TENSE, QUANTIFIERS, AND CONTEXTS 
Erhard W. Hinrichs 
Department of Linguistics 
University of Illinois 
Urbana, IL 61801 
This paper describes a compositional semantics for temporal expressions as part of the meaning 
representation language (MRL) of the JANUS system, a natural language understanding and generation 
system under joint development by BBN Labs and ISI. The analysis is based on a higher-order 
intensional logic described in detail in Hinrichs (1987a). Temporal expressions of English are translated 
into this language as quantifiers over times that bind temporal indices on predicates. The semantic 
evaluation of time-dependent predicates is defined relative to a set of discourse contexts, which, 
following Reichenbach (1947), include the parameters of speech time and reference time. The resulting 
context-dependent and multi-indexed interpretation of temporal expressions solves a set of well-known 
problems that arise when traditional systems of tense logic are applied to natural language semantics. 
Based on the principle of rule-to-rule translation, the compositional nature of the analysis provides a 
straightforward and well-defined interface between the parsing component and the semantic-interpre- 
tation component of JANUS. 
1 INTRODUCTION 
JANUS is a natural language understanding and gener- 
ation system that allows the user to interface with 
several knowledge bases maintained by the U.S. Navy. 
The knowledge bases contain, among other things, 
information about the deployment schedules, locations, 
and readiness conditions of the ships in the Pacific 
Fleet. 
I. a. Did the admiral deploy the ship? 
b. List all ships as of 4-1-86. 
c. Which C3 ships are now C4? 
d. When will Vincent arrive in Hawaii? 
e. Who was Frederick's previous commander? 
f. Every admiral has to deploy a ship today. 
As the sample queries in (1) demonstrate, much of this 
information is highly time-dependent: ships change lo- 
cations in accordance with their deployment schedules. 
They can incur equipment failures or undergo personnel 
changes. Such events, in turn, can affect the ships' 
readiness ratings, which are expressed by codes such as 
C3 or C4. Much of the information that the JANUS user 
is trying to access is time-dependent in that an appro- 
priate answer can be given only if the time of the query 
and/or the time of the events in question are taken into 
account. It is, therefore, imperative that at the level of 
semantic representation of the natural language input an 
adequate analysis can be provided for those linguistic 
expressions that carry time information: for example, 
tenses, temporal adverbials, and temporal adjectives. 
The rest of this paper is organized as follows: In 
Section 2, I will sketch the basic ideas of the framework 
of logical semantics, or more specifically, of Montague 
Grammar, the framework that I will use for my analysis. 
Section 2 also gives a brief overview of the conceptual 
modularity of the JANUS system, which demonstrates 
how Montague Grammar as a linguistic theory can be 
applied in natural-language processing research. In sec- 
tions 3-8, I will address the subject matter of temporal 
semantics itself. My own analysis of temporal semantics 
is very much a response to the kinds of analyses that 
have been provided in classical tense logic. Section 3, 
therefore, provides a brief overview of analyses of the 
latter type. In Section 4, I will review some well-known 
problems that arise when one applies classical tense 
logics to the semantics of natural language. In Section 5, 
I will show how a logic with multiple indices that is 
based on Reichenbach's analysis of English tense can 
overcome most of the problems that standard tense 
logic cannot. While this richer logic will solve most of 
our problems, the issue of tense and noun-phrase (NP) 
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Computational Linguistics, Volume 14, Number 2, June 1988 3 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
quantification does require additional refinements of the 
analysis. Section 6 will show how giving narrow scope 
to tense quantifiers enables us to provide adequate 
scope relations with respect to NP quantifiers. In addi- 
tion, I will show how a contextual analysis of nouns and 
noun phrases lets us account for the kind of temporal 
phenomena that were first discussed in Enc 1981, 1986. 
In Section 7, I argue that the context-dependent feature 
of the analysis does not add extra complexity to my 
treatment of time-dependent expressions, but is needed 
for purposes of discourse understanding in general. 
Finally, I will demonstrate in Section 8 how the narrow 
scope of tense also leads to a compositional syntax and 
semantics of tensed sentences in English. 
2 THE SEMANTIC FRAMEWORK 
The semantic theory that I have adopted in my research 
• is that of truth-conditional semantics. More specifically, 
I have adopted the framework of Montague Grammar, a 
version of truth-conditional semantics that has been 
developed by the logician Richard Montague (cf. Mon- 
tague 1973).1 Montague Grammar shares the fundamen- 
tal assumption of all truth-conditional theories of mean- 
ing, namely that natural language semantics has to 
relate in a systematic fashion linguistic expressions such 
as words, phrases, and sentences to nonlinguistic, real- 
world objects, events, and states of affairs. In particu- 
lar, a semantic theory has to provide a rigorous defini- 
tion of the truth conditions for the sentences of a 
language. The emphasis in Montague Grammar lies on 
the descriptive aspect of language use. Sentences say 
something true or false about the world. For a speaker 
to know the meaning of a sentence amounts to knowing 
what state of affairs has to obtain in the world, in order 
for the sentence to be true. 
In a Montague Grammar the meanings of sentences, 
phrases, and words are interpreted relative to a model 
that assigns meanings of the appropriate type to such 
linguistic entities. In his papers Montague develops 
various instantiations of his theory. The one that is most 
commonly used by linguists is the one that Montague 
(1973) uses in his paper "The Proper Treatment of 
Quantification in Ordinary English" (commonly abbre- 
viated as PTQ). In that paper Montague associates 
meanings with linguistic expressions in an indirect fash- 
ion. As shown in Figure 1, syntactic expressions of 
English are first translated into a language of higher- 
order intensional logic, which in turn is interpreted 
model-theoretically. This indirect method of semantic 
interpretation obeys Frege's Principle of Composition- 
ality, which says that the meaning of a complex phrase 
is a function of two things: (1) the meanings of its 
constituent parts, and (2) the way in which these parts 
are syntactically combined. Formally speaking, the 
meaning of a complex expression is the homomorphic 
image of its syntactic composition. In more practical 
Translation 
.tdgorithm 
Syntactic Expressions of a 
Natural Language 
(e.g., English words, phrases, 
and sentences) 
Syntactic Expressions of a 
Higher-order Intensional Logic 
Model-theoretic 
Interpretation ..................... 
Denotations as set-theoretic 
objects 
Figure 1. Montague Grammar--Syntax and Semantics. 
terms, a translation procedure from English into inten- 
sional logic that is based on Frege's Principle has to 
specify two things: (1) for each lexical item, the proce- 
dure has to specify a translation into the appropriate 
type of the logic, and (2) for each syntactic rule, the 
procedure has to specify how the translations of the 
input constituents combine in the translation for the 
output constituent of the syntactic rule. 
Montague Grammar provides a simple and elegant 
interface between the syntactic and semantic compo- 
nents of a grammar. Since each syntactic operation is 
mirrored by a semantic operation, semantic interpreta- 
tion is in a sense syntax-driven. Moreover, syntactic 
analysis and semantic interpretation can proceed in 
paraHeh while a sentence or phrase is being parsed in 
accordance with the syntactic rules, its logical form can 
be computed by the translation rules. This inherent 
parallelism is one of the features that makes Montague 
Grammar an attractive theory for natural language 
processing. Everything else being equal, a system in 
which syntax and semantics can operate in parallel is 
computationally more efficient than one in which they 
have to operate sequentially. 
Another attractive feature is the strict modularity 
between syntax and semantics. Modularity is not only 
good practice in software engineering, it is particularly 
important in building natural language interfaces. If one 
wants to extend the coverage of the grammar of a given 
system, one wants to do so in an incremental fashion 
and without having to modify the control structure 
between major components. Montague Grammar allows 
one to upscale a system in this way: in order to extend 
the coverage of the grammar, one simply writes addi- 
tional syntactic rules and translation rules that cover the 
new data. 
Apart from these methodological considerations, it 
turns out that the same three components (syntax, 
translation, and model-theoretic interpretation) that are 
of importance in Montague's theory form an integral 
part in the functional components of natural language 
interface systems such as JANUS. z Figure 2 shows that 
4 Computational Linguistics, Volume 14, Number 2, June 1988 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
Syntactic Tree 
Ambiguous Semantic Expression (EFL) 
Unambiguous Semantic 
Expression (WML) 
Database Language Expression 
English Input 
Parser I 
............. -~ ~ 
............. . 
I EFL-to-WML 
Translation 
I WML-Io-DBL I Translation 
\[ Code Generation I 
I I '°° I I I 
Figure 2. Components of JANUS. 
the English input is fed into the syntactic parser of 
JANUS, which yields as output a parse tree, which in 
turn forms the input to the translation component. The 
translation component generates some logical expres- 
sion that represents the meaning of the English input. 
This logical expression is then evaluated with respect to 
the database, which one can take to be a proxy for a 
partial model of the real world, in the case of JANUS a 
model of the objects and states of affairs pertaining to 
the Pacific Fleet. 
The translation component of JANUS is somewhat 
more elaborate than the one Montague 1973 formulates. 
At the first level of translation, every lexical item of 
English is translated into some logical expression of an 
English-oriented formal language called EFL. At the 
EFL level, no attention is given to the context that may 
contribute to the interpretation of the English input. 
Neither is any attempt made at the EFL level to 
disambiguate lexical meanings. Lexical disambiguation 
is provided by a domain model, which, among other 
things, captures all the information about lexical mean- 
ings known to the system) 
Apart from domain knowledge, the system keeps 
track of those aspects of a user's question-answer 
session that are relevant for determining the reference 
of context-dependent queries such as (2). 
2. a. Question: Where were the carriers yesterday? 
b. Answer: In the Indian Ocean. 
c. Question: How long have they been there? 
The discourse model contains parameters such as the 
time at which the question-answer session is taking 
place. This parameter is necessary to calculate the 
referent of deictic time adverbials such as yesterday in 
(2a). In addition, the discourse model keeps track of 
locations such as the Indian Ocean and referents of 
noun phrases such as the carriers in order to interpret 
locational adverbs such as there and anaphoric pro- 
nouns such as they in (2c). 
Input from the domain model and the discourse 
model leads to translation to a world-model language 
(WML), which in turn is translated into expressions of 
the query language of the appropriate knowledge base: 
a database IDB, an expert system FRESH, or a display 
knowledge base OSGP. In this paper I will for the most 
part concentrate on the level of syntax to EFL transla- 
tion, although the context-dependent aspects of my 
treatment of temporal semantics will lead to some 
discussion of the discourse model of JANUS in sections 
6 and 7 below. 
3 APPLYING CLASSICAL TENSE LOGIC TO NATURAL 
LANGUAGE SEMANTICS 
With this much of an introduction, let me now turn to 
the topic of temporal semantics itself. My own analysis 
is very much a response to the kinds of analyses that 
have been provided in classical tense logic. When I refer 
to classical tense logic, I mean the kinds of logics that 
originate in the work of the logician Arthur Prior (cf. 
Prior 1967) and that have subsequently been applied to 
natural language semantics (cf. Montague 1973 and 
Mort 1973). 
In classical tense logic time-dependency of informa- 
tion enters into the definition of the notion of a propo- 
sition. Propositions are defined as functions from a set 
of times (TI) to the set of truth values (T--"true") and 
(F---"false"). Declarative sentences of natural language 
are taken to express propositions. The sentence It is 
raining can be taken to be that proposition that yields 
the value true for those times at which it is raining, and 
false for those at which it is not. 
Tense operators can be defined in such a logic as in 
(3) and (4). Formula 3 defines a past operator P, which, 
applied to a proposition p, yields the value true for some 
time t ifp is true at some time t' prior to t. Likewise, (4) 
defines a Y operator, where Y is mnemonic for yester- 
day, with the expected truth conditions: Yp is true at t 
if p is true at some time t' that falls within the day prior 
to the day in which t falls. 
3. \[P P\]t = Tiff \[P\]t'- T for some time t' < t. 
4. \[Y Pit = Tiff \[P\]t' ---- T for some time 
t' C_ \[DAY (t) - 1\]. 
All of this sounds rather plausible. However, it turns 
out that if one tries to apply tense operators such as P 
and Y in natural-language semantics, a set of well- 
known problems arises. 4 
Computational Linguistics, Volume 14, Number 2, June 1988 5 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
4. INADEQUACIES OF CLASSICAL TENSE LOGIC 
4.1 INTERACTION OF TENSE AND TIME ADVERBIALS 
The first such problem, which I pointed out in Hinrichs 
1981 and which was independently noted in Dowty 
1982, concerns the interaction between tense and time 
adverbials. If for Sentence 5, one interprets the past 
tense in (5) by the P operator and the adverbial yester- 
day by the Y operator, then one of the two operators 
has to have scope over the other. 
5. Vincent left yesterday. 
6. P \[ Y \[ leave' (Vincent') \] \] 
7. Y \[ P \[ leave' (Vincent') \] \] 
However, neither the formula in (6), nor the one in (7) 
gives adequate truth conditions for (5). The truth con- 
ditions imposed by (6) are inadequate, since the sen- 
tence in (5) would, for example, count as true when 
uttered on January 15, 1988, if the ship Vincent left not 
on January 14, 1988, but instead on May 23, 1986. This 
is because the P operator can shift the temporal evalu- 
ation of the proposition Y \[leave' (Vincent')\] from the 
speech time to any past time (t"), for example to some 
time (t") on May 24, 1986. In this case the Y operator 
will, in turn, shift evaluation to t' within the day prior to 
t", i.e., to some time on May 23, 1986. Hence the 
proposition leave' (Vincent') will be evaluated with 
respect to that day, instead of the day prior to the 
speech time. 
Formula 7 can assign wrong truth conditions as well. 
Here the Y operator shifts evaluation to some time 
within the day prior to the speech time. But the P 
operator, in turn, shifts evaluation to some time prior to 
that, but necessarily not within the same day. 
4.2 INTERACTION OF TENSE AND NEGATION 
Similar problems arise when one uses standard tense 
logic for sentences in which tense interacts with sen- 
tence negation as in (8). As was first pointed out in 
Partee 1973, one can assign the past-tense operator (P) 
either narrow scope with respect to negation as in (9), or 
wide scope as in (10). 
8. Vincent did not leave. 
9. --1 \[ P \[ leave' (Vincent') \]\] 
10. P \[ --1 \[ leave' (Vincent') \]\] 
However, neither the formula in (9), nor the one in (10) 
assigns adequate truth conditions to (8). Formula 9 says 
that there exists no time in the past at which the 
proposition is true, clearly not capturing the meaning of 
(8). Formula 10 makes (8) true if at any time in the past 
Vincent did not leave. Given that ships participate in 
events other than arrivals at some point during their 
existence, (10) will be trivially satisfied, but does not 
capture adequately the truth conditions of (8). 
4.3 TENSE AND QUANTIFIED NOUN PHRASES 
The third type of inadequacy of standard tense logic has 
to do with the interaction of tense and quantified NPs 
and was first pointed out in Enc 1981, 1986. Enc points 
out that Priorean tense operators fail to capture certain 
readings of sentences such as (11). 
1 I. Every admiral was (once) a cadet. 
12. V x \[ admiral' (x) --> P \[ cadet' (x) \]\] 
13. P \[ V x \[ admiral' (x) --> cadet' (x) \]\] 
Since P is a propositional operator, it can take scope 
over the consequent of the material implication in (12). 
Formula 12 represents the reading that everyone who is 
an admiral now was a cadet at some time in the past. 
The second reading in (13), where P has scope over the 
entire formula, assigns the somewhat absurd truth con- 
ditions that at some time in the past every admiral was 
simultaneously a cadet. However, as Enc observes 
correctly, with propositional tense operators we cannot 
obtain the perfectly natural reading that everyone who 
is an admiral now or who was an admiral at some time 
in the past was a cadet at some time prior to being an 
admiral. 
4.4 TEMPORAL ANAPHORA 
There is a fourth problem that arises when one uses 
tense operators of standard tense logic for the semantic 
interpretation of pieces of discourse or of single sen- 
tences that describe multiple events. 
14. Vincent was hit by a harpoon, was abandoned by 
its crew, and sank. 
The most natural interpretation of (14) is one in which 
the events are understood to have happened in the same 
temporal order as they are sequenced in the sentence. 
However, if one uses a Priorean P operator to interpret 
each occurrence of the past tense in (14), one arrives at 
an interpretation, which incorrectly allows for any 
temporal ordering. 
5 A TENSE LOGIC WITH MULTIPLE INDICES 
It turns out that most of the problems that we have just 
discussed can be solved if one recognizes more than one 
parameter of temporal evaluation. In the models given 
to tense logics such as the ones first developed by Prior, 
one standardly evaluates propositions with respect to a 
single time that we may call the event time, the time at 
which an event happens or at which a state of affairs 
obtains. The point of speech is taken to be a special case 
of this parameter. 
An alternative to models with only one temporal 
parameter was given in Reichenbach 1947. Reichenbach 
argues for distinguishing between three parameters, 
which he calls speech time, event time, and reference 
time. The meaning of the first two parameters should be 
self-explanatory. It is the third parameter, reference 
6 Computational Linguistics, Volume 14, Number 2, June 1988 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
time, that requires explanation. Reichenbach conceives 
of reference time as the temporal perspective from 
which an event is viewed, as opposed to the event time, 
the time at which the event occurs. Reference time can 
be either implicit in the discourse context or explicitly 
specified by temporal adverbials such as yesterday. For 
each individual tense, reference time is temporally 
ordered with respect to the other two parameters. 
Reference time plays a crucial role in Reichenbach's 
account of the distinction between the simple past and 
the present perfect in English. In both cases event time 
precedes speech time. But while for the simple past, the 
event time is viewed from a perspective in the past, the 
event is viewed from the perspective of the present in 
the case of the present perfect. 
As first shown in Aqvist 1976 and Guenthner 1979, 
Reichenbach's analysis can be formalized in a tense 
logic in which tense operators are evaluated with re- 
spect to multiple indices. For example, a Reichen- 
bachean past operator (P) can be defined as in (15). 
15. \[P P\]ts,tr,te -- T iff \[P\]ts,tr,t' for some time t' such 
that t' < ts and t' C_ tr. 
The parameters of evaluation in (15), ts, tr, and te, stand 
for speech time, reference time, and event time, respec- 
tively. The operator P shifts evaluation of the event time 
te to some time (t') in the past such that t' falls within 
some reference time tr. Note that contrary to Reichen- 
bach's original account of the past tense, the parameters 
of reference time and speech time are not directly 
ordered in (15), but only indirectly by virtue of the 
temporal ordering between event time t' and the speech 
time ts. This weaker ordering between tr and ts is 
motivated by sentences such as (16), in which the 
reference time denoted by the adverbial today contains 
the speech time ts. 
16. Vincent arrived today. 
In the intended models of interpretation for the P 
operator in (15), times are taken to be time intervals. 
Since (15) requires that the event time t' be located prior 
to ts and be contained in tr, (15) imposes as a restriction 
on tr that a subinterval of tr be ordered prior to ts. In 
order for (16) to be true, the subinterval of tr that lies in 
the past has to be a proper subinterval of tr, whereas for 
(17) all of tr has to precede ts. 
17. Vincent left yesterday. 
Given Reichenbach's parameters, the definition of the 
Y operator, given earlier in (5), can be modified as in 
(18). 
18. \[Y P\]ts,tr.te = Tiff \[P\]ts,DAY(ts)-l,te = T. 
Unlike the P operator in (15), Y in (18) does not shift te; 
instead, it Operates on tr and shifts that parameter to 
day prior to ts. 
With the redefined operators P and Y, one can now 
give adequate truth conditions for sentences involving 
tense and time adverbials. The logical form for (17), for 
example, can be evaluated as in (19): Y specifies the 
reference time to be the day prior to the speech time, 
and the P operator, in turn, correctly locates the event 
time as being within that reference time. 
19. \[Y \[ P \[ leave' (Vincent') \] \] \]ts,tr,te = Tiff 
\[ P \[leave' (Vincent') \]ts,\[DAY(ts)-l\],t = Tiff 
\[ leave' (Vincent') \]ts,\[DAY(ts)-l\],t' = T 
for some t' < t and t' C_ \[DAY (ts)-l\]. 
The P and Y operators, defined in (15) and (18) above, 
differ from the operators found in Aqvist, Guenthner, 
and Dowty in that in my analysis all three of Reichen- 
bach's parameters are taken to be separate for purposes 
of evaluation, while Aqvist, Guenthner, and Dowty 
define operators that are evaluated with respect to two 
parameters only. This is because Dowty considers the 
speech time as a special case of the reference time, 
while Aqvist and Guenthner consider speech time to be 
a special case of the event time. 
As I have argued elsewhere (cf. Hinrichs 1981, 1986) 
and as was noted independently in Dowty 1982, the 
need for tense operators with three separate parameters 
arises in the context of sentences such as (20). 
20= Vincent rescued a ship yesterday which is now in 
Hawaii. 
As first noted in Kamp 1971, the interpretation of now 
requires that the speech point of the utterance be 
carried along at every stage of evaluating sentences 
such as (20), whose logical form can be represented as 
in (21). 
21. Y \[P \[::Ix \[ship' (x) & rescue' (Vincent', x) & NOW 
\[be-in' (x,Hawaii')\]\]\]\] 
In the evaluation of (21), the Y operator, as defined in 
(18), fixes the reference time as the day prior to ts, while 
the P operator from (15) shifts the event time to some 
time within that reference time. NOW, the third tempo- 
ral operator in (21), appears in the scope of the Y and 
the P operator. NOW, which can be defined as in (22), 
can be interpreted correctly in the context of (20), only 
if the speech time is kept as a separate index and held 
constant even though reference time and event time 
have been changed by the P and Y operators. 
22. \[NOW P\]ts,tr,te = Tiff \[P\]ts,tr',te = T for ts C_ tr'. 
Using temporal operators with multiple indices of eval- 
uation, one can also account correctly for the interac- 
tion of tenses and negation. In the evaluation of (23) 
shown in (24), the past operator locates the event time 
t' prior to speech time and within some reference time 
tr, which in the case of (23) has to be taken to be 
contextually specified. 
23. Vincent did not leave. 
24. \[ 7 \[ P \[ leave' (Vincent') \]\]\]ts,tr,te = T iff 
\[ P \[ leave' (Vincent') \]\]ts,tr.te = F iff 
Computational Linguistics, Volume 14, Number 2, June 1988 7 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
\[leave' (Vincent') \]ts,tr,t' = F for all times t' 
such that t' < ts and t' _C tr. 
Sentence 23 is true according to Formula 24 if there is 
no time within tr at which the untensed proposition 
leave' (Vincent') is true. 
It turns out that a multi-indexed tense logic provides 
the basis for an adequate account of tense in discourse. 
By associating event times with respect to temporally 
ordered reference times, as sketched in (26), one can 
indirectly induce an ordering among the events them- 
selves. Moreover, by updating such reference times 
after each event description, one can order multiple 
events as described in (25) in the appropriate way. The 
relations < and C_ in (26) are meant to stand for temporal 
precedence and temporal inclusion, respectively. 
25. Vincent \[was hit by a harpoon\]e~, \[was 
abandoned by its crew\]e2, and \[sank\]~3. 
26. trl < tr2 < tr3 
Ul Ul Ul 
tel te2 te3 
In order to induce the correct temporal orderings among 
events and states of affairs in a given discourse, refer- 
ence times have to be updated appropriately during 
discourse processing. Formula 26 shows the simplest 
case of such updating. A new reference time is intro- 
duced after processing each event so that the temporal 
order of the events becomes isomorphic to the order in 
which the events are introduced. However, for more 
complicated pieces of discourse the conditions under 
which new reference times are introduced can be far 
more complex. The aspectual properties of the events in 
question, event-subevent relations, causal connections 
obtaining among events and states of affairs, as well as 
the overall structure of the discourse itself are among 
the conditioning factors. It will not be possible to give a 
detailed account of these issues here; for a more thor- 
ough discussion of how to interpret temporal structures 
in discourse on the basis of a multi-indexed tense logic, 
I refer the reader to Hinrichs 1981, 1986 and Partee 
1984. 
Let us consider next two alternative logical represen- 
tations for Sentence 27 in such a multi-indexed logic. 
27. Vincent left yesterday. 
28. \[Y \[ P \[ leave' (Vincent') \] \] \]ts,tr,te 
29. 3t'\[t' <ts&tr = \[DAY(ts)- 1 \] 
& t' C_ tr & leave' (Vincent') (t') \] 
The formula in (28) we have already discussed. In (28) 
past tense is translated into a propositional operator 
whose semantics is implicit in the truth conditions 
imposed with respect to the model-theory. In (29) the 
past tense leads to existential quantification over times. 
The existential quantifier binds variables which appear 
as extra argument positions on predicates. Thus, leave', 
which is ordinarily a one-place predicate, turns into a 
two-place predicate that takes individuals and times as 
its arguments. The variables ts and tr occur as free 
variables in (29) and, as stated earlier, stand for the 
Reichenbachean speech time and reference time, re- 
spectively. 
Although the two formulas in (28) and (29) are 
logically equivalent in the sense that both are true under 
the same set of models, I will adopt the style of logical 
representation in (29) for the remainder of this paper. 
This is because in the context of the JANUS system it 
is important to explicitly quantify over times, since in 
the database times are explicitly entered as dates, time 
stamps, etc. In order to be able to access them, it is 
important to incorporate time information explicitly at 
the level of logical form. 
A second reason for preferring the style of represen- 
tation in (29) over the one in (28) concerns the interac- 
tion between tenses and quantified NPs. Since formulas 
such as (29) explicitly quantify over times, scope rela- 
tions with respect to quantification over individuals 
become completely transparent. 
6 TENSE AND QUANTIFIED NOUN PHRASES 
Using the style of representation exemplified by for- 
mula (29), let me then return to the issue of tense and 
quantification, which is still unresolved. Consider once 
again the types of examples that, as Enc points out, 
cannot be handled in a tense logic that gives temporal 
operators scope over entire propositions. 
30. Every admiral graduated from Annapolis. 
31. V x \[admiral' (x) --~ P \[graduate-from' 
(x,Annapolis')\]\] 
32. P \[Vx \[admiral' (x) ~ graduate-from' 
(x,Annapolis')\]\] 
If tense operators such as P have propositional scope, P 
can either scope over an entire formula, as in (32), or 
over the consequent of the material implication, as in 
(31). Now, as we saw earlier, neither formula captures 
the reading that all present or past admirals graduated 
from the Naval Academy in Annapolis prior to their 
being admirals. 
Enc 1981 provides an interesting solution to the 
problem posed by examples such as (30). Her solution is 
based on two assumptions: 1. Semantically, tenses 
should have scope only over verb meanings, but not 
over any larger elements in a sentence, and 2. verb 
meanings as well as noun meanings are indexical in the 
sense that their interpretations depend on the context of 
the utterance in the same way that demonstrative pro- 
nouns such as that and anaphoric pronouns such as she 
and they do. 
As shown in Formula 33, which represents the trans- 
lation for (30) in my analysis, I adopt Enc's first 
8 Computational Linguistics, Volume 14, Number 2, June 1988 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
assumption and assign tense scope only over the main 
verb of the sentence. 
33. V x \[3t \[ admiral' (x) (t) & R (x) (t) \] 
3t'\[t'<ts&t'C_tr& 
graduate-from' (Annapolis') (x) (t')\]\] 
In accordance with the Reichenbachean analysis of 
tense outlined in the previous section, the past tense of 
sentence (30) contributes to (33) the existential quanti- 
fication over times t' that precede the speech point ts 
and are contained in some contextually specified refer- 
ence time tr. Following Enc, tense is thus given scope 
only over the predicate that corresponds to the main 
verb. However, I do not follow Enc in her second 
assumption, namely, her treatment of nouns and verbs 
as indexicals. It is characteristic of true indexicals such 
as I, there, or you that their denotation is completely 
determined by a certain aspect of the context of the 
utterance. I refers to the speaker, you to the address- 
ee(s), there to some contextually salient location, etc. In 
contrast to such indexical expressions, the (temporal) 
evaluation of nouns and verbs does not always depend 
on a single contextual parameter. In the case of complex 
nouns such as former admiral, last readiness rating, or 
previous nautical position, temporal evaluation has to 
be shifted twice: first from the speech point to some 
contextually salient reference point and then in turn to 
some second time relative to which the nouns admiral, 
readiness rating, and nautical positions themselves are 
evaluated. In order to accommodate complex temporal 
evaluations of nouns and verbs, their corresponding 
predicates in logical form, such as admiral' and gradu- 
ate-from' in (36), carry a time-denoting argument posi- 
tion as part of their function-argument structure. Since 
the temporal evaluation of such predicates can be 
shifted freely, their interpretation differs crucially from 
that of true indexicals whose interpretation can be 
completely determined with respect to a single contex- 
tual parameter. 
Even though I do not follow Enc in treating nouns 
and verbs as indexical expressions, I do recognize that 
the interpretation of noun phrases such as every admiral 
in (30) is in part dependent on the context in which the 
sentence is used. Speakers asserting (30) are not likely 
to make the claim that every admiral who ever served in 
the navy of any country that has naval forces graduated 
from the Naval Academy in Annapolis. Typically, (30) 
will be used to make a claim about a much restricted set 
of admirals, say all the admirals in the U.S. Navy or all 
admirals in the Pacific Fleet. Exactly which set of 
admirals a speaker focuses on will depend on the 
discourse context in which the sentence is used. This 
phenomenon of restricted quantification of noun 
phrases is certainly not restricted to the interpretation 
of every admiral in (30), but applies to quantified noun 
phrases in general, as Stalnaker (1973), who cites ex- 
amples such as (34), was among the first to point out. 
34. Everyone is having a good time. 
In (34) the interpretation of everyone typically does not 
involve the set of all individuals currently alive, but 
rather the set of all individuals in a given context; for 
example, everyone at a certain party, at a certain 
location, and at a given time. 
In order to accommodate this contextual aspect of 
the interpretation of noun phrases in my analysis, I 
introduce into the translation of quantified NPs a pred- 
icate (R), which is meant to range over properties that 
are salient in a given context and which serve to narrow 
down the reference of the noun phrase in question. Let 
me illustrate the context-dependent evaluation of quan- 
tified NPs by once again focusing on Sentence 30 and its 
translation in (33). 
30. Every admiral graduated from Annapolis. 
33. V x \[3t \[ admiral' (x) (t) & R (x) (t) \] 
3t' \[t' < ts & t' C_tr& 
graduate-from' (Annapolis') (x) (t')\]\] 
Imagine that (30) is uttered in a context in which all 
current admirals in the Pacific Fleet are under discus- 
sion. In that context, R could be instantiated as in (35), 
i.e., as the intension of the set of individuals (x) who are 
in the Pacific Fleet at a time which equals the speech 
time ts. 
35. A t A y \[be-in' (Pac-Fleet') (y) (t) & t = ts\] 
Substituting (35) for R in (33), we arrive at the formula 
in (36). 
36. ~' x \[3t \[admiral' (x) (t) & be-in' (Pac-Fleet') (x) (t) 
&t = ts \] ---~ \[3 t' \[t' < ts&t' C_ tr& 
graduate-from' (Annapolis') (x) (t') \]\] 
In a context in which all present or past admirals in the 
Pacific Fleet are under discussion, a reading that, as we 
pointed out in Section 4.3, one cannot capture using 
Priorean tense operators, we can capture by instantiat- 
ing R as in (37), where -< stands for the relation 
temporally preceding or equal to. 
37. A t A y \[be-in' (Pac-Fleet') (y) (t) & t -< ts \] 
Notice that the contextual variable R serves double 
duty in my analysis. This double role derives from the 
fact that R is a two-place predicate with individuals and 
time intervals as its two arguments. The argument 
ranging over individuals serves to restrict the denota- 
tion of the noun that R is associated with; for example, 
it restricts the denotation of admiral in (33). The argu- 
ment of R that ranges over time intervals, on the other 
hand, serves to restrict the time interval at which the 
associated noun denotation is evaluated; for example, if 
R is instantiated by (35) or (37), temporal evaluation of 
the associated predicate admiral in (33) is restricted to 
the speech point or to time intervals prior to or including 
the speech point. 
Temporal evaluation of the verbal predicates is, thus, 
Computational Linguistics, Volume 14, Number 2, June 1988 9 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
kept separate from the temporal evaluation of predi- 
cates corresponding to other constituents in the sen- 
tence. As first pointed out by Enc, this strategy makes 
it possible to account for sentences such as 1138) and 
(39), whose translations require that the predicates 
secretary and fugitive be evaluated relative to a time 
that is distinct from the evaluation time of the predicate 
corresponding to the verb. s 
38. Oliver North's secretary testified before the com- 
mittee. 
39. Every fugitive is now in jail. 
In contrast to an analysis that interprets the past tense 
in terms of a Priorean P operator, the narrow-scope 
analysis of tense also avoids the dilemma of inducing a 
simultaneity reading for Sentence 30, if P has scope 
over the entire formula, as in the Translation 40 of (30). 
30. Every admiral graduated from Annapolis. 
40. P \[ V x \[ admiral' (x) 
graduate-from' (Annapolis') (x)\]\] 
The reading in (40) is factually implausible for two 
reasons: I. It imposes simultaneity as part of the truth 
conditions and requires that all admirals graduated at 
the same time, and 2. since the P operator forces 
temporal evaluation of all predicates in its scope at the 
same index, in the case of (40) it requires that every 
admiral graduated from Annapolis as an admiral, and 
not, as is actually the case, subsequent to graduation 
from the Naval Academy. 
Notice that the formula in (33), which represents the 
translation of (30) in my analysis, avoids both problems 
associated with (40). 
33. V x \[ 3 t \[ admiral' (x) (t) & R (x) (t) \]--~ 
3t' \[t' < ts & t' C_tr& 
graduate-from' (Annapolis') (x) (t') \]\] 
Since temporal evaluation of the predicates admiral' 
and graduate-from' are kept separate, the first problem 
does not arise. Since the predicates are existentially 
quantified over independently, (33), in contrast to (40), 
also avoids having to assign a simultaneity reading to 
(30). 
As I have outlined in this section, my treatment of 
tense and quantification is based on two basic assump- 
tions: 1. Verbal predicates and nominal predicates both 
have an argument position that ranges over time inter- 
vals; however, evaluations of verbal and nominal pred- 
icates are independent of one another. The evaluation of 
verbal predicates is governed by quantification over 
time intervals that involve Reichenbach's parameters of 
speech time, event time, and reference time. 2. The 
denotation of quantified NPs is restricted by the predi- 
cate R, which ranges over properties that are salient in 
the context of utterance. In conjunction with the nar- 
row-scope analysis of tense, it is this context dependent 
feature of my analysis that makes it more flexible than 
a wide-scope analysis of tense. 
One of the counterarguments that one may raise 
against this context-dependent aspect of my analysis of 
temporal semantics concerns the fact that tracking the 
salience of objects and their properties in natural- 
language discourse is a notoriously difficult problem. 
However, I will argue in the next section that whatever 
mechanisms are needed to track saliency, such mecha- 
nisms are independently motivated by semantic and 
pragmatic phenomena that go beyond the phenomenon 
of temporal interpretation. 
7 EVALUATING TIME-DEPENDENT PREDICATES IN 
CONTEXT 
Objects and certain of their properties can receive or 
maintain salience in a discourse in any number of ways. 
The notions of focus (Sidner 1983), of common ground 
(Stalnaker 1973), and of mutual knowledge (Clark and 
Marshall 1981) are certainly cases in point. In this 
section I will concentrate on two such mechanisms that 
play a role in the context-dependent interpretation of 
time-dependent predicates. In each case I will argue 
that the mechanism is needed for purposes other than 
temporal interpretation and, therefore, does not add 
complexity to my analysis of temporal semantics. 
The first such mechanism concerns the way in which 
objects and their properties can become salient in the 
discourse context by virtue of the goals that the dis- 
course participants are trying to accomplish over the 
course of a given interaction. Consider a user of the 
JANUS system whose goal it is to deploy a set of ships. 
As part of achieving this goal, the user interacts with 
JANUS by asserting (41a) and then by querying (41b), 
whose translation is given by the formula in (42). 
41. a. I need to deploy a ship immediately for a search- 
and-rescue mission. 
b. Which ships are in the Indian Ocean? 
42. QUERY \[ ^Ax \[ x ~ POW \[ A y 3 t' \[ ship' (y) (t') 
&R(y)(t')\]\]&3t\[t = ts&tCtr& 
in' (Indian-Ocean') (x) (t) \]\]\] 
Following Scha 1983, I base the semantics of questions 
on speech-act operators, such as QUERY, which take 
the intensional meaning of the question as an argument. 
The " symbol in (42) stands for the intension operator as 
defined in Montague 1973. POW stands for the power- 
set operation, which I use for the interpretation of plural 
nouns. 6 POW in (42) is used to form the set of those 
objects that at some time t have the property of being a 
ship. 7 For the technical details concerning the seman- 
tics of the QUERY operator I refer the reader to Scha 
1983. For the purposes of this paper, it should suffice 
that QUERY has the effect of consulting the underlying 
knowledge bases of the system as to which members of 
the power set of ships, if any, have the property of being 
in the Indian Ocean at the time of the query. 
10 Computational Linguistics, Volume 14, Number 2, June 1988 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
The point that I want to concentrate on with respect 
to the formula in (42) concerns the instantiation of the 
context-dependent predicate (R) that is associated with 
the translation of the noun phrase which ships. Given 
that the system recognizes the user's goal to be that of 
immediate ship deployment for a search-and-rescue 
mission, ships with a current readiness rating of C3 or 
better are salient in the context, since only such ships 
are deployable. By instantiating R appropriately, the 
formula in (42) turns into (43). 
43. QUERY \[ ^ A x \[x ~ POW \[h y 3 t' \[ ship' (y) (t') 
& readiness-rating' (y) (t') >- C3 & t' = ts\]\] & 
3 t \[t = ts & t C_ tr & in' (Indian-Ocean') (x) (t)\]\]\] 
The instantiation of R in (42) follows from recognizing 
the user's plan as that of immediate ship deployment. 
The importance of plan recognition for designing ques- 
tion-answering systems that generate cooperative re- 
sponses was emphasized in Allen/Perrault 1980, Allen 
1983, and Pollack 1986. In the context of Example 41, if 
it turned out that two ships, Frederick and Vincent, are 
in the Indian Ocean, but both ships are rated C4, then a 
cooperative response would be (44), instead of merely 
listing the ship names. 
41. a. I need to deploy a ship immediately for a search- 
and-rescue mission. 
b. Which ships are in the Indian Ocean? 
44. Frederick and Vincent, but they are rated C4 and 
cannot be deployed. 
Recognizing the user's intention, which in the given 
context leads to the recognition of the current readiness 
rating of ships as a salient property, will make such a 
response possible. It, therefore, turns out that tracking 
properties that are salient in context is needed not only 
for evaluating predicates in the approach to temporal 
semantics that I have developed in this paper, but 
constitutes a task that is independently needed for the 
purposes of generating cooperative responses in ques- 
tion-answering. 
The issue of plan recognition in discourse demon- 
strates that objects and their properties can become 
salient implicitly in discourse, that is, without explicit 
linguistic reference. However, salience of objects and 
properties can, of course, also be achieved at any point 
within a discourse by virtue of the previous linguistic 
context. Consider a sequence of user-system interac- 
tions as in (45). 
45. a. Query: Did every admiral deploy a ship yester- 
day? 
b. Answer: Yes. 
c. Query: Which ships will arrive in Hawaii? 
The person who asks the follow-up query (45c) to the 
system's affirmative answer to the initial query (45a) is 
not interested in being informed about all ships that at 
some time in the future will arrive in Hawaii. Instead, 
the user is interested in a much more restricted set of 
ships that will arrive there, namely, the ones that were 
deployed by some admiral the day before. The noun 
ship in the final query in (45) has to be interpreted 
relative to the discourse context, and the temporal 
evaluation of the predicate is determined with respect to 
that context, rather by the tense of the sentence, in this 
case, the future. It turns out that a detailed proposal for 
how to construct such a mechanism does, in fact, 
already exist in the literature. Webber (1978, 1983) in 
her work on the interpretation of pronouns in discourse, 
has developed a framework that constructs during the 
interpretation of a discourse a context that consists of a 
set of what she calls discourse entities. These discourse 
entities then become available as objects that pronouns 
can refer to. One of the examples that Webber discusses 
is the interpretation of the pronoun they in (47) in the 
context of sentence (46). 
46. Every admiral deployed a ship yesterday. 
47. They arrived. 
Clearly, they refers to the set of ships deployed by some 
admiral} In order to derive the appropriate discourse 
entity for the interpretation of they, Webber suggests 
the rule schema such as (48). Formula 48, which is a 
slightly simplified version of Webber's original rule 
schema, says that for any formula that meets the 
structural description (SD), a discourse entity identified 
by the ID formula is to be constructed. 
48. SD: Vyl. • "Yk3 x\[P--~Q\] 
ID: Ax3 Yl" " 'Yk\[P&Q\] 
Instantiated for Sentence 49 and its translation (50), the 
rule produces the expression in (51). 
49. Every admiral deployed a ship yesterday. 
50. V x 3 y,t,t',t" \[ admiral' (x) (t) & R~ (x) (t) --~ 
ship' (y) (t') & R z (y) (t') & tr = \[DAY(ts) - 1\] 
& t" < ts & t" C_ tr & deploy' (y) (x) (t") \] 
51. A y 3 x,t,t',t" \[ ship' (y) (t) & R 2 (y) (t) 
& admiral' (x) (t') & R 1 (x) (t') & tr = \[DAY(ts) - 1\] 
& t" < ts & t" C tr & deploy' (y) (x) (t") \] 
Formula 50 imposes as truth conditions for (49) that 
each member of a contextually specified set of admirals 
deployed some contextually salient ship at some time t' 
within the day prior to the given speech time ts. 
Contextual salience enters into the translation in (50) 
since the predicates ship' and admiral' are associated 
with distinct occurrences of the contextual variable R. 
Which ships and which admirals are salient will, once 
again, depend on the particular context. In a context in 
which activities within the Pacific Fleet on the day prior 
to the speech time are at issue, R1 and R2 in (50) will be 
instantiated in such a way that the denotations of ship' 
and admiral' are restricted to ships and admirals from 
that particular fleet. Formula 51, the output of Rule 
Computational Linguistics, Volume 14, Number 2, June 1988 11 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
Schema 48 applied to (50), further restricts which ships 
are salient, namely, the set of ships contextually spec- 
ified by R1, which, in addition, were deployed on the 
previous day by one of the admirals in question. The 
discourse entity with the description, in turn, becomes 
available for the interpretation of the pronoun they in a 
follow-up sentence such as (47). 
It turns out that the method of constructing discourse 
entities is not only relevant to the interpretation of 
pronouns, but also to the contextual interpretation of 
nouns and noun phrases that I am concerned with here. 
In particular, the discourse entity with the description in 
(51) can serve not only for interpreting pronouns, but 
also for instantiating R for the interpretation of the noun 
ship in (45c) in the context of (45a). 9 
45. a. Query: Did every admiral deploy a ship yester- 
day? 
b. Answer: Yes. 
c. Query: Which ships will arrive in Hawaii? 
Since the discourse entity in (51), which ranges over a 
set of ships, is described in terms of the property of 
having been deployed by some admiral the day prior to 
the day of the speech point, that property can be taken 
to be salient in the discourse context. If one substitutes 
R in Translation 52 of (45c) by this contextually salient 
property, the temporal evaluation of the predicate ship' 
in resulting Formula 53 is no longer governed by the 
existential quantifier t for the future tense, but rather by 
the quantifier t' introduced by the contextually salient 
property. As a consequence of this instantiation of R, 
the set of ships under consideration is restricted in the 
appropriate way. 
52. QUERY \[ ^h z \[ z E POW \[h y 3 t' \[ ship' (y) (t') 
& R(y) (t')\]\] & 3 t \[ t > ts & t C_ tr 
& arrive' (Hawaii') (z) (t) \]\]\] 
53. QUERY \[ ^h z \[ z @ POW\[A y 3 t' \[ship' (y) (t') 
& 3 x, t", t" \[admiral' (x) (t") & R 1 (x) (t") 
& tr = \[DAY(ts) - 1\] & t'" _C tr 
& deploy' (y) (x) (t'") \]\]\] & 3 t \[ t > ts 
& t _C tr' & arrive' (Hawaii') (z) (t) \]\]\] 
The mechanism for deriving contextually salient prop- 
erties that are introduced through the previous linguistic 
discourse may strike the reader as rather complicated in 
detail. However, the point that I made earlier in this 
section with respect to tracking saliency as a side effect 
of plan recognition applies to the tracking of properties 
introduced by the linguistic context as well: tracking 
such properties is important not only for temporal 
evaluation, but is independently motivated by other 
discourse phenomena such as anaphoric reference, as 
Webber (1978, 1983) has convincingly shown. 
8 A COMPOSITIONAL SYNTAX AND SEMANTICS OF 
TENSE 
In the previous sections I have focused on the semantic 
and pragmatic aspects of my analysis of temporal ex- 
pressions, which concern in particular the features of 
narrow-scope assignment and of context-dependent in- 
terpretation of quantified NPs. In this section I will 
concentrate on matters of syntax and will demonstrate 
how the narrow-scope analysis makes it possible to 
construct a straightforward compositional syntax and 
semantics of tense in the framework of Montague 
Grammar, the linguistic theory on which my analysis is 
based. 
Syntactically, tenses in English appear as inflectional 
morphemes on verbs. In the notation of categorial 
grammar, we may assign a syntactic tree as in (55) to 
Sentence 54. The infinitival form of the verb arrive of 
Category IV is combined with the past-tense morpheme 
-ed to form a tensed intrasensitive verb IV*. Morpho- 
syntactically, tenses are therefore items that apply to 
individual words. 
54. Every ship arrived. 
55. Every ship arrived, S 
Every ship, S/IV* arrived, IV* 
Every, S/IV*/CN ship, CN arrive, IV 
Since I assign tense narrow scope in the semantics and 
let temporal quantifiers bind only the temporal index 
associated with the main verb, I arrive at an analysis of 
tense whose syntactic domain coincides with its seman- 
tic domain. Compared to analyses in which tense is 
assigned wide scope over formulas that correspond to 
entire sentences (Montague 1973) or over entire verb 
phrases (Bach 1980), the narrow-scope analysis, which 
I have developed in this paper, has the advantage of 
leading to a straightforward compositional syntax and 
semantics of tense. In the syntax the tense morpheme 
turns an untensed verb into its tensed counterpart, 
while the corresponding translation rule existentially 
quantifies over the time index of the predicate that 
translated the untensed verb. 
56. 
57. 
If a E pIV/"NP and then F~ (a) E pIV*/"NP, where 
F~ = a-ed. 
If a E pIV/"NP and a translates into a', then F~ (a) 
translates intoAS~. • .S, Ax\[3t'\[t'<ts 
& t' C_ tr & a' (SO • • (Sn) (X) (t') \]\]. 
12 Computational Linguistics, Volume 14, Number 2, June 1988 
Erhard W. Hinrichs Tense, Quantifiers, and Contexts 
Rule Schema 56 ranges over untensed intrasensitive 
verbs (IV), transitive verbs (IV/NP), ditransitive verbs 
(IV/NP/NP), etc. The notation IV/nNp thus stands for 
an IV followed by n slashed NPs. The corresponding 
translation schema in (57) denotes a function from the 
type of meanings associated with object NPs, if any, to 
functions from individuals to truth values. Although 
these rule schemata are rather technical, their meaning 
should become clear when one considers a concrete 
example. Consider once again Example 54, whose syn- 
tax has been given in (53). 
54. Every ship arrived. 
• The translation of the entire sentence can be built up in 
a compositional fashion as in (57), which mirrors the 
syntactic composition of (53). 
58. arrived translates as: 
Ax\[3t'\[t'<ts&t'C_tr&arrive'(x)(t')\]\] 
every translates as: 
A P A Q V x \[3 t \[ P (x) (t) & R (x) (t) \] ~ Q (x) \] 
every ship translates as: 
h Q V x \[3 t \[ ship' (x) (t) & R(x) (t) \] ---> Q(x) \] 
Every ship arrived translates as: 
1. h Q V x \[3 t \[ship' (x) (t) & R(x) (t)\] ---> Q (x)\] 
(h y \[3 t' \[t' < ts & t' c_ tr & arrive' (y) (t')\]\]) 
2. v x \[3 t \[ship' (x) (t) & R (x) (t)\] --> 
h y \[ 3 t' \[t' < ts & t' C_ tr & arrive' (y) (t')\]\] (x)\] 
3. V x \[3 t \[ship' (x) (t) & R (x) (t)\] --> 3 t' \[ t' < ts 
& t' C_ tr & arrive' (x) (t') \]\] 
The phrase every ship is formed by supplying the 
predicate ship' as an argument to the translation of 
every. Notice that R is introduced by the translation of 
the quantifier every. The translation of the entire sen- 
tence is formed by supplying the translation of the 
tensed verb arrived, which is produced by the transla- 
tion rule in (57), to the translation of the subject NP. 
The reduced translation results from two steps of 
lambda reduction. 
9 CONCLUSION 
In this paper I have argued that a logical semantics for 
temporal expressions can provide adequate representa- 
tions for natural-language input to an interface such as 
JANUS. The temporal logic is based on Reichenbach's 
models for the semantics of English tense and uses 
multiple indices for semantic interpretation. This multi- 
indexed logic overcomes the kinds of problems that 
arise when systems of tense logics are used that rely on 
just one index of evaluation. 
I have demonstrated how giving narrow scope to 
tense quantifiers enables us to provide adequate scope 
relations with respect to NP quantifiers and to interpret 
such NPs relative to a given discourse context. I have 
argued that the context-dependent feature of the analy- 
sis does not add extra complexity to my treatment of 
time-dependent expressions, but is needed for purposes 
of discourse understanding in general. Finally, I have 
demonstrated how the narrow scope of tense results in 
a fully compositional syntax and semantics of tensed 
sentences in English. 
ACKNOWLEDGMENTS 
The work presented here was supported under DARPA 
contract #N00014-85-C-0016. The views and conclu- 
sions contained in this document are those of the author 
and should not be interpreted as necessarily represent- 
ing official policies, either expressed or implied, of the 
Defense Research Projects Agency or the United States 
Government. An earlier version of the present paper 
was presented at the 1987 meeting of the ACL at 
Stanford University and was published as Hinrichs 
1987b. I am grateful to John Nerbonne, Remko Scha, 
Barry Schein, and Bonnie Webber for comments on 
earlier drafts of this paper. My indebtedness to the work 
of Hans Reichenbach and Murvet Enc on matters of 
temporal semantics will be evident throughout the pa- 
per. 
NOTES 
For a detailed introduction to Montague's theory, see Dowty, 
Wall, and Peters 1981. 
2. The components shown in the diagram are based on the architec- 
ture of the PHLIQUA system described in Scha 1983. 
3. For details on how the domain model functions in the overall 
system see Ayuso, Shaked; and Weischedel 1987. 
4. In fairness to Prior, it has to be pointed out that he designed his 
temporal modal logics as purely formal systems and did not design 
then't with idea of applying them to natural language. However, 
Priorean tense logic has, nonetheless, been applied to natural 
language semantics. It is those studies that are subject to the 
criticisms presented in sections 4.1-4.4. 
5. Recall that Fawn Hall, North's secretary, testified before the 
committee when she was no longer North's secretary. The 
example is due to an editorial in the Boston Globe. 
6. The reader may prefer some other approach to the semantics of 
plurals or questions, say the lattice-theoretic approach to plurality 
developed in Link 1983 or the analysis of questions found in 
Groenendijk/Stokhof 1982 over the approach based on power sets 
and the QUERY operator, respectively. These approaches are 
also consistent with the point that I want to concentrate on with 
respect to the formula in (42)---that is, the instantiation of the 
context-dependent predicate (R). 
7. Note that it follows from the narrow-scope analysis of tense 
developed in Section 4 that the time at which the set of objects x 
are ships need not be the same as the time at which that set of 
objects is in the Indian Ocean. This aspect of (42) may strike the 
reader as counterintuitive. Notice, however, that (42) represents 
the first level of translation (the EFL level of Figure 2 with no 
input from the domain model). It will be part of the domain 
knowledge, however, that there are two kinds of properties: a. 
properties such as being an admiral, which can hold of an 
individual for certain subperiods; and b. properties such as being 
a ship, which hold of an entity throughout its existence. It is on 
the basis of such domain knowledge that at lower levels of 
translation the two evaluation times at issue in (42) can, in fact, be 
equated. 
8. What is interesting about the example in its own right is that 
syntactically there is no plural noun phrase in the preceding 
discourse that could serve as the referent for the plural pronoun 
they. 
9. I am indebted to Bonnie Webber for pointing out to me that the 
discourse entity evoked by (45a) can be used to restrict the 
interpretation of the noun phrase which ships in (45c), only if the 
answer to (45a) is affirmative. Thus, whether a discourse entity 
can serve as a restrictor for the interpretation of subsequent NP's 
is in part a function of the type of sentence that evokes the 
discourse entity. If the expression that evokes a discourse entity 
occurs in a declarative sentence, the discourse entity will auto- 
matically be available as a potential restrictor for the interpreta- 
tion of subsequent NPs. However, if the discourse entity is 
evoked within an interrogative sentence and the existence of the 
enZity is not already presupposed by the question, the discourse 
entity is licensed as a potential restrictor, only if the question has 
an affirmative answer. 

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