics is effected, not by schematic 
lambda expressions, but by LISP procedures that operate 
on NFLT expressions to produce new expressions. NFLT 
has a number of features that make it well-suited {'or nat- 
ural language translations, including predicates of variable 
arity in which explicitly marked situational roles supercede 
order-coded argument positions, sortally restricted quan- 
tification, a compositional (but nonextensional) semantics 
that handles causal contexts, and a princip\[ed conceptual 
raising mechanism that we expect to lead to a computation- 
ally tractable account of propositional attitudes. The use 
of semantically compositional LiSP procedures in place of 
lambda-schemas allows us to produce fully reduced trans- 
lations on the fly, with no need for post-processing. This 
approach should simplify the task of using semantic infor- 
mation (such as sortal incompatibilities) to eliminate bad 
parse paths. 
I. Introduction 
Someone who knows a natural language is able to use 
utterances of certain types to give and receive information 
about the world, flow can we explain this? We take as 
our point of departure the assumption that members of a 
language community share a certain mental system -- a 
grammar -- that mediates the correspondence between ut- 
terance types and other things in the world, such as individ- 
u~ds, relations, and states of ~ffairs, to a large degree, this 
system i~ the language. According to the relation theory 
of meaning (Barwise & Perry !1983!), linguistic meaning is 
a relation between types of utterance events and other as- 
pects of objective reality. We accept this view of linguistic 
meaning, but unlike Barwise and Perry we focus on how the 
meaning relation is mediated by the intersubjective psycho- 
logical system of grammar. 
\[n our view, a computational semantics \['or a natural 
language has three essential components: 
172 
a. a system of conceptual representation for internal use 
as a computational medium in processes of information 
retrieval, inference, planning, etc. 
b. a system of linkages between expressions of the natural 
language and those of the conceptual representation, 
and 
c. a system of linkages between expressions in the concep- 
tual representation and objects, relations, and states of 
affairs in the external world. 
\[n this paper, we shall concentrate almost exclusively on 
the first two components. We shall sketch our ontologi- 
cal commitments, describe our internal representation lan- 
guage, explain how our grammar (and our computer im- 
plementation) makes the connection between English and 
the internal representations, and finally indicate the present 
status and future directions of our research. 
Our internal representation language. NFLT. is due to 
Creary 119831. The grammatical theory in which the present 
research is couched is the theory of head grammar (HG) set 
forth in \[Pollard 1984\] and \[Pollard forthcoming i and imple- 
mented as the front end of the HPSG (Head-driven Phrase 
Structure Grammar) system, an English \[auguage database 
query system under development at Hewlett-Packard Lab- 
oratories. The non-semantic aspects of the implementation 
are described in IFlickinger, Pollard, & Wasow t9851 and 
\[Proudian & Pollard 1.9851. 
2. Ontological Assumptions 
To get started, we make the following assumptions 
about what categories of things are in the world. 
a. There are individuals. These include objects of the 
usual kind (such as Ron and Nancy) as well as situations. 
Situations comprise states (such as Ron's being tall) and 
events (such as Ron giving his inaugural address on January 
21, 1985). 
b. There are relations (subsuming properties). Exam- 
ples are COOKIE (= the property of being a cookie) and BUY 
(= the relation which Nancy has to the cookies she buys). 
Associated with each relation is a characteristic set of roles 
appropriate to that relation (such as AGENT, PATIENT, LO- 
CATION, etc.) which can be filled by individuals. Simple 
situations consist of individuals playing roles in relations. 
Unlike properties and relations in situation semantics 
\[Barwise & Perry 1983\[, our relations do not have fixed ar- 
ity (number of arguments). This is made possible by taking 
explicit account of roles, and has important linguistic con- 
sequences. Also there is no distinguished ontological cate- 
gory of locations~ instead, the location of an event is just 
the individual that fills the LOCATION role. 
c. Some relations are sortal relations, or sorts. Associ- 
ated with each sort {but not with any non-sortal relation) 
is a criterion of identity for individuals of that sort \[Coc- 
chiarella 1977, Gupta 1980 I. Predicates denoting sorts oc- 
cur in the restrictor-clanses of quantifiers (see section 4.2 
below), and the associated criteria of identity are essential 
to determining the truth values of quantified assertions. 
Two important sorts of situations are states and events. 
One can characterize a wide range of subsorts of these 
(which we shall call situation types) by specifying a par- 
ticular configuration of relation, individuals, and roles. For 
example, one might consider the sort of event in which Ron 
kisses Nancy in the Oval Office, i.e. in which the relation is 
KISS, Ron plays the AGENT role, Nancy plays the PATIENT 
role, and the Oval Office plays the LOCATION role. One 
might also consider the sort of state in which Ron is a per- 
son, i.e. in which the relation is PERSON, and Ron plays 
the INSTANCE role. We assume that the INSTANCE role is 
appropriate only for sortal relations. 
d. There are concepts, both subjective and objective. 
Some individuals are information-processing organisms that 
use complex symbolic objects (subjective concepts) as com- 
putational media for information storage and retrieval, in- 
ference, planning, etc. An example is Ron's internal rep- 
resentation of the property COOKIE. This representation 
in turn is a token of a certain abstract type ~'COOKIE, 
an objective concept which is shared by the vast majority 
of speakers of English. t Note that the objective concept 
~COOKIE, the property COOKIE, and the extension of that 
property (i.e. the set ofall cookies) are three distinct things 
that play three different roles in the semantics of the Eng- 
lish noun cookie. 
e. There are computational processes in organisms for 
manipulating concepts e.g. methods for constructing com- 
plex concepts from simpler ones, inferencing nmchanisms, 
etc. Concepts of situations are called propositions; organ- 
isms use inferencing mechanisms to derive new propositions 
from old. To the extent that concepts are accurate repre- 
sentations of existing things and the relations in which they 
stand, organisms can contain information. We call the sys- 
tem of objective concepts and concept-manipulating mech- 
anisms instantiated in an organism its conceptual ~ystem. 
Communities of organisms can share the same conceptual 
system. 
f. Communities of organisms whose common concep- 
tual system contains a subsystem of a certain kind called 
a grammar can cornnmnicate with each other. Roughly, 
grammars are conceptual subsystems that mediate between 
events of a specific type (calh:d utterances) and other as- 
pects of reality. Grammars enable organisms to use utter- 
ances to give and receive information about the world. This 
is the subject of sections 4-6. 
3. The Internal 
Representation Language: NFLT 
The translation of input sentences into a logical for- 
malism of some kind is a fairly standard feature of com- 
puter systems for natural-language understanding, and one 
which is shared by the HPSG system. A distinctive feature 
of this system, however, is the particular logical formalism 
involved, which is called NFLT (Neo-Fregean Language of 
Thought). 2 This is a new logical language that is being 
developed to serve as the internal representation medium 
in computer agents with natural language capabilities. The 
language is the result of augmenting and partially reinter- 
preting the standard predicate calculus formalism in sev- 
eral ways, some of which will be described very briefly in 
this section. Historically, the predicate calculus was de- 
ve|oped by mathematical logicians as an explication of the 
logic of mathematical proofs, in order to throw light on 
the nature of purely mathematical concepts and knowledge. 
Since many basic concepts that are commonplace in natu- 
ral language (including concepts of belief, desire, intention, 
temporal change, causality, subjunctive conditionality, etc.) 
play no role in pure mathematics, we should not be espe- 
cially surprised to find that the predicate calculus requires 
supplementation in order to represent adequately and natu- 
rally information involving these concepts. The belief that 
such supplementation is needed has led to the design of 
NFLT, 
While NFLT is much closer semantically to natural lan- 
guage than is the standard predicate calculus, and is to 
some extent inspired by psycho\[ogistic considerations, it 
is nevertheless a formal logic admitting of a mathemati- 
cally precise semantics. The intended semantics incorpo- 
rates a Fregean distinction between sense and denotation, 
associated principles of compositionality, and a somewhat 
non-Fregean theory of situations or situation-types as the 
denotations of sentential formulas. 
3.1. Predicates of Variable Arity 
Atomic formulas in NFLT have an explicit ro\[e-marker 
for each argument; in this respect NFLT resembles seman- 
tic network formalisms and differs from standard predicate 
t We regard this notion of obiective concept as the appro- 
priate basis on which to reconstruct, ia terms of informa- 
tion processing, Saussure's notions of ~ignifiant (signifier) 
and #ignifig (signified) \[1916!, as well an Frege's notion of 
Sinn (sense, connotation) \[1892 I. 
~" The formalism is called ~neo-Fregean" because it in- 
corporates many of the semantic ideas of Gottlob Frege, 
though it also departs from Frege's ideas in several signif- 
icant ways. It is called a "language of thought" because 
unlike English, which is first and foremost a medium of 
communication, NFLT is designed to serve as a medium 
of reasoning in computer problem-solving systems, which 
we regard for theoretical purposes as thinking organisms, 
(Frege referred to his own logical formalism, Begriffsschrift, 
an a "formula language for pure thought" \[Frege 1879, title 
and p. 6 (translation)\]). 
17"3 
calculus, in which the roles are order-coded. This explicit 
representation of roles permits each predicate-symbol in 
NFLT to take a variable number of arguments, which in 
turn makes it possible to represent occurrences of the same 
verb with the same predicate-symbol, despite differences 
in valence (i.e. number and identity of attached comple- 
ments and adjuncts). This clears up a host of problems 
that arise in theoretical frameworks (such an Montague se- 
mantics and situation semantics) that depend on fixed-arity 
relations (see \[Carlson forthcoming\] and \[Dowry 1982\] for 
discussion). In particular, new roles (corresponding to ad- 
juncts or optional complements in natural language) can be 
added as required, and there is no need for explicit existen- 
tial quantification over ~missing arguments". 
Atomic formulas in NFLT are compounded of a base- 
predicate and a set of rolemark-argument pairs, as in the 
following example: 
(la) English: 
Ron kissed Nancy in the Oval Office on April 
1, 1985. 
(lb) NFLT Internal Syntax: 
(kiss (agent . con) 
(patient . nancy) 
(location . oval-office) 
(time . 4-i-85) ) 
(lc) NFLT Display Syntax: 
( KISS agt: RON 
p~:nt: NANCY 
loc: OVAL-OFFICE 
art: 4-i-8S) 
The base-predicate 'KISS' takes a variable number of argu- 
ments, depending on the needs of a particular context. \[n 
,iLe display syntax, the arguments are explicitly introduced 
by abbreviated lowercase role markers. 
3.2. Sortal Quantification 
Quantificational expressi..s in NFLT differ from those 
in predicate calculus by alway~ rontaining a restrictor-clause 
consisting of a sortal predication, in addition to the u, sual 
scope-clause, as in the following example: 
(2a) English: 
Ron ate a cookie in the Oval Office. 
(2b) NFLT Display Syntax: 
{ SOME XS 
(COOKIE inst: XS) 
(EAT agt:RON ptnt:X5 
Io¢: OVAL-OFFICE) } 
Note that we always quantify over instances of a sort, i.e. 
the quantified variable fills the instance role in the restrictor- 
clause. 
This style of quantifier is superior in several ways to 
that of the predicate calcuhls for the purposes of represent- 
ing commonsense knowledge. It is intuitively more natu- 
ral, since it follows the quantificational pattern of English. 
More importantly, it is more general, being sufficient to 
handle a number of natural language determiners such as 
many, most, few, etc., that cannot be represented using only 
the unrestricted quantification of standard predicate calcu- 
lus (see \[Wallace 1965\], {Barwise & Cooper 1981\]). Finally, 
information carried by the sortal predicates in quantifiers 
(namely, criteria of identity for things of the various sorts 
in question) provides a sound semantic basis for counting 
the members of extensions of such predicates (see section 
2, assumption c above). 
Any internal structure which a variable may have is 
irrelevant to its function as a uniquely identifiable place- 
holder in a formula, in particular, a quantified formula can 
itself serve as its own ~bound variable". This is how quanti- 
tiers are actually implemented in the HPSG system; in the 
internal (i.e. implementation) syntax for quantified NFLT- 
formulas, bound variables of the usual sort are dispensed 
with in favor of pointers to the relevant quantified formu- 
las. Thus, of the three occurrences of X5 in the display- 
formula (2b), the first has no counterpart in the internal 
syntax, while the last two correspond internally to LISP 
pointers back to the data structure that implements (2b). 
This method of implementing quantification has some im- 
portant advantages. First, it eliminates the technical prob- 
lems of variable clash that arise in conventional treatments. 
There are no ~alphabetic variants", just structurally equiv- 
alent concept tokens. Secondly, each occurrence of a quanti- 
fied ~bound variable" provides direct computational access 
to the determiner, restrictor-clause, and scope-clause with 
which it is associated. 
A special class of quantificational expressions, called 
quantifier expressions, have no scope-clause. An example 
is: 
(3) NFLT Display Syntax: 
(SOME gl (COOKIE inst: xl) ) 
Such expressions translate quantified noun phrases in En- 
glish, e.g. a cookie. 
3.3. Causal Relations and 
Non-Extensionality 
According to the standard semantics for the predicate 
calculus, predicate symbols denote the extensions of rela- 
tions (i.e. sets of ordered n-tuples) and sentential formu- 
las denote truth values. By contrast, we propose a non- 
eztensional semantics for NFLT: we take predicate symbols 
to denote relations themselves (rather than their exten- 
sions), and sentential formulas to denote situations or situ- 
ation types (rather than the corresponding truth values). 3 
The motivation for this is to provide for the expression of 
propositions involving causal relations among situations, as 
in the following example: 
a The distinction between situations and situation types 
corresponds roughly to the fnite/infinitive distinction in 
natural language. For discussion of this within the frame- 
work of situation semantics, see \[Cooper 1984\]. 
174 
(4a) English: 
John has brown eyes because he is of genotype 
XYZW. 
(4b) NFLT Display Syntax: 
( C~USE 
conditn: (GENOTYPE-XYZW inst:JOHN) 
result: (BROWN-EYED bearer:JOHN} ) 
Now, the predicate calculus is an extensional language 
in the sense that the replacement of categorical subparts 
within an expression by new subparts having the same 
extension must preserve the extension of the original ex- 
pression. Such replacements within a sentential expression 
must preserve the truth-value of the expression, since the 
extension of a sentence is a truth-value. NFLT is not ex- 
tensional in this sense. \[n particular, some of its predicate- 
symbols may denote causal relations among situations, and 
extension-preserving substitutions within causal contexts 
do not generally preserve the causal relations. Suppose, 
for example, that the formula (4b) is true. While the ex- 
tension of the NFLT-predicate 'GENOTYPE-XYZW' is the 
set of animals of genotype XYZW, its denotation is not this 
set, but rather what Putnam I1969\] would call a "physical 
property", the property of having the genotype XYZW. As 
noted above (section 2, assumption d) a property is to be 
distinguished both from the set of objects of which it holds 
and from any concept of it. Now even if this property were 
to happen by coincidence to have the same extension as 
the property of being a citizen of Polo Alto born precisely 
at noon on I April \].956, the substitution of a predicate- 
symbol denoting this latter property for 'GENOTYPE-XYZW' 
in the formula (4b) would produce a falsehood. 
However, NFLT's lack of extensionality does not involve 
any departure from compositional semantics. The deno- 
tation of an NFLT-predicate-symbol is a property; thus, 
although the substitution discussed earlier preserves the 
extension of 'GENOTYPE-XYZW', it does not preserve the 
denotation of that predicate-symbol. Similarly, the deno- 
tation of an NFLT-sentence is a situation or ~ttuation-type, 
as distinguished both from a mere truth-val,e and from a 
propositionJ Then, although NFLT is not at~ extensional 
language in the standard sense, a Fregean a.alogue of the 
principle of extensionality does hold for it: The replace- 
ment of subparts within an expression by new subparts 
having the same denotation must preserve the denotation 
of the original expression (see \[Frege 18921). Moreover, such 
replacements within an NFLT-sentence must preserve tile 
truth-value of that sentence, since the truth-value is deter- 
mined by the denotation. 
3.4. Intentionality and 
Conceptual Raising 
The NFLT notation for representing information about 
propositional attitudes is an improved version of the neo- 
Fregean scheme described in \[Creary 1979 I, section 2, which 
is itself an extension and improvement of that found in 
\[McCarthy 1979\]. The basic idea underlying this scheme 
is that propositional attitudes are relations between peo- 
ple (or other intelligent organisms) and propositions; both 
ternm of such relations are taken as members of the do- 
main of discourse. Objective propositions and their com- 
ponent objective concepts are regarded a.s abstract enti- 
ties, roughly on a par with numbers, sets, etc. They are 
person-independent components of situations involving be- 
lief, knowledge, desire, and the like. More specifically, ob- 
jective concepts are abstract types which may have as to- 
ken~ the subjective concepts of individual organisms, which 
in turn are configurations of information and associated 
procedures in various individual memories (cf. section 2, 
assurnption d above). 
Unlike Montague semantics \[Montague 19731, the se- 
mantic theory underlying NFLT does not imply that an 
organism necessarily believes all the logical equivalents of 
a proposition it believes. This is because distinct propo- 
sitions have as tokens distinct subjective concepts, even if 
they necessarily have the same truth-value. 
Here is an example of the use of NFLT to represent 
information concerning propositional attitudes: 
(5a) English: 
Nancy wants to tickle Ron. 
(5b) NFLT Display Syntax: 
(WANT appr: NANCY 
prop: t(TICKLE agt:I ptnt:RON)) 
\[n a Fregean spirit, we assign to each categorematic 
expression of NFLT both a sense and a denotation. For ex- 
ample, the denotation of the predicate-constant 'COOKIE' 
is the property COOKIE, while the sense of that constant is 
a certain objective concept - the ~standard public" concept 
of a cookie. We say that ~COOKIE' expresses its sense and 
denotes its denotation. The result of appending the "con- 
ceptual raising" symbol ' l" to the constant "COOKIE' is 
a new constant, ' TCOOKIE', that denotes the concept that 
'COOKTE' expresses (i.e. ' 1"' applies to a constant and forms 
a standard name of the sense of that constant). By ap- 
pending multiple occurrences of ' T' to constants, we obtain 
new constants that denote concepts of concepts, concepts 
of concepts of concepts, etc. 5 
\[n expression (5b), ' 1" is not explicitly appended to 
a constant, but instead is prefxed to a compound expres- 
sion. When used in this way, " 1" functions as a syncat- 
egorematic operator that "conceptually raises" each cate- 
gorematic constant within its scope and forms a term incor- 
porating the raised constants and denoting a proposition. 
4 Thus, something similar to what Barwise and Perry call 
"situation semantics" 119831 is to be provided for NFLT- 
expressions, insofar as those expressions involve no ascrip- 
tion of propositional attitudes (the Barwise-Perry semantics 
for ascriptions of propositional attitudes takes a quite dif- 
ferent approach from that to be described for NFLT in the 
next section): 
s For further details concerning this Fregean conceptual 
hierarchy, see \[Creary 1979 I, sections 2.2 and 2.3.1. Cap- 
italization, '$'-postfixing, and braces are used there to do 
the work done here by the symbol ' t'. 
175 
Thus, the subformula ' T (TICKLE aqt:I ptnt:RON) ' is 
the name of a proposition whose component concepts are 
the relation-concept TTICKLE and the individual concepts 
TI and I'RON. This proposition is the sense of the unraised 
subformula ' (TICKLE agt: I pint: RON) '. 
The individual concept TI, the minimal concept of self, 
is an especially interesting objective concept. We assume 
that for each sufficiently self-conscious and active organism 
X, X's minimal internal representation of itself is g token of 
TI. This concept is the sense of the indexical pronoun I, and 
is itself indexical in the sense that what it is a concept of is 
determined not by its content (which is the same for each 
token), but rather by the context of its use. The content 
of this concept is partly descriptive but mostly procedural, 
consisting mainly of the unique and important role that it 
plays in the information-processing of the organisms that 
have it. 
4. Lexicon 
HPSG's head grammar takes as its point of departure 
Saussure's \[1916 t notion of a sign. A sign is a conceptual ob- 
ject, shared by a group of organisms, which consist,~ of two 
associated concepts that we call (by a conventional abuse of 
language) a phonolooical representation and a semantic rep- 
resentation. For example, members of the English-speaking 
community share a sign which consists of an internal rep- 
resentation of the utterance-type /kUki/ together with an 
internal representation of the property of being a cookie. 
In a computer implementation, we model such a concep- 
tual object with a data object of this form: 
(6) (cookie ;COOKIE} 
Here the symbol 'cookie' is a surrogate for a phonological 
representation (in fact we ignore phonology altogether and 
deal only with typewritten English input). The symbol 
'COOKIE' (a basic constant of NFLT denoting the prop- 
erty COOKIE) models the corresponding semantic represen- 
tation. We call a data object such as (6) a lezical entry. 
Of course there must be more to a language than simple 
signs like (6). Words and phrases of certain kinds can char- 
acteristically combine with certain other kinds of phrases to 
form longer expressions that can convey :,nformation about 
the world. Correspondingly, we assume that a grammar 
contains in addition to a lexicon a set of grammatical rules 
(see next section) for combining simple signs to produce 
new signs which pair longer English expressions with more 
complex NFLT translations. For rules to work, each sign 
must contain information about how it figures in the rules. 
We call this information the (syntactic) category of the 
sign. Following established practice, we encode categories 
as specifications of values for a finite set of features. Aug- 
mented with such information, lexical signs assume forms 
such as these: 
(7a) {cookie ; COOKIE; \[MAJOR: N; AGR: 3RDSGI} 
(7b) (kisses ; KISS; \[MAJOR: V; VFORM: FINI} 
Such features as MAJOR (major category), AGR (agree- 
ment), and VFORM (verb form) encode inherent syntactic 
properties of signs. 
Still more information is required, however. Certain 
expressions (heads) characteristically combine with other 
expressions of specified categories (complements) to form 
larger expressions. (For the time being we ignore optional 
elements, called adjuncts.) This is the linguistic notion of 
subcategoeization. For example, the English verb touches 
subcategorizes for two NP's, of which one must be third- 
person-singular. We encode subcategorization information 
as the value of a feature called SUBCAT. Thus the value 
of the SUBCAT feature is a sequence of categories. (Such 
features, called stack-valued features, play a central role 
in the HG account of binding. See \[Pollard forthcomingi. ) 
Augmented with its SUBCAT feature, the \[exical sign (2b) 
takes the form: 
(8) {kisses ; KZflS; \[MAJOR: V; VFORM: FIN 1 
SUBCAT: NP, NP-3RDSG} 
(Symbols like 'NP' and 'NP-3RDSG' are shorthand for cer- 
tain sets of feature specifications). For ease of reference, 
we use traditional grammatical relation names for comple- 
ments. Modifying the usage of Dowry \[1982\], we designate 
them (in reverse of the order that they appear in SUBCAT) 
as subject, direct object, indirect object, and oblique objects. 
(Under this definition, determiners count as subjects of the 
nouns they combine with.) Complements that themselves 
subcategorize for a complement fall outside this hierarchy 
and are called controlled complements. The complement 
next in sequence after a controlled complement is called its 
controller. 
For the sign (8) to play a communicative role, one ad- 
ditional kind of information is needed. Typically, heads 
give information about relation.~, while complements give 
information about the roles that individuals play in those 
relations. Thus lexical signs must assign roles to their com- 
plements. Augmented with role-assignment information, 
the lexical sign (8) takes the form: 
(9) (kisses ; KISS; IMAJOR: V: VFORM: FIN i 
SUBCAT: ~NP, patient), 
(NP-3RDSG, agent? } 
Thu~ (9) assign,, the roles AGENT and PATIENT to the sub- 
ject and direct object respectively. (Note: we assume that 
nouns subcategorize for a determiner complement and as- 
sign it the instance role. See section 6 below.) 
5. Grammatical Rules 
\[n addition to the lexicon, the grammar must contain 
mechanisms for constructing more complex signs that me- 
diate between longer English expressions and more complex 
NFLT translations. Such mechanisms are called grammat- 
ical rules. From a purely syntactic point of view, rules can 
be regarded as ordering principles. For example, English 
grammar has a rule something like this: 
(lO) If X is a sign whose SUBCAT value contains just 
one category Y, and Z is a sign whose category is 
consistent with Y, then X and Z can be combined 
to form a new sign W whose expression is got by 
178 
concatenating the expressions of X and Z. 
That is, put the final complement (subject} to the left of 
the head. We write this rule in the abbreviated form: 
(11) -> C H \[Condition: length of SUBCAT of H = 11 
The form of (11) is analogous to conventional phrase struc- 
ture rules such as NP - > DET N or S - > NP VP; 
in fact (11) subsumes both of these. However, (11) has 
no left-hand side. This is because the category of the 
constructed sign (mother) can be computed from the con- 
stituent signs (daughters) by general principles, as we shall 
presently show. 
Two more rules of English are: 
(12) -> H C \[Condition: length of SUBCAT of H = 2 I 
(13) -> I-I C2 C1 
\[Condition: length of SUBCAT of H = 31 
(12) says: put a direct object or subject-controlled comple- 
ment after the head. And (13) says: put an indirect object 
or object-controlled complement after the direct object. As 
in (11), the complement signs have to be consistent with 
the subcategorization specifications on the head. In (13), 
the indices on the complement symbols correspond to the 
order of the complement categories in the SUBCAT of the 
head. 
The category and translation of a mother need not be 
specified by the rule used to construct it. Instead, they are 
computed from information on the daughters by universal 
principles that govern rule application. Two such princi- 
ples are the Head Feature Principle (HFP) (14) and the 
Subcategorization Principle (15): 
(14) Head Feature Principle: 
Unless otherwise specified, the head features on a 
mother coincide with the head features on the head 
daughter. 
(For present purposes, assume the head features are all fea- 
tures except SUBCAT.) 
(15) Subcategorization Principle: 
The SUBCAT value on the mother is got by deleting 
from the SUBCAT value on the head daughter those 
categories corresponding to complement daughters. 
(Additional principles not discussed here govern control and 
binding.} The basic idea is that we start with the head 
daughter and then process the complement daughters in the 
order given by the indices on the complement symbols in the 
rule. So far, we have said nothing about the determination 
of the mother's translation. We turn to this question in the 
next section. 
6. The Semantic Interpretation Principle 
Now we can explain how the NFLT-translation of a 
phrase is computed from the translations of its constituents. 
The basic idea is that every time we apply a grammar rule, 
we process the head first and then the complements in 
the order indicated by the rule (see \[Proudian & Pollard 
1985i). As each complement is processed, the correspond- 
ing category-role pair is popped off the SUBCAT stack of 
the head; the category information is merged (unified) with 
the category of the complement, and the role information is 
used to combine the complement translation with the head 
translation. We state this formally as: 
(16) Semantic Interpretation Principle (SIP): 
The translation of the mother is computed by the 
following program: 
a. Initialize the mother's translation to be the 
head daughter's translation. 
b. Cycle through the complement daughters, set- 
ting the mother's translation to the result of 
combining the complement's translation with 
the mother's translation. 
c. Return the mother's translation. 
The program given in (16) calls a function whose ar- 
guments are a sign (the complement), a rolemark (gotten 
from the top of the bead's SUBCAT stack), and an NFLT 
expression (the value of the mother translation computed 
thus far). This function is given in (17). There are two 
cases to consider, according as the translation of the com- 
plement is a determiner or not. 
(17) Function for Combining Complements: 
a. If the MAJOR feature value of the comple- 
ment is DET, form the quantifier-expression 
whose determiner is the complement transla- 
tion and whose restriction is the mother trans- 
lation. Then add to the restriction a role link 
with the indicated rolemark (viz. instance} 
whose argument is a pointer back to that quan- 
tifier-expression, and return the resulting quan- 
tifier-expression. 
b. Otherwise, add to the mother translation a role 
link with the indicated rolemark whose argu- 
ment is a pointer to the complement transla- 
tion (a quantifier-expression or individual con- 
stant). \[f the complement translation is a quan- 
tifier-expression, return the quantificational ex- 
pression formed from that quantifier-expression 
by letting its scope-clause be the mother trans- 
lation; if not, return the mother translation. 
The first case arises when the head daughter is a noun 
and the complement is a determiner. Then (17) simply re- 
turns a complement like (3). In the second case, there are 
two subcases according as the complement transiation is 
a quantifier-expression or something else (individual con- 
stant, sentential expression, propositional term, etc.) For 
example, suppose the head is this: 
(18) {jogs ; JOG; \[MAJOR: V; VFORM: FIN I 
SUBCAT: <NP-3RDSG, agent) } 
If the (subject) complement translation is 'RON' (not a quan- 
tifier-expression), the mother translation is just: 
(19) {JOG aqt:RON); 
but if the complement translation is 
'{I~LL P3 (PERSON inst:P3)}' 
(a quantifier-expresslon), the mother translation is: 
177 
concatenating the expressions of X and Z. 
That is, put the final complement (subject) to the left of 
the head. We write this rule in the abbreviated form: 
(11) -> C H \[Condition: length of SUBCAT of H = 11 
The form of (11) is analogous to conventional phrase struc- 
ture rules such as NP - > DET N or S - > NP VP; 
in fact (U) subsumes both of these. However, (11) has 
no left-hand side. This is because the category of the 
constructed sign (mother) can be computed from the con- 
stituent signs (daughter8) by general principles, as we shall 
presently show. 
Two more rules of English are: 
(12) -> H C \[Condition: length of SUBCAT of H = 2\[ 
(13) ->HC2C1 
\[Condition: length of SUBCAT of H = 3\] 
(12) says: put a direct object or subject-controlled comple- 
ment after the head. And (13) says: put an indirect object 
or object-controlled complement after the direct object. As 
in (11), the complement signs have to be consistent with 
the subcategorization specifications on the head. In (13), 
the indices on the complement symbols correspond so the 
order of the complement categories in the SUBCAT of the 
head. 
The category and translation of a mother need not be 
specified by the rule used to construct it. instead, they are 
computed from information on the daughters by universal 
principles that govern rule application. Two such princi- 
ples are the Head Feature Principle (HFP) (14) and the 
Subcategorization Principle (15): 
(14) Head Feature Principle: 
Unless otherwise specified, the head features on a 
mother coincide with the head features on the head 
daughter. 
(For present purposes, assume the head features are all fea- 
tures except SUBCAT.) 
(15) Subcategorization Principle: 
The SUBCAT value on the mother is got by deleting 
from the SUBCAT value on the head daughter those 
categories corresponding to complement daughters. 
(Additional principles not discussed here govern control and 
binding.) The basic idea is that we start with the head 
daughter and then process the complement daughters in the 
order given by the indices on the complement symbols in the 
rule. So far, we have said nothing about the determination 
of the mother's translation. We turn to this question in the 
next section. 
6. The Semantic Interpretation Principle 
Now we can explain how the NFLT-translation of a 
phrase is computed from the translations of its constituents. 
The basic idea is that every time we apply a grammar rule, 
we process the head first and then the complements in 
the order indicated by the rule (see !Proudiaa & Pollard 
19851). As each complement is processed, the correspond- 
ing category-role pair is popped off the SUBCAT stack of 
the head; the category information is merged (unified) with 
the category of the complement, and the role information is 
used to combine the complement translation with the head 
translation. We state this formally as: 
(16) Semantic Interpretation Principle (SIP): 
The translation of the mother is computed by the 
following program: 
a. Initialize the mother's translation to be the 
head daughter's translation. 
b. Cycle through the complement daughters, set- 
ting the mother's translation to the result of 
combining the complement's translation with 
the mother's translation. 
c. Return the mother's translation. 
The program given in (16) calls a function whose ar- 
guments are a sign (the complement), a rolemark (gotten 
from the top of the head's SUBCAT stack), and an NFLT 
expression (the value of the mother translation computed 
thus far). This function is given in (17). There are two 
cases to consider, according as the translation of the com- 
plement is a determiner or not. 
(17) Function for Combining Complements: 
a. If the MAJOR feature value of the comple- 
ment is DET, form the quantifier-expression 
whose determiner is the complement transla- 
tion and whose restriction is the mother trans- 
lation. Then add to the restriction a role link 
with the indicated rolemark (viz. instance) 
whose argument is a pointer back to that quan- 
tifier-expression, and return the resulting quan- 
tifier-expression. 
b. Otherwise, add to the mother translation a role 
link with the indicated rolemark whose argu- 
ment is a pointer to the complement transla- 
tion (a quantifier-expression or individual con- 
stant). If the complement translation is a quan- 
tifier-expression, return tile quantificational ex- 
pression formed from that quantifier-expression 
by letting its scope-clause be the mother trans- 
latio,; if not, return the mother translation. 
The first case arises when the head daughter is a noun 
and the complement is a determiner. Then (17) simply re- 
turns a complement like (3). In the second c,~e. there are 
two subcases according as the complement translation is 
a quantifier-expression or something else (individual con- 
stant, sentential expression, propositional term, etc.) For 
example, suppose the head is this: 
(18) {jogs ; JOG; \[MAJOR: V; VFORM: FIN I 
SUBCAT: <NP-3RDSG, agent.>} 
If the (subject) complement translation is 'RON' (not a quan- 
tifier-expression), the mother translation is just: 
(19) {JOG agt:RON); 
but if the complement translation is 
'{ALL P3 (PERSON inst:P3))' 
(a quantifier-expression), the mother translation is: 
177 
son, Yale University Press, New Haven and London, 
1974. 
Pollard, Carl \[19841 . Generalized Phrase Structure Gram- 
mars, Head Grammars, and Natural Language. Doc-, 
torsi dissertation, Stanford University. 
Pollard, Carl \[forthcomingl. ~A Semantic Approach to 
Binding in a Monostratal Theory." To appear in 
Linguistics and Philosophy. 
Proudian, Derek, and Carl Pollard \[1985\]. ~Parsing Head- 
driven Phrase Structure Grammar." Proceedings 
of the ~Srd Annual Meeting of the Association for 
Computational Linouistics. 
Putnam, Hilary \[1969 I. "On Properties." In Essays in 
Honor o/Carl G. Hempel, N. Rescher, ed., D. Rei- 
del, Dordrecht. Reprinted in Mind, Language, and 
Reality: Philosophical Papers (Vol. I, Ch. 19), Cam- 
bridge University Press, Cambridge, 1975. 
Saussure, Ferdinand de \[1916\]. Gouts de Linguistiquc Gen- 
erale. Paris: Payot. Translated into English by 
Wade Baskin as Course in General Linguistics, The 
Philosophical Library, New York, 1959 (paperback 
edition, McGraw-Hill, New York, 1966). 
Wallace, John \[1965 I. "Sortal Predicates and Quantifica- 
tion." The Journal o\[ Philosophy 62, 8-13. 
179 
