Picking Reference Events from Tense 
A Formal, Implement able Theory of 
English Tense-Aspect Semantics 
Trees: 
Lenhart K. Schubert and Chung Hee Hwang 
Department of Computer Science, University of Rochester 
Rochester, New York 14627, U. S. A., and 
Department of Computing Science, University of Alberta 
Edmonton, Alberta, Canada T6G 2H1 
Abstract. Despite numerous investigations into English 
tense-aspect semantics, the problem of formally inter- 
preting tense and aspect remains in large part unsolved. 
A formal solution requires (a) a well-defined mapping 
from a subset of English covering the most common 
tense-aspect constructions (including embedded tensed 
clauses) to a formal meaning representation, and (b) 
a well-defined denotational semantics for the meaning 
representation, which accords with speakers' intuitions 
about the original text. We propose a simple structure 
called a tense tree (or a set of connected tense trees) 
as a basis for interpreting tense-aspect constructions 
and some time adverbials in a context-dependent way. 
The de-indexicalization process simultaneously trans- 
forms tense trees and logical forms, the former in accord 
with simple recursion equations and the latter in accord 
with formal equivalences between context-indexed and 
context-independent logical forms. The rules have been 
implemented, and yield meaning representations in a for- 
mal episodic logic for narrative understanding. 
I. Introduction 
Narratives describe and relate episodes (events, situa- 
tions, eventualities). The episodes successively intro- 
duced appear to "line up" in systematic ways as a func- 
tion of the text structure, with tense and aspect playing 
a crucial role. (1-2) illustrate this familiar phenomenon: 
(1) John grinned at Mary. She frowned. 
(2) John knocked, but soon realized Mary had left. 
Each of the verbs in (1) appears to introduce an episode; 
the past inflection places them before the utterance event 
(or speech time), and the surface ordering suggests tem- 
poral sequencing, and probably a causal connection. In 
(2) we appear to have at least three episodes, a "knock- 
ing," a "realizing" and a "leaving." The past perfect aux- 
iliary relates the "leaving" to a past episode serving as 
reference point. (This reference point seems closely cor- 
related with the "realizing" episode, but on our theory is 
not identical with it.) As well, the adverb soon implic- 
itly references and relates the "knocking" and "realizing" 
episodes. 
The problem of automatically extracting these rela- 
tionships is complicated by a number of subtle issues: 
• How many episodes (events, situations, etc.) does 
a sentence implicitly introduce? We remarked that 
the introduction of episodes appears correlated with 
verbs; but in 
(3) John did not elude the tackle and score a 
touchdown, disappointing the fans. 
the causally relevant episode is characterized by the 
non-occurrence of successive "eluding" and "scor- 
ing" events; and in 
(4) When each guest congratulated Mary and 
gave her a present, she felt quite overwhelmed. 
the focus is on a "quantified" event consisting of any 
number of "congratulating" and "giving" events. 
What are the relative (semantic) scopes of tense and 
aspect, relative to NPs, VPs, adverbials, negation, 
etc.? Syntax suggests that tense scope is confined 
to the tensed verb or VP, yet in a sentence like 
(5) For a whole week this summer, no rain fell. 
this simple view is troublesome: if the past tense is 
confined to the VP (so that fell means "falls-before- 
now"), then the sentence is true if we can find a 
week any time this summer in which there are no 
past rainfalls- a property that holds of all remaining 
(i.e., future) weeks of the summer! 
Do simple past or present-tense sentences make def- 
inite or indefinite reference to episodes (or times)? 
Davidson\[3\], Harman\[5\], Reichenbach\[13\] and a ma- 
jority of writers after them took event reference in 
simple past and present to be indefinite (existen- 
tial), and this seems in accord with intuition in such 
sentences as 
(6) John got married last year. 
where there is no definite commitment as to the time 
of the event (apart from its being confined to last 
year). On the other hand, Partee\[12\] pointed out 
the seemingly anaphoric character of tense reference 
in sentences like 
(7) I left the stove on. 
Also, Leech\[8\], McCawley\[9\], Webber\[19\] and many 
others have noted that the simple past normally in- 
volves a "point of orientation" such as an immedi- 
34 
ately preceding event, and that Reichenbach's "ref- 
erence time" appears to be definite at least in the 
case of perfect. 
Our goal is a comprehensive account of how episodes 
and their relationships are determined by syntax, seman- 
tics, and pragmatics. The account is to be an intrinsic 
part of a general theory of the understanding process, 
and is to be formulated in a mathematically precise and 
computationally implementable way. At the most gen- 
eral level, the task can be viewed in terms of the following 
sort of schema: 
English (~) \[ (~) 
--t- ' \[ MR ........ WORLD 
Context 
Suitable for 
inference 
I.e., English in conjunction with suitable context struc- 
tures needs to be mapped to a formal meaning repre- 
sentation (O), and this MR needs to be formally inter- 
pretable (Q), with truth conditions that are in intuitive 
accord with intuitions about the original English text. 
Thus we will have some assurance that inferences based 
on the MR will be those intuitively warranted. 
With respect to this schema, most previous studies of 
tense and aspect have been more formally explicit about 
(~) than about (~). The MR is often some dialect of first- 
order logic, or a modal or intensional logic, with formal 
semantics in the traditional vein (e.g., possible-worlds 
models with multiple time indices). 
The description of (~), however, is often very infor- 
mal or limited to a very restricted set of constructions. 
Furthermore, the formalized accounts (e.g., \[4\], \[6\], \[14\]) 
tend to take context for granted - the focus is on truth 
conditions, and so the model is simply assumed to sup- 
ply the needed reference times. AI-motivated work on 
tense and aspect has emphasized their pragmatic signif- 
icance, e.g., for discourse segment structure (see \[1\], cA. 
13 & 14), and their role in the practical extraction of 
temporal relationships from discourse in applied NL sys- 
tems (e.g., see several of the articles in Computational 
Linguistics 11(2), 1988). Much of this work has treated 
(~) heuristically, restricting attention to simple types of 
sentences and viewing tense and aspect as phenomena 
to be handled by a separate module, rather than as an 
integral part of a compositional mapping from text to 
meaning representations. 
Non-compositional approaches based on simple sen- 
tence types run the risk of being ungeneralizable. For 
instance, they may tie event introduction to verb phrases 
in a way that doesn't generalize to logical compounds (as 
in sentences (3) and (4)). Also, they may get the seman- 
tics of embedded sentences wrong. For instance, simple 
sentence types suggest that past tense places an event 
before the speech time. But in 
(8) Mary will realize a year from now that her wed- 
ding to John, which takes place tomorrow, was a 
big mistake. 
the past tense is used for a future event. Thus we 
need to characterize the semantics of particular syntactic 
constructs - including tense-aspect constructs - in a way 
that holds for all syntactic environments in which the 
constructs may occur. 
On the issue of compositionality, we should also re- 
mark that we find much of the work on tense and aspect 
"unduly Reichenbachian". Though the importance of 
Reichenbach's seminal work in this area is undisputed, 
it is based on the dubious view that tensed perfects are 
complex variants of "simple" past, present and future 
tense. Since these "complex" tenses appear to involve 
a reference time (besides the event and speech times), 
Reichenbach attributed such a reference time to "sim- 
ple" tenses as well. But from a compositional perspec- 
tive, it is much more natural to view tense (past and 
present) and perfect as making separate contributions to 
the VP or sentence meaning. After all, each can occur in 
a VP without the other ("John probably forgot", "John 
is likely to have forgotten"). Thus semantic dependence 
on Reichenbach's reference time may well be particular 
to the perfect -just as dependence on speech time (or a 
more general sentence reference time) seems particular 
to tense. 
In the remaining sections of the paper we report our 
progress so far on the tense-aspect problem within the 
above schema. Section 2 briefly elaborates our concep- 
tion of the understanding process. Section 3 explains 
the intuitive idea behind our method of transforming 
indexical logical forms (LFs) to nonindexical LFs in 
a principled way, using context structures called tense 
trees. These provide the "points of orientation" (ref- 
erence episodes) needed to interpret tense and aspect, 
and are transformed in the course of "de-indexicalizing" 
LFs in a way that can be concisely stated by recursion 
equations. Section 4 provides a formal statement with 
examples of the basic de-indexicalization rules for tense 
and aspect. Section 5 summarizes our progress and work 
left to be done. 
In the course of the paper, we make commitments 
about key aspects of the issues enumerated above. 
Briefly, our view is that at the level of LF, tensed En- 
glish sentences contain separate past, pres, perf and futr 
operators; (will and would have separate tense and futr 
components); that not only past, pres, perf, and futr in- 
troduce episodes, but that various logical operators do 
so as well, including negation, conjunction, and quan- 
tification; that past and pres are sentence-level operators 
generally taking wide scope (despite syntactic appear- 
ances); and that the episodes introduced by past and 
pres, and indeed by any operators, are indefinite (ex- 
istentially quantified). This last claim applies even to 
the past in the past perfect, consistently with our com- 
positional view of tense and aspect. The way the past 
perfect auxiliary connects up with a pre-existing "point 
of orientation" is not by direct anaphoric reference, but 
by a mechanism that applies to all statives. 
35 
II. A Formal View of the Understanding 
Process 
The following illustrates our current view of the stages of 
the understanding process, at a theoretical level. (At the 
procedural level these stages are interleaved.) This view 
incorporates ideas from GPSG, HPSG, DRT and situa- 
tion semantics, and evolved in the course of our own re- 
search on mapping English into logic \[17\], \[18\] and story 
understanding \[15\], \[16\]. 
0. Assume that an episode e0 has just been described. 
e0: After their doubles victory, Mary and Sue were 
surrounded by their fans. 
New sentence: A man kissed Mary 
1. GPSG parser: 
\[s \[NP \[Det a\] \[N man\]\] \[vP Iv kissed\] \[NP Mary\]\]\] 
2. Rule-by-rule LF computation: 
\[<3 man> <past kiss> Mary\] 
3. Scoping: (past (3:e: \[z man\]\[x kiss Mary\])) 
4. De-indexicalization (using context structure C): 
(3e:\[\[e before Now3\] A \[e0 orients e\]\] 
\[(3x:\[z man\]\[x kiss Mary\]) ** e\]) 
5. Pragmatic inference: 
(3e:\[\[e before Now3\] A \[e right-after e0\]\] 
\[(3:e:\[x man\]Ix kiss Mary\]) ** el) 
6. Inference based on MPs & world knowledge: 
The man liked Mary a lot; 
he was happy about her victory; etc. 
A preliminary unscoped, indexical LF is derived via 
semantic rules paired with phrase structure rules. Pred- 
icate infixing (with the predicate following its "subject" 
argument and followed by additional arguments, if any) 
is used for readability. Angle brackets indicate unscoped 
operators that are to be "raised" to some sentence-level 
position. Scoping quantifiers involves variable introduc- 
tion and conversion of the restriction predicate to a re- 
striction formula. Note that after the third stage the 3- 
quantifier and past operator are scoped in the example; 
in general we take tense to have a strong, though not ab- 
solute, wide-scoping tendency (but like quantifiers, it is 
"trapped" by scope islands, such as embedded clauses). 
The fourth stage is our main focus in this paper. 
In this stage the scoped, but still indexical, LF is de- 
indexicalized. In particular, explicit episodic variables 
are introduced, and tense and aspect operators are re- 
placed by relationships among episodes. This process 
makes use of tense trees as part of a context s~ructure, 
modifying these trees by adding branches and episode to- 
kens as a "side effect". In general we envisage this stage 
as also performing other kinds of de-indexicMization, 
most importantly the explicit augmentation of anaphoric 
expressions (such as (The x: Ix man\] ...)) by Context- 
derived predications (such as (The z: \[\[x man\] A \[z has- 
possible-antecedents (tuple ...)\]\] ...)). 
Note the connective "**" in the nonindexical formulas, 
connecting a formula to an episode which it characterizes 
(or completely describes). This is a strengthened version 
of "*", or partially describes, an operator that is essen- 
tially the same ms Reichenbach\[13\]'s "*", and similar to 
Barwise\[2\]'s ~. For semantics see \[16\]. 
Note also the orients relationship in 4th stage (itali- 
cized) sample result. This is intended to echo Leech's 
notion of a "point of orientation" (as cited in \[19\]). 
We refer to this relation, and certain others derived 
from context (including has-possible-antecedents above) 
as context-charged. The idea is that their meaning is 
to be "discharged" using uncertain (probabilistic) infer- 
ence. For instance, the fact that e0 in the example ori- 
ents (serves as point of orientation for) e suggests among 
other possibilities that e immediately follows e0 (in e0's 
"consequent" or "result" phase, in the terminology of 
\[10\] or \[11\]). Given the assumed types of e0 (Mary and 
Sue being surrounded by their fans) and e (a man kiss- 
ing Mary), this is a very plausible inference, but in other 
cases the most plausible conclusion from the orients rela- 
tion may be a subepisode relation ("It was a great party. 
Mary did her Chef impression"), an explanatory relation 
("John went shopping. Mary's birthday was in a week"), 
or any of the discourse relations that have been discussed 
in the literature (e.g., \[7\]). 
The de-indexicalization stage is followed by inference 
stages which discharge context-charged relations and 
more generally do input-driven plausible inference based 
on the text interpreted so far, meaning postulates (MPs) 
and world knowledge. In these stages unique referents 
for referring expressions, predictions, and explanations 
are computed which ultimately give a causally coherent 
elaboration of what has been said. 
We now turn to a detailed account of the de- 
indexicalization stage. For a much more complete de- 
scription of our overall approach to knowledge represen- 
tation, inference and understanding, the reader is re- 
ferred to \[15\] and \[16\]. 
III. De-Indexicalization: Traversing 
Tense Trees 
A formal theory of how indexical formulas are converted 
to nonindexical ones as a function of context requires an 
explicit specification of the type of context structure to 
be used. We will not attempt a full specification, since 
we are not addressing all aspects of de-indexicalization 
(such as anaphoric processing). 
Rather, we will specify a new type of context compo- 
nent called a tense tree (or a set of embedded trees), 
which serves the purpose of context-dependent tense- 
aspect interpretation. Apart from this, we assume a 
"clock" which generates a succession of Now-points, 
hearer and speaker parameters, and whatever additional 
information a more complete discourse theory may call 
for; e.g., a nested segment structure which records the 
evolving set of relationships among discourse segments, 
36 
Figure 1. Tense Trees 
embedding pres 
node . ........... ""~e is home 
He left ~,,b~,c~,d ~ 
\[ ~ Hehasleft \] 
perfl , fu~xxxx 1 
.o,c ®b,e 
He had left He would leave 
He will leave 
perf 
@ 
He will have left 
including time, hearer and speaker parameters for those 
segments, history lists or focus lists of entities referenced 
within them, etc. In fact, we may want to view our tense 
tree structures as part of the "fine-grained" structure 
of discourse segments, recording the pragmatic relation- 
ships among the clauses and subclauses of a segment. 
The form of a tense tree is illustrated in Figure 1. Each 
node has up to three branches, a diagonally leftward one 
corresponding to a past operator, a vertical one to a perf 
operator, and a diagonally rightward one to a futr op- 
erator. As an indexical LF is processed in a recursive 
top-down manner to de-indexicalize its tense and aspect 
operators (and adverbials, etc.), the tense tree is tra- 
versed in a way dictated by the operators encountered. 
The position of the current traversal is called the focal 
node, or focus, of the tense tree structure and is indicated 
as ®. Where branches do not exist, they are created, 
and as new episode variables are introduced into the LF, 
copies of these variables are added to lists maintained at 
the nodes of the tense tree. As an aid to intuition, the 
nodes in Figure 1 are annotated with simple sentences 
whose indexical LFs would lead to those nodes in the 
course of de-indexicalization. 
Subordinating constructions (as in VPs with that- 
complement clauses) cause one tree to embed another, 
and this is indicated by horizontal embedding links from 
a (non-root) node of a tense tree to the root node of 
another. A set of trees connected by embedding links 
is called a tense tree structure. (This is in effect a tree 
of tense trees, since a tense tree can be embedded by 
only one other tree.) In Figure 1 an embedding link to 
the root is shown, since we assume that the utterances 
of a speaker (or sentences of a text, etc.) are ultimately 
represented in terms of performative modal predications, 
such as (pres \[Speaker assert (that ~)\]) or (pres \[Speaker 
ask (whether ~)\]). Here that and whether are "facsimi- 
les" of the nominalization operators That and Whether. 
By that we mean that they are semantically indistin- 
guishable from the latter, but since they were in effect 
"inserted" by the hearer, they are treated slightly differ- 
ently in the tree traversals (as will be seen). 
The additional annotations a, br, cr, d at the past node 
in Figure 1, and b, c at the past-perfand past-futr nodes, 
are based on the following two short passages: 
(9) a. John entered the room. 
b. Mary had taken down his paintings, 
c. and had hung up Schwarzenegger posters. 
d. He groaned. 
(10) a. Mary's note made up John's mind. 
b. He would leave, 
c. and would let her live her own life. 
d. He began to pack. 
The a at the past node indicates that an episode token 
for the event of John's entering the room in (9) a, or the 
event of Mary's note making up John's mind in (10) a, is 
added at that node in de-indexicalizing the LFs of those 
sentences. Similarly the br indicates that an episode to- 
ken for the reference point of the perfect in (9) b or (10) b 
is added at the past node in processing the LFs of these 
sentences; similarly for b, cr, c, and d. 
We will specify these operations formally, but what 
we have said so far allows us to explain intuitively how 
occurrences of tense-aspect operators are converted to 
explicit episode relationships. The idea is that episode 
tokens adjacent at a node (e.g., tokens for a and br 
above) generate orienting relationships (e.g., \[a orients 
b~\]); the episode last added at a past node is before 
a correlated episode at the mother's embedding node 
(which will be a speaking episode, thinking episode, or 
the like);(simplifying a bit) the episode last added at a 
perf node lasts at least until a correlated episode at the 
mother; and similarly for futr. 
A crucial observation about (9) is that the tokens for 
the "entering" event in a and the "taking down paint- 
ings" event in b are not placed at the same node - 
whereas the "groaning" event in d does end up at the 
same node as a. Assuming that the "reference episodes" 
b~ and c~ can be inferred to be at approximately the 
same time as the entering event a (and it turns out that 
they can), then the "groaning" event d can be inferred 
to be shortly after the "entering". As well, note that the 
"taking down paintings" and "hanging up Schwarzeneg- 
get posters" episodes b and c are adjacent at the past-parr 
node, so that b orients c. So the collocation of episode 
tokens in the tense tree is such that we can "read off' 
the relationships implicit in the tense-aspect operators 
and surface ordering of sentences. 
We can now make the de-indexicalization process and 
associated tense tree transformations more precise. 
IV. Basic Tense-Aspect Rules 
Assume that we already have a tense tree structure T, 
with a particular node in focus, as a result of process- 
ing previous inputs and partially processing the current 
input. (If not, we generate a one-node tree using the 
"new-tree" function ~ .) Then de-indexicalization of an 
LF formula with a top-level pres operator, relative to T, 
is defined by the equivalence 
Pres: (pres ~)T ~ (3aT: \[\[aT at-about EmbT\] A 
\[Last T orients aT\] \] 
37 
\[~OT ** eT\]), 
tree transformation: (pres 9)" r = 9. (or) 
Here e T is assumed to be a new episode variable name 
uniquely defined for any given T (e.g., the letter e with 
subscript i where i is the least integer such that ei does 
not yet occur in T). "OT" means "store e T at the focal 
node of T." Emb T denotes the last-added episode at the 
node which directly embeds the tree containing the focal 
node of T. (This is usually an episode corresponding to 
a performative or attitude verb.) If there is no embed- 
ding node, Emb T is the Now-point of the current context. 
Last T is the last-stored episode variable at the focus of 
T. 
Thus the de-indexicalization rule "creates" a new 
episode token, which it predicates to be at about the time 
of embedding event (e.g., the assertion of the sentence 
being processed), designates the last-stored episode at 
the current focus as the point of orientation for the new 
episode, and states that the formula 9 on which pres op- 
erates, after recursive de-indexicalization (with e T now 
stored at the focus), characterizes the new episode. 
The tree transformation which is induced by this de- 
indexicalization (in the implementation, as a side effect) 
is separately stated above. The dot symbolizes the tree- 
structure transformation function, 
• : LF-expressions × Tense-tree structures 
Tense-tree structures 
Thus, the effect of (pres 9) on T is just storage of e T at 
the focus of T, followed by whatever additional transfor- 
mations 9 induces. (Note that the function composition 
in "9 • (OT)" is read "from the inside to the outside," 
as usual.) 
Next, the de-indexicalization of past is given by 
Past: (past 9)T ~ (JET: \[\[e T before EaUbT\] A 
\[Last/, T orients eT\] \] 
\[(I~./T ** eT\] ), 
tree transformation: (past if)" T = T(9" (O~,/T)) 
Here "l T" signifies T with the focus displaced to the left 
(i.e., past) daughter, with creation of a new daughter if 
necessary. Thus the orienting episode for the new past 
episode e T is the last-stored episode at the past daugh- 
ter of the focal node. (So for a succession of simple 
past-tensed sentences, each episode generated will orient 
the next one. As well, all of them will be before their 
embedding episode, i.e., the appropriate sentence utter- 
ance.) Again, the recursively de-indexicalized 9 (with 
the T-focus shifted left and e T stored there) is taken to 
characterize the new episode. In the tree transformation 
equation, the upward arrow signals upward displacement 
of the focus to the mother. This restores the focus to its 
original position, assuming that recursive processing of 
q~ has no net effect on the focus (which it doesn't, thanks 
to the way the remaining rules work). 
Actually, the above Past-rule is a slight simplifica- 
tion. It applies as stated only when the focal node is not 
"past-dominated," i.e., if there are no past-branches in 
its ancestry (with embedding links counting as ancestry 
links). If the focus is past-dominated, \[e T before ErabT\] 
is replaced by \[e T at-or-before EmbT\]. Here at-or-before 
is regarded as a context-charged relation, with different 
probable consequences depending on the aspectual class 
of its first argument. In particular, for stative eT, \[e T at- 
or-before EmbT\] strongly suggests \[e T at ErabT\]. This is 
aimed at "sequence of tense" phenomena, observable in 
sentences like 
(11) John knew that Mary left. 
(12) John knew Mary had a cold. 
For (11), our rules predict that the "leaving" is strongly 
preferred to be prior to the "knowing" (though a variant 
like "John noticed that Mary winked at him" forces a 
concurrent-event reading); while for (12), they predict 
that the "cold" episode is strongly preferred to be at the 
same time as the "knowing" episode (though a variant 
like "John remembered that Mary had a cold when they 
got married" forces an earlier-episode reading). 
To understand the next rule, recall that we take will 
and would (in their future and future-in-the-past read- 
ings) to consist logically of tense plus the futr operator. 
Thus the futr operator is encountered only after its im- 
plicit tense operator has been processed, so that a char- 
acterizing ("**") relation will already embed the (futr 
if) expression. 
Futr: \[(futr 9)T ** ~\] ~-~ \[(JET: \[\[e T after r/\] A 
\[Last\r orients er\] \] 
** et\]) ** (F 
tree transformation: (futr 9)" r = T (~" (O\ r)) 
This is quite analogous to pres and past, except that the 
temporal location of the new episode e T is specified rel- 
ative to the episode 7/(usually a present or past episode) 
characterized by "having 9 true in its future," rather 
than relative to an "embedding episode." Also, (F r/) in 
the rule denotes "the facts about r/." Roughly speaking, 
this is needed because the formula preceding "** (F r/)" 
is an atemporal characterization of the propositional con- 
tent of r/ (one that is simply true or false, rather than 
true of some episodes and false of others); whereas (futr 
9)W is a temporal characterization of r/("being followed 
at some future time by a 9-episode" can be true of some 
episodes - namely, those that do precede a 9-episode - 
and false of others). The "** (F ~)" could be dropped 
without falsifying the forward direction of the equiva- 
lence. 
For the perfect, we need to assume an ambiguity: the 
present perfect auxiliary (has or have) is always trans- 
lated as APAz<pres (pert1 \[z P\])> (so that apart from 
the tense, the perfect is logically pert1); but when occur- 
ring untensed or in combination with past, the perfect is 
logically either pert1 or pert2. 
Pert(l): \[(perfl ¢)T ** 7/\] 
\[(3eT: \[e T until r/\]\[Col r @ eT\] ) ** (F r/)\], 
tree transformation: 
(perfi ¢)" T : T (9" (OIT)), (i = 1,2); 
where @ • for ¢ stative; 
\[~ @ ~\] ~ (Je:\[e recent-subep ~\]\[9 * el), otherwise. 
38 
Here recent-subep is another context-charged relation, 
which for a state-change e of type ¢ as first argument 
suggests the truth of \[~ * (fin r\])\], whenever \[¢ ** eli 
entails \[~ • (fin el)\] for all el (where fin means "final 
moment of'). For instance, consider 
(13) John has been sleeping. 
(14) John has woken up. 
For (13), we will get a subformula \[(prog \[John sleep\]) 
@ e~\], for some i. Since progressives are stative, this 
is equivalent to \[(prog \[John sleep\]) * ei\], meaning that 
John is sleeping over the entire episode ei. This episode 
lasts until "rf' in the complete formula, which is nothing 
else but the reference episode for the perfect (correspond- 
ing to Reichenbach's reference time). For (13), this 7/is 
a "present" episode (by the Pres-rule), so (13) means, in 
effect, that John has been sleeping until now. We take 
this to be the desired inference. 
For (14), we will get a subformula \[\[John wake-up\] @ 
ei\], and since this is nonstative, 
(Je: \[e recent-subep ei\] \[\[John wake-up\] * e\]). 
Since further \[\[John wake-up\] ** el\] entails \[\[John awake\] 
• (fin el)\] for all el (via suitable meaning postulates), 
this suggests 
\[\[John awake\] * (fin ei)\], 
where as in (13), ei lasts until r\], the (present) refer- 
ence episode. In other words, John is still awake. Note 
that this is only an implication, since we can perfectly 
well say, without contradiction, "John has woken up and 
fallen asleep again." 
The second variant of perfect is simpler, amounting to 
a "relative past": 
Perf(2): \[(perfz ¢)T ** r\]\] 
\[(JET: \[\[e T before rl\] A \[Last~T orients eT\] \] 
\[¢o,T ** eT\]) ** (f r\])\] 
Note that in the Perf(1)-rule, episode e T was taken to 
last until the reference episode, and to be only indirectly 
characterized by • (via "@"); here e T is before the ref- 
erence episode, and is directly characterized by ¢ (after 
de-indexicalization). The two main consequences are, 
first, that there is no longer an implication that a sta- 
tive episode persists to the reference time; and second, 
the episode stored in the tense tree is now the actual 
if-event, not an episode which by inference contains a 
C-event. The differences between perfl and perf2 help 
to account for the following contrasts: 
(15) a. *John has left yesterday. 
b. John had left the day before. 
c. John will have left the day before. 
(16) a. John has woken up and *has immediately 
dressed. 
b. John had woken up and had immediately 
dressed. 
c. John will have woken up and will immediately 
have dressed. 
On our account, only perfl is available in the a- 
sentences; so in (15)a, we do not get "John's leaving" 
stored in the tense tree, but only an episode containing 
John's leaving and lasting till now - but that cannot 
possibly be contained in yesterday. Similarly in (16)a, 
John's waking up is not directly stored in the tense tree, 
and so is not directly available in the interpretation of 
immediately. (We think that there may be a recovery 
mechanism in the interpretation of adverbials, which 
looks for suitable points of orientation in the history list 
(where we assume that all indefinites and definites are 
recorded, whether explicitly mentioned or inferred) after 
failing to find them in the tense tree.) In the b and c 
sentences in (15) and (16), no difficulties are encountered 
because of the availability of the perf2 reading. 
Perhaps the most important point about our treat- 
ment of the perfect, alluded to earlier, is that the refer- 
ence episode is introduced simply by the normal effect 
of operators (usually past, pres or futr) "exterior" to it. 
Briefly reconsidering (9)b, for example, we see that the 
(wide-scope) past will generate an episode in the past 
relative to the time of speech, and oriented by the "en- 
tering" episode in (9)a. It is this past episode which 
becomes the reference episode for the perfect. Now the 
key to the seemingly anaphoric character of this refer- 
ence episode is this: if \[el orients e2\], and e2 is stative, 
then there is a strong suggestion that e2 is either con- 
current with el (namely, when ex is stative as well) or 
contiguous with its end point (when el is nonstative). 
This is apparent, for instance, in the following variant of 
(9): 
(177) a. John entered the room. 
b. His paintings were gone. 
c. In their place were Schwarzenegger posters. 
In b, the episode of the paintings being gone covers (at 
least) a short time-span immediately following John's 
entering. In c, the episode of the posters being in place 
is concurrent with the paintings being gone, since both 
episodes are stative. Now, recognizing that perfect ref- 
erence episodes are stative (because the state of being 
after some given type of event can persist indefinitely, 
and holds of the subintervals of any intervals of which it 
holds), the same analysis places the past episode in (9) b 
(serving as reference episode for the perfect) right after 
John's entering, contiguous with it. This is tantamount 
to making the end of John's entering the "reference time" 
for the perfect. So we get the desired "anaphoric" effect, 
without treating past as anaphoric, and without singling 
out the past in past perfect for special treatment. 
Next we mention the de-indexicalization rules for 
That- and that-nominalizations: 
That(l): (That ~)T =(That ~T), 
tree transformation: 
(That ¢)" T = ~ (~" (~--~T)) 
That(2): (that ¢)T =(That CUT), 
tree transformation: 
(that ,I~)" T = ~ (~" (¢--+ T)) 
The rules cause focus shifts to the root of an embed- 
ded tree, indicated by the ~ and ~ operations. The 
39 
first of t:hese always adds a new embedding link whose 
destination is a new root node, whereas the second only 
does so if no embedding link exists at the current focus; 
otherwise, it causes re-traversal of the last embedding 
link added at the current focus. The leftward arrows 
in the two rules indicate focus restoration much like the 
upward arrows in the preceding rules. Intuitively, the 
distinction between a sentence nominalization derived 
explicitly from the text and one introduced through an 
implicit performative is motivated by the following sort 
of contrast: 
(18) a. John knows that Mary got home before mid- 
night• 
b. He also knows that she watched a movie• 
(19) a. Mary got home before midnight. 
b. She watched a movie. 
In (18) the sentences about Mary in a and b are ob- 
jects of attitudes, and it is much less clear than in (19) 
whether they refer to successive episodes. Now, the 
LFs for (19)a,b will contain performative predicates 
and that-nominalization operators; since the rule for 
that causes re-traversal of embedding links, the a and b 
episodes will end up at the same node. But in (18) only 
the "knowing" episodes map to the same node, while 
the episodes involving Mary map to different embedded 
nodes. Thus it will be harder to establish a connec- 
tion between them (i.e., tense structure alone Will not 
establish a connection though inference based on other 
information still might). 
Before proceeding to further rules we illustrate some 
of the ones so far with a "trace" of an LF de- 
indexicalization, namely, that of sentence (21), uttered 
right after (20): 
(20) Mary looked pale. 
(21) John realized that Mary was tired. 
The tree structure after processing of (20) will be 
T= ®'e~p ° 
- e 1 
where e0 corresponds to the added performative - i.e., 
the speaker's utterance of (20), and el corresponds to 
Mary's looking pale at a point in the past. The logical 
form of (121) is initially (without performative) 
\[John <past realize> (That \[Mary <past tired>\])\]. 
and after scoping and addition of the implicit performa- 
tive, 
(pres \[Speaker assert (that (past \[John realize 
(That (past \[Mary tired\]))\]))\]). 
By the Pres-rule, the first step of the de-indexicalization 
relative to T yields 
(3e2:\[\[e2 at-about Now2\] A \[e0 orients e2\]\] 
\[\[Speaker assert (that (past \[John realize 
(That (past \[Mary tired\]))\]))\]T, ** e2\]) 
eoe2 
where T' = (~)....-po el / 
Next, a simple rule we have not mentioned moves the 
T ~ inward to the that-clause. The That(2)-rule causes 
retraversal of the embedding link, and the Past-rule then 
gives the following altered form of the outer that-clause: 
(That (3e3:\[\[e3 before e2\] A \[el orients e3\]\] 
\[\[John realize (That 
(past \[Mary tired\]))\]T,, ** e3\])) 
eoe2 where T" = • ......... 
Again T" is moved inward to the embedded That-clause, 
and the That (1)-rule generates a new embedding link 
and tree root at the focal node. It then remains to pro- 
cess the innermost tensed clause (past \[Mary tired\])T,, 
with 
eoe2 T Ill 
= • ......... "'.'.Z.'.'.... 
ele3 
One more application of the Past-rule, but keeping in 
mind that we are now at a past-dominated node, con- 
verts the tensed clause to 
(3e4:\[e4 at-or-before ea\] \[\[Mary tired\] ** e4\]) 
assuming the orienting predication is omitted when there 
is no orienting episode. The final tree structure will be 
Since e4 is stative (given its characterization \[Mary 
tired\]), the inference from the context-charged predica- 
tion is that e4 is concurrent with e3 (i.e., John's real- 
ization), in the absence of contrary information. Also 
the earlier context-charged relation \[el orients e3\] will 
lead to the inference that John's realization was during 
Mary's looking pale, in view of the fact that el is stative 
and e3 nonstative. (As well, a causal relation can be 
tentatively inferred.) The results of de-indexicalization 
thus seem to be in complete accord with intuition. 
Besides the above rules, our current theory includes 
rules for conjunction, negation, quantification, and some 
adverbials and nominalizations. However, space limita- 
tions prevent inclusion of any details. Untensed conjunc- 
tions, negation and quantification introduce episodes for 
• the clauses they operate on, explaining phenomenon like 
illustrated in (3) and (4). Adverbs and PP-adverbials of 
temporal location, duration, and manner are treated in a 
uniform way that de-indexicalizes them into predications 
about episodes. However, we make no attempt as yet to 
40 
interpret anaphoric NPs in those PPs (such as the NP 
in before ¢he war). Also, relative clauses and clausal ad- 
verbials remain largely beyond the scope of our present 
work. 
V. Conclusions and Further Work 
We have described a new, principled approach to tense 
and aspect interpretation within a compositional frame- 
work for language understanding. The central concept 
is that of a tense tree structure as part of a more gen- 
eral context structure. This provides a straightforward 
and easily visualized way of converting originally index- 
ical LFs to representations of the meaning of an utter- 
ance which are context-independent at least as far as the 
episodic relations implicit in the tense-aspect structure 
are concerned. This includes the most common "orient- 
ing" relations between episodes, and some of the more 
subtle relations conveyed by perfective aspect. 
Our Common Lisp implementation of the de- 
indexicalization process allows rules to be straightfor- 
wardly represented and easily edited; example sentences 
of the type in this paper (modulo simplification of some 
of the adverbials) run in roughly a tenth of a second on 
a Sun SPARCstation 1. 
Future work will focus on extension of the rules so as to 
cover more types of adverbials (especially clausal ones), 
tenseless VPs and clauses (some of which we already han- 
dle, such as action nominalizations like "To have loved 
and lost is not unusual"), and relative clause. A prelimi- 
nary look at some of these phenomena, especially clausal 
adverbials and relative clauses, suggests that an opera- 
tion on pairs of trees may be required, something one 
might call a "two-point overlay" Ti:T2, where the root 
node of T1 and another node of T1 are aligned with two 
nodes of T2, creating orienting relationships between cer- 
tain episodes stored at the aligned nodes. In any case, 
the potential of our approach has certainly not been ex- 
hausted. 
Acknowledgements 
We are grateful for some interesting suggestions from 
Bob Wilensky concerning the semantics of perfect, which 
caused us to modify our rules. The research was 
supported by NSERC Operating Grant A8818 (LKS), 
an Izaak W. Killam Memorial Scholarship (CHH), the 
Boeing Co. under Purchase Contract W-288104, and 
ONR/DARPA research contract no. N00014-82-K-0193. 
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