A COMPOSITIONAL SEMANTICS OF TEMPORAL EXPRESSIONS IN 
ENGLISH 
Erhard W. Hinrichs 
BBN Laboratories Inc. 
10 Moulton St. 
Cambridge, MA 02238 
Abstract 
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 sys- 
tem under joint development by BBN Laboratoires 
and the Information Sciences Institute. 1 The analysis 
is based on a higher order intansional logic described 
in detail in Hinrichs, Ayuso and Scha (1987). Tem- 
poral expressions of English are translated into this 
language as quantifiers over times which bind tem- 
poral indices on predicates. The semantic evaluation 
of time-dependent predicates is defined relative to a 
set of discourse contexts, which, following Reichen- 
bach (1947), include the parameters of speech time 
and reference time. The resulting context-dependent 
and multi-indexed interpretation of temporal expres- 
sions 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 interpretation component of JANUS. 
1 Introduction 
JANUS is a natural language understanding and 
generation system which allows the user to interface 
with several knowledge bases maintained by the US 
NAVY. The knowledge bases contain, among other 
things, information about the deployment schedules, 
locations and readiness conditions of the ships in the 
Pacific Reet. 
(1) a. Did the admiral deploy the ship? 
b. Which C3 ships are now C4? 
c. When will Vincent arrive in Hawaii? 
d. Who was Frederick's previous 
commander? 
As the sample queries in (1) demonstrate, much of 
IThe work presented here was supported under DARPA contract 
#N00014-85-C-0016. The views and conclusions contained in this 
document are those of the authors and should not be interpreted as 
necessarily representing the official policies, either expressed or 
implied, of the Defense Advanced Research Projects Agency or of 
the United States Government. 
this information is highly time-dependant: Ships 
change locations in accordance with their deployment 
schedules, incur equipment failures or undergo per- 
sonnel changes which can lead to changes in the 
ship's readiness rating. 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 infor- 
mation, for example, tenses, temporal adverbials and 
temporal adjectives. 
2 Applying Classical Tense Logic To Natural Language Semantics 
My own treatment of temporal expressions 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 
orginate in the work of the logician Arthur Prior (Prior 
1967) and that have been applied by Montague 
(Montague 1973) and others to natural language 
semantics. 
In classical tense logic time-dependency of infor- 
mation enters into the definition of the notion of a 
proposition. Propositions are defined as functions 
from a set of times TI to the set of truth values true 
and false. Declarative sentences of natural language 
are taken to express propositions. The sentence It is 
raining can be taken to be that proposition which 
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 (2) and (3). (2) defines a past operator capital P 
which, applied to a proposition p, yields the value true 
for some time t if the proposition p is true at some 
time t' prior to t. Likewise, (3) defines a Y operator, 
where Y is mnemonic for yesterday, with the expected 
truth conditions: Yp is true at t if p is true at some time 
t' that falls within the prior to the day in which t falls. 
(2) \[P P\]t =' T iff \[P\]r = T for some time t' < t. 
(3) \[Y Pit = Tiff \[P\]r = T for some time 
t' ¢ \[DAY(t) - 1\]. 
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 arise. 2 
3 Inadequacies Of Classical Tense Logic 
3.1 Interaction of Tense and Time Adverbials 
The first such problem, which I pointed out in Hin- 
richs (1981) and which has been independently noted 
by Dowty (1982), concerns the interaction between 
tense and time adverbials. If for sentence (4), one 
interprets the past tense in (4) by the P operator and 
the adverbial yesterday by the Y operator, then one of 
the two operators has to have scope over the other. 
(4) Vincent left yesterday. 
(5) P \[ Y \[leave' (Vincent') \] \] 
(6) Y \[ P \[leave' (Vincent') \] \] 
However, neither the formula in (5), nor the one in (6) 
gives adequate truth conditions for (4). In (5) the P 
operator shifts the temporal evaluation of the proposi- 
tion Y\[leave'(Vincent')\] from the speech time to some 
past time t' and then the Y operator shifts evaluation 
to some time t" within the day prior to t', instead of the 
day prior to the speech time. (6) assigns wrong truth 
conditions as well. Here the Y operator shifts evalua- 
tion to some time within the day prior to the speech 
time. But then the P operator in turn shift evaluation 
to some time prior to that, but necessarily within the 
same day. 
3.2 Interaction of Tense and Negation 
Similar problems arise when one uses standard 
tense logic for sentences in which tense interacts with 
sentence negation as in (7). As was first pointed out 
by Partee (1973), one can assign the past tense 
operator P either narrow scope with respect to nega- 
tion as in (8) or wide scope as in (9). 
(7) Vincent did not leave. 
(8) ~ \[ P \[leave' (Vincent') \]\] 
(9) P \[-~ \[ leave'(Vincent') \]\] 
However, neither the formula in (8), nor the one in (9) 
assigns adequate truth conditions to (7). Formula (8) 
says that there exists no time in the past at which the 
proposition is true, clearly not capturing the meaning 
of (7). (9) makes (7) true if at any time in the past 
=In fairness to Prior, it has to be pointed out that he designed his 
temporal mo0al logics as purely formal systems anti did not design 
them w~ 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 3.1 - 3.4 
Vincent did not leave. Given that ships participate in 
events other than arrivals at some point during their 
existence, (9) will be trivially satified, but does not 
capture adequately the truth conditions of (7). 
3.3 Tense and Quantified NP 
The third type of inadequacy of standard tense 
logic has to do with the interaction of tense and quan- 
tified NP's and was first pointed out by Enc (1981). 
Enc points out that Priorean tense operators fail to 
capture certain readings of sentences such as (10). 
(10) Every admiral was (once) a cadet. 
(1 1) V x \[ admiral'(x) --, P \[ cadet'(x) \]\] 
(12) P \[ ~" x \[ admiral'(x) --~ cadet'(x) \]\] 
Since the past tense operator P is a propositional 
operator, it can take scope over the consequent of the 
material implication in (11). (11) represents the read- 
ing that everyone who is an admiral now was a cadet 
at some time in the past. The second reading in (12), 
where P has scope over the entire formula assigns 
the somewhat absurd truth conditions that at some 
time in the past every admiral as simultaneously a 
cadet. However, as Enc observes correctly, with 
propositional tense operators one cannot obtain the 
perfectly natural reading that everyone who is an ad- 
miral now or who was an admiral at some time in the 
past was a cadet at some time prior to being an ad- 
miral. 
3.4 Temporal Anaphora 
There is fourth problem that arises when one uses 
tense operators of standard tense logic for the seman- 
tic interpretation of single sentences or pieces of dis- 
course that describe multiple events. 
(13) Vincent was I~it by a harpoon, was aban- 
doned by its crew, and sank. 
The most natural interpretation of (13) 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 (13), one arrives at an interpretation, which 
incorrectly allows for any temporal ordering. 
4 A Tense Logic with Multiple Indices 
It turns out that most of the problems that I 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 
9 
developed by Prior, one standardly evaluates proposi- 
tions with respect to a single time which one 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 has been given by 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 time, that requires explanation. 
Reichenbach conceives of reference time as the tem- 
poral perspective from which an event is viewed, as 
opposed to event time as 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 betwen the simple past and the present 
perfect in English. In both cases event time preceeds 
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. 
Given the distinction between reference time and 
event time, one can then formalize Reichenbach's 
analysis of the past tense as in (14). The operator P 
shifts evaluation of the event time t to some time t' in 
the past such that t' falls within some reference time r. 
(14) \[P P\]r,t = Tiff \[P\]r,r for some time t' such that 
t' < t and t' ~; r. 
The Y operator on the other hand, does not shift the 
event time t, rather it operates on the reference time r 
in the obvious way. 3 
(15) ~/P\]r,t == Tiff \[P\]\[DAY(t=)-I\],t = T. 
With the redefined operators P and Y, one can now 
give adequate truth conditions for sentences involving 
tense and time adverbials. In the formula in (16) Y 
specifies the reference time r to be the day prior to the 
speech time, and then the P operator locates the 
event time as being within that reference time. 
(16) \[Y \[ P \[ leave' (Vincent') \] \]r,t = T 
iff \[ P \[leave' (Vincent') \]\]\[DAY(t=)-I\].t == T 
iff \[ leave' (Vincent') \]\]\[OAY(t ).l\],t' == T for 
some t'< t and t'~; \[DAY(ts)-I \]. 
Likewise for tense and negation, the past operator 
locates the event time t prior to speech time and 
within some reference time r which in the case of (17) 
has to be taken to be contextually specified. 
"=Operators similar to the redefined P and Y operators have first 
been suggested in the literature by Acquist (1976). 
(17) Vincent did not leave. 
(18) \[7 \[P \[leave'(Vincent')\]\]\]r,t = T 
iff \[ P\[leave'(Vincent')\]\]r, t =, F 
iff \[leave'(Vincent') \]r,r = F for all times t' 
such that t' < t and t' <;; r. 
(17) is true according to (18) if there is no time within 
the reference time r at which the untensed proposition 
/eave'(Vincent') is true. 
It turns out that a multi-indexed tense logic also 
gives an adequate account of tense in discourse. A 
detailed account of this can be found in Hinrichs 
(1981, 1986); here I will only sketch the basic idea: 
By ordering event times with respect to reference 
times, as sketched in (20), and by updating such ref- 
erence times after each event description, one can 
order multiple events as described in (19) in the ap- 
propriate way. The relations < and ~; in (20) are 
meant to stand for temporal precedence and temporal 
inclusion, respectively. 
(19) Vincent \[was hit by a harpoon\]%, \[was aban- 
doned by its crew\]e =, and \[sank\]%. 
(20) r 1 < r 2 < r 3 
ul Ul Ul 
• I • 2 • 3 
Let us consider next two alternative logical 
representations for sentence (21) in such a multi= 
indexed logic. 
(21) Vincent left yesterday. 
(22) \[Y \[ P \[leave' (Vincent') \] \] \]r,t 
(23) 3 t' \[t' < t s & t r - \[DAY(ts) - 1\] & t' ¢ t r 
& leave'(Vincent')(t') \] 
The one in (22) I have already discussed. In (22) past 
tense is translated into a propositional operator whose 
semantics is implicit in the truth conditions imposed 
with respect to the model-theory. In the formula in 
(23) the past tense leads to existerltial quantification 
over times. The existential quantifier binds variables 
which appear as extra argument positions on predi- 
cates. So, ship" which is ordinarily taken to be a 
one-place predicates turns into a two-place predicate 
that takes individuals and times as its arguments. 
The variable t r occurs as a free variable in (23) and 
stands for the Reichenbachean reference time. 
Although the two formulas in (22) and (23) 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 (23) for 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 
10 
representation in (23) over the one in (22) concerns 
the interaction between tenses and quantified NP's. 
Since formulas such as (23) explicitly quantify over 
times, scope relations with respect to quantification 
over individuals become completely transparent. 
5 Tense and Quantified Noun Phrases 
Using the style of representation exemplified by 
formula (23), 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 standard tense logic. 
(24) Every admiral was (once) a cadet. 
(25) V x \[ admirar(x) ---> P \[ cadet'(x) \]\] 
(26) P \[ ~" x \[ admiral'(x) --e cadet'(x) \]\] 
If tense operators like P have scope over proposi- 
tions, P can either scope over an entire formula as in 
(25) or over the consequent of the material implication 
as in (26). Now, as we saw earlier, neither formula 
captures the reading that all present or past admirals 
were cadets prior to their being admirals. 
Enc (1981) provides an interesting solution to the 
problem posed by examples such as (24). Her solu- 
tion 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 indexi- 
cal in the sense their interpretations depend on the 
context of the utterance in the same way that 
demonstrative pronouns such as that and anaphoric 
pronouns such as she and they do. 
As the formula in (27) shows, which represents 
the translation for (24) in my analysis, I adopt Enc's 
first assumption and assign tense scope only over the 
main verb of the sentence. 
(27) V x \[ 3 t \[ admiral'(x)(t) & R (x)(t) \] --~ 
\[ :1 t' \[ t' < t s & t' ~ t r & graduate-from'(West- 
Point')(x)(t') \]\] 
The predicate R in (27), whose role I will comment on 
in more detail shortly, is meant to range over 
properties which are salient in a given context. The 
past tense of sentence (24) contributes the existential 
quantification over times t' that precede the speech 
point t s and are contained in some contextually 
specified reference time t r. Following Enc, tense is 
thus given scope only over the predicate that cor- 
responds to the main verb. However, the formula in 
(27) also shows that I do not follow Enc in her second 
assumption, namely her treatment of nouns as indexi- 
cals. In contrast to true indexicals, whose denotation 
depends solely on the context of utterance, I treat the 
denotation of predicates corresponding to nouns as 
being time-dependent in an absolute sense, since 
predicates such as admira/do carry a time-denoting 
argument position as part of their function-argument 
structure. Without such an argument, it seems impos- 
sible to give a satisfactory account of temporal adjec- 
tives such as former and previous or/ast, whose func- 
tion it is to shift the temporal evaluation of the predi- 
cate that they combine with. However, I do recognize 
an element of context dependency inherent in the in- 
terpretation of noun phrases such as every admiral 
since I interpret such noun phrases with respect to 
some contextually salient property R. This predicate 
makes it possible to account for the well-known 
phenomenon of restricted quantification, namely that 
in sentences such as (28) the interpretation of 
everyone does not involve the set of all students in 
the world, but rather the set of all individuals in a 
given context; for example everyone at a certain 
party. 4 
(28) Everyone is having a good time. 
Temporal evaluation of the verbal predicate is, thus, 
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 
(29) and (30) whose translations require that the 
predicates secretary and fugitive be evaluated relative 
to a time which is distinct from the evaluation time of 
the predicate corresponding to the verb. s 
(2g) Oliver North's secretary testified before the 
committee. 
(30) Every fugitive is now in jail. 
In contrast to an analysis which 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 (31), if 
the tense operator P has scope over the entire for- 
mula as in the translation (32) of (31). 
(31) Every admiral graduated from West Point. 
(32) P \[ 'd x \[admiral'(x) ~ graduate-from'(West- 
Point')(x)\]\] 
The reading in (32) is factually implausible for two 
reasons: 1. It imposes simultaneity as part of the truth 
conditions and requires that all admirals graduated at 
the same time, 2. since the P operator forces tem- 
poral evaluation of all predicates in its scope at the 
same index, in the case of (31) it requires that every 
admiral graduated from West Point 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 (31) in my analysis, avoids both 
problems associated with (32). 
(33) ~' x \[ 3 t \[ admiral'(x)(t) & R (x)(t) \] --~ 
\[ 3 t' \[ t' < t s & t' s t r & graduate-from'(West- 
Point')(x)(t') \]\] 
4The example is due to Stalnaker (1973). 
SRecail 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 
11 
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 (32), also avoids having to assign a simul- 
taneity reading to (31). 
A crucial element of my analysis is the inclusion of 
the predicate R, which is meant to restrict the denota- 
tion of quantified NP's such as every ship by 
properties that are salient in the context of utterance. 
Apart from keeping the temporal evaluation of verbal 
predicates and nominal predicates independent of 
one another, it is this context dependent feature of my 
analysis that makes it more flexible than a wide scope 
analysis of tense. Let me illustrate how the context- 
dependent evaluation of quantified NP's by once 
again focusing on example (34). 
(34) Every admiral graduated from West Point. 
Imagine that (34) is uttered in a context in which all 
current admirals assigned to the Pacific Fleet are un- 
der discussion. In that context, R could be instan- 
tiated as in (35), i.e. as the intension of the set of 
individuals x which are assigned to the Pacific Fleet at 
a time which equals the speech time t s. 
(35) ;Lt ~.y \[assigned-to'(Pac.Fleet')(y)(t) & t = ts\] 
Substituting R by (35) in (36), one then arrives at the 
formula in (37). 
(36) V x \[ :1 t \[ admirar(x)(t) & R(x)(t) \] --+ 
\[ 3 t' \[ t' < t s & t' e t r & graduate-from'(West- 
Point')(x)(t') \]\] 
(37) V x \[ 3 t \[ admiral'(x)(t) & assigned-to'(Pac- 
Fleet')(x)(t) & t = t s \] ~ \[ =1 t' \[ t' < t s & t' ¢ t r & 
graduate-from'(West-Point')(x)(t') \]\] 
In a context in which all present or past admirals in 
the Pacific Fleet are under discussion, a reading 
which, as I pointed out in section 3.3, one cannot 
capture using Priorean tense operators one can cap- 
ture by instantiating R as in (38), where < stands for 
the relation temporally preceding or equaJ to. 
(38) ~.t ~.y \[assigned-to'(Pac-Fleet')(y)(t) & t < ts\] 
The idea behind using the variable R in my analysis 
is, thus, to have it instantiated appropriately by the 
discourse context. 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 mechanisms are 
motivated independently by semantic and pragmatic 
phenomena that go beyond phenomenon of temporal 
interpretation. 
6 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 1978) and of mutual knowledge 
(Clark and Marshall 1981) are certainly cases in point. 
In this section I will concentrate on one such 
mechanism which plays a role in the context- 
dependent interpretation of time dependent predi- 
cates. 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. 
Consider a typical sequence of queries that a user 
may present to JANUS. 
(39) a. Did every admiral deploy a ship 
yesterday? 
b. Which ships will arrive in Hawaii? 
The person asking (39b) is not interested in being 
informed about all ships that at some time in the fu- 
ture will go to Hawaii. Instead, the user is interested 
in a much more restricted set of ships that will go 
there, namely the ones that were deployed by some 
admiral the day before. In order to arrive at such an 
interpretation, the free variable R in the translation 
formula in (40) has to be bound appropriately by the 
context. 
(40) QUERY \[ Z z \[ z ~ POW\[Z y 3 t' \[ ship'(y)(t') 
& R(y)(t')\]\] & =1 t \[ t > t s & t ~ t r 
& go-to'(Hawaii')(z)(t) \]4 \] 
QUERY is a speech act operator which takes the 
propositional content of the question as an argument 
and causes to evaluate it at some temporal index, in 
this case the point of speech t s. In (40) QUERY ap- 
plies to a lambda-abstract over those sets of objects x 
which are the speech time t s in the Indian Ocean and 
whose members y at some time t have the property of 
being a ship and which are in addition distinguished 
by some contextually salient property R. POW stands 
for the power set operation which I use for the inter- 
petation of plural nouns. Now if the reader prefers 
some other approach to the semantics of plurals, say 
the lattice-theoretic approach of link (1983), over the 
approach based on power sets I am not going to ar- 
gue with them. The point that I want to concentrate 
on with respect to the formula in (40) concerns the 
instantiation of the context-dependent predicate 
R. The predicate ship' has to be interpreted relative to 
the discourse context, and the temporal evaluation of 
the predicate is determined with respect to that con- 
text, rather by the tense of the sentence, in this case 
the future. 
It turns out that a detailed proposal for how to 
track objects and their properties does, in fact, already 
exist in the literature. In her work on the interpretation 
12 
of pronouns in discourse, Webber (1978,1983) has 
developed a framework that constructs during the in- 
terpretation of a discourse a context which consists of 
a set of what she calls discourse entities. These dis- 
course 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 (42) in the context of sentence (41). 
(41) Every admiral deployed a ship yesterday. 
(42) They arrived. 
Clearly they refers to the set of ships deployed by 
some admiral. What is interesting, of course, about 
the example is that syntactically there is no plural 
noun phrase in the preceding discourse that could 
serve as the referent for the plural pronoun they. 
In order to derive the appropriate discourse entity 
for the interpretation of they, Webber suggests the 
rule schema as in (43). (43) says that for any formula 
that meets this structural description, a discourse en- 
tity identified by this formula is to be constTucted. 
(43) SD: V Y1"''¥k 3 x \[P --~ Q\] 
ID: k x 3 YI"''Yk \[P & Q\] 
Instantiated for sentence (41) and its translation (44), 
the rule produces the expression in (457. 
(44) V x ":1 y,t,t',t" \[ admirar(x)(t) & Rl(X)(t ) 
ship'(y)(t') & R2(Y)(t' ) & t r = \[DAY(ts)-I \] 
& t" s t r & deploy'(y)(x)(t') \] 
(45) Z y =J x,t,t',t" \[ ship'(y)(t) & R2(Y)(t ) 
& admiral'(x)(t') & Rl(x)(t' ) & t r = \[DAY(ts)-I \] 
& t" ¢ tr & deploy'(y)(x)(t') \]\] 
(45) denotes the set of ships that have been deployed 
by some admiral. This discourse entity with that 
description then becomes available for the interpreta- 
tion of the pronoun they. 
It turns out that the method of constructing dis- 
course entities is not only relevant for the interpreta- 
tion of pronouns, but also for the contextual interpreta- 
tion of nouns and noun phrases that I am concerned 
with here. 
The discourse entity with the description in (45) 
cannot only serve for interpreting pronouns, but also 
for instantiating the contextually specified variable R 
for the interpretation of the noun ship in (46b) in the 
context of (46a). 
(46) a. Did every admiral deploy a ship 
yesterday? 
b. Which ships will arrive in Hawaii? 
Since the discourse entity in (457, 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 the context variable R in the translation 
(47) of (46b) by this contextually salient property, the 
temporal evaluation of the predicate ship' in the result- 
ing formula (48) is no longer governed by the existen- 
tial 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 
the context variable R, the set of ships under con- 
sideration is restricted in the appropriate way. which 
are assumed to be bound by the discourse context. 
(47) QUERY \[ ;L z \[ z ¢ POW\[A y 3 t' \[ ship'(y)(t') 
& R(y)(t')\]\] & 3 t \[t > t s & t ~ t r 
& go-to'(Hawaii')(z)(t) \]4 \] 
(48) QUERY \[ X z \[ z s POW\[X y 3 t' \[ ship'(y)(t') 
& =J x,t',t'" \[ admiral'(x)(t') & Rl(x)(t") & t r = 
\[DAY(ts)-I \] & t"' ¢ t r & deploy'(y)(x)(t"') 1\] 
& =1 t \[ t • t s & t s t' r & go-to'(Hawaii')(z)(t) \]4 \] 
Notice that (48) contains two reference time 
parameters t r and t' r, which are associated with quan- 
tifiers ranging over past and future times, respectively. 
I am assuming here that each tense has associated 
reference time which is updated during discourse 
processing. 6 
The mechanism for deriving contextually salient 
properties which are introduced through the previous 
linguistic discourse may strike the reader as rather 
complicated in detail. However, as I have argued in 
this sec~on, 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. 
7 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 expressions, that concern in particular the 
feature of narrow scope assignment of tense and the 
feature of context-dependent interpretation of quan- 
tified NP's. In this section I will concentrate on mat- 
ters of syntax and will demonstrate how the narrow 
scope analysis of tense makes it possible to construct 
a straightforward compositional syntax and semantics 
of temporal expressions. 
Syntactically tenses in English appear as inflec- 
tional morphemes on verbs. In the notation of 
categorial grammar, I assign a syntactic tree as in 
(50) to sentence (49). The untensed form of the verb 
arr/ve of category IV is combined with the past tense 
morpheme -ed to form a tensed intransitive verb IV*. 
Morpho-syntactically, tenses are therefore items that 
apply to individual words. 
(49) Every ship arrived. 
eSee Hinrichs (1981) for more details on this point 
13 
(50) Zvez'lv =h£p a.c=:i.ved, S 
Zvez.'y shJ.p, 8/ZV* ="'¢~.ved, ZV* 
Zvez'y, S/ZV~/CN =b.i.p, CN =.~=:~.vo, ZV 
Since I assign tense narrow scope in the semantics 
and let temporal quantiflers bind only the temporal 
index associated with the main verb, I arrive at an 
analysis of tense where its syntactic domain coincides 
with its semantic domain. Compared to analyses in 
which tense is assigned wide scope over formulas 
which 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 straightfor- 
ward compositional syntax and semantics of tense. In 
the syntax the tense morpheme turns an untensed 
verb into its tensed counterpart, while in the cor- 
responding translation rule tense has the effect of ex- 
istentially quantifying over the time-index of the predi- 
cate which translates the untensed verb. 
(51) $17. If c¢ s PIVPNP and then Fl1(c¢ ) s PIVPNP 
with F11 - c¢ -ed. 
(52) T17. If o. s PIVrNP and ¢¢ translates into c¢', 
then, then F 11 (c¢) translates into 
~,S 1... Sn~.x\[=\]t'\[t'<ts&t'¢t r& 
o¢'(S 1)...(Sn)(x)(t') \]. 
$17 is a rule schema which ranges over untensed 
intransitive verbs (IV), transitive verbs (IV/NP), ditran- 
sitive verbs (IV/NP/NP), etc. The notation IV/nNP, 
thus, stands for an IV followed by n slashed NP's. 
The corresponding translation schema T17 denotes a 
function from the type of meanings associated with 
object NP's, if any, to functions from individuals to 
truth values. Although these rule schemata are rather 
technical, their meaning should become clearer, when 
one considers a concrete example. Consider once 
again the example (53) whose syntax has been given 
in (50). 
(53) Every ship arrived. 
The translation of the entire sentence can be built up 
in a compositional fashion as in (54), which mirrors 
the syntactic composition of (50). 
(54) arrived translates as: 
K x \[ =1 t' \[ t' < t s & t' ¢ t r & arrive'(x)(t') \]\] 
every translates as: 
KP;kQ V x \[3 t \[ P(x)(t) & R(x)(t) \] --, Q(x)\] 
every ship translates as: 
;LQ V x ~ t \[ship'(x)(t) & R(x)(t) \] ..-, Q(x) \] 
Every ship arrived translates as: 
1. ~.Q V x \[3 t \[ ship'(x)(t) & R(x)(t) \] --~ Q(x)\] 
(K y \[ 3 t' \[ t' < t s & t' s t r & arrive'(y)(t') \]\]) 
2. V x \[3 t \[ ship'(x)(t) & R(x)(t) \] ~ K y \[ =1 t' \[ t' < t s 
& t' s t r & arrive'(y)(t') 1\] (x) \] 
3. V x \[3 t \[ ship'(x)(t) & R(x)(t) \] --~ =1 t' \[ t' < t s 
& t' ¢ t r & arrive'(x)(t') \]\] 
The phrase every ship is formed bY supplying the 
predicate ship' as an argument to the translation of 
every. Notice that the context-variable R is introduced 
by the translation of the quantifier every. The trans- 
lation of the entire sentence is formed by supplying 
the translation of the tensed verb arrived, which is 
produced by the translation T17, to the translation of 
the subject NP. The reduced translation results from 
two steps of lambda-reduction. 
8 Conclusion 
In this paper I have argued that a logical seman- 
tics for temporal expressions can provide adequate 
representations for natural language input to an inter- 
face such as JANUS. The temporal logic is based on 
Reichenbach's models for the semantics of English 
tense and uses multiple indices for semantic inter- 
pretation. 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 evalua- 
tion. 
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 NP's relative to a given discourse con- 
text. I have argued that the context-dependent fea- 
ture 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 have demonstrated how the narrow 
scope of tense results in a fully compositional syntax 
and semantics of tensed sentences in English. 
9 Acknowledgements 
I am grateful to Remko Scha and Barry Schein for 
comments on earlier drafts of this paper. My in- 
debtedness to the work of Hans Reichenbach and 
Murvet Enc on matters of temporal semantics will be 
evident throughout the paper. 
14 
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15 
