Logical Form of Complex Sentences 
in Task-Oriented Dialogues* 
Cecile T. Balkanski 
Harvard University, Aiken Computation Lab 
Cambridge, MA 02138 
Introduction 
Although most NLP researchers agree that a level of 
"logical form" is a necessary step toward the goal of rep- 
resenting the meaning of a sentence, few people agree on 
the content and form of this level of representation. An 
even smaller number of people have considered the com- 
plex action sentences that are often expressed in task- 
oriented dialogues. Most existing logical form represen- 
tations have been developed for single-clause sentences 
that express assertions about properties or actual actions 
and in which time is not a main concern. In contrast, 
utterances in task-oriented dialogues often express unre- 
alized actions, e.g., (la), multiple actions and relations 
between them, e.g., (lb), and temporal information, e.g., 
(lc): 
(1) a. What about rereading the Operations manual? 
b. By getting the key and unlocking the gate, you 
get ten points. 
c. When the red fight goes off, push the handle. 
In the following sections, I discuss the issues that arise 
in defining the logical form of these three types of sen- 
tences. The Davidsonian treatment of action sentences 
is the most appropriate for my purposes because it treats 
actions as individuals \[7\]. For example, the logical form 
of "Jones buttered the toast" is a three place predicate, 
including an argument position for the action being de- 
scribed, i.e., 3x butter(jones, toast, x). The presence of 
the action variable makes it possible to represent op- 
tional modifiers as predications of actions and to refer 
to actions in subsequent discourse. Furthermore, and 
more importantly for the present purpose, it facilitates 
the representation of sentences about multiple actions 
and relations between them. 
Unrealized-action sentences 
A Davidsonian logical form of sentence (la), namely 
3x reread(us, manual, x), makes the claim that there 
exists a particular action x. But this is not the intended 
meaning of the sentence. Instead, this sentence con- 
cerns a hypothetical action. The same problem arises 
with sentences (lb) and (lc) which state how typical 
actions are related or when to perform a future action. 
Apparently, Davidson did not have these types of action 
in mind when suggesting his theory of logical form. 
In fact, a closer look at the literature shows that 
the problem of representing action sentences that do 
*This research has been supported by U S West Advanced 
Technologies, by the Air Force Office of Scientific Research 
under Contract No.AFOSR-89-0273, and by an IBM Grad- 
uate Fellowship. 
331 
not make claims about actions that have or are oc- 
curring (i.e., actual actions) has been virtually ignored. 
Hobbs, who also adopts a Davidsonian treatment of ac- 
tion sentences, is one notable exception \[11\]. His "Pla- 
tonic universe" contains everything that can be spoken 
of and the predicate Exist is used to make statements 
about the existence in the actual universe of individu- 
als in the Platonic universe. For example, the formula 
Exists(x) Arun'(x, john) says that the action of John's 
running exists in the actual universe, or, more simply, 
that John runs. The approach I am currently investi- 
gating is to extend Itobbs' representation by introduc- 
ing predicates stating the existence of actions in future, 
hypothetical or typical worlds as well as in the actual 
world. 
Another possibility is to adopt the standard philo- 
sophical approach to the representation of properties, 
and for that matter, of actions, that are not actually 
instantiated, namely possible worlds (cf. \[13, 2\]). Fur- 
thermore, and independently of the approach that is 
adopted, there is a need to identify the different types 
of unrealized actions and determine whether they should 
be distinguished in the logical form. 
Multi-clause sentences 
Another area of logical form that has not received much 
attention is the representation of sentences about multi- 
ple actions and relations between them. I have been 
investigating sentences including by- and to- purpose 
clauses because they are used to communicate two ac- 
tion relations, namely generation and enablement, which 
I have defined elsewhere \[3\]. In a Davidsonian logical 
form, the connectives "by" and "to" can be represented 
as two-place predicates ranging over action tokens1; e.g.: 
(2) To learn how to use the system, read the manual. learn(you, system, xa ) 
A read(you, manual, x2)A 
inorderto(x2, xa) 
Clauses may also be joined with coordination con- 
junctions, e.g., (3a), and the resulting constituent may 
participate in another action relation, as in (lb) and 
repeated below in (3b). I therefore represent these con- 
neetives by a three place predicate, e.g., and(xl, x2, x4) 
which is true if action x4 is the conjunction of actions 
xl and x2. In (3a), the action token x4 might seem 
superfluous, but note that it becomes necessary if that 
action is referred to in subsequent discourse (e.g., "Do 
aAlthough this problem interacts with the one discussed 
in the previous section, for the purpose of this presentation, 
I call Davidson's action variables action tokens and represent 
them as constants in the logical form. 
it fast!"); in (3b), the action token z4 can then be used 
as the first argument to the by predicate: 
(3) a. Get the key and unlock the gate. 
get(you, key, xl ) ^ unZock(yo,,, gate, x2 )^ 
and(xl, x2, x4) 
b. By getting the key and unlocking the gate, you 
get ten points. 
get(you, key, xl) ^ unlock(you, gate, z2)^ 
get(you, lOpoints, z3) ^ and(z1, z2, z4) ^ by(x4, za) 
In the above logical forms, I assume that the by and 
inorderto predicates denote a two place relation express- 
ing the "ideal meaning" of the corresponding English 
connective \[9\]. There is not necessarily a one-to-one 
mapping between particular linguistic expressions and 
action relations, and subsequent pragmatic processing 
of the logical forms will further interpret these relations. 
Representing the embedded clause as an additional ar- 
gument to the predicate representing the matrix clause 
(e.g., \[5\]), or representing the relation as a binary sen- 
tential operator (e.g., \[16\]) are alternative representa- 
tions, both of which suffer from problems discussed by 
Davidson because action tokens become irrelevant. Fur- 
thermore, the first does not capture the intuitive notion 
that these sentences express action relations, and the 
second introduces a lack of homogeneity between logical 
forms of sentences involving action relations and those 
that do not. 
Time 
Still another feature that has been overlooked in the 
study of logical form is time. Although a number of pa- 
pers include time in their logical forms, most do not dis- 
cuss their treatment of time and consider primarily past 
and present tense examples about actual actions (e.g., 
\[1, 5, 1412). The lack of concern for temporal issues is 
also characteristic of the literature on semantic interpre- 
tation (e.g., \[10, 15, 16\]). On the other hand, there is a 
vast literature on the interpretation and representation 
of tense, aspect and temporal modifiers, but these pa- 
pers do not describe the logical forms from which their 
representations are generated (e.g., \[4, 6, 8, 12, 17, 18\]). 
Clearly, there is a missing link between the literature 
on logical form and that on tense and aspect. Providing 
such a link is one of the goals of this research. David- 
son's treatment of action sentences does not provide a 
fully satisfying starting point. Although his initial pa- 
per does not include any example of temporal modi- 
fiers, he would probably represent them as predicates 
over action tokens, e.g., next_week(x), a representation 
that does not make explicit reference to time (to which 
anaphors might refer). Introducing a time predicate, 
e.g., time(z, next_week), solves this particular problem, 
but introduces other complexities because this predicate 
would not be adequate for all temporal modifiers (e.g., 
compare Sue will leave in two hours and Sue reached the 
top in two hours). Given that the aspectual type and 
tense of the verb, along with the presence of adverbials 
and common sense knowledge all interact in the inter- 
pretation of the temporal information in a sentence \[12\], 
it might be preferable for such reasoning to be performed 
with the logical form as input rather than as output. 
2Moore \[14\] addresses time issues, but omits future tense 
sentences and acknowledges problematic interactions be- 
tween his event abstraction operator and time. 
Conclusion 
Although many researchers have proposed formalisms 
for simple action sentences, very few of them have ad- 
dressed the issues that arise when extending those for- 
malisms to the more complex sentences that occur in 
task-oriented dialogues. There has been work in each of 
the above areas, but this research has been fragmentary 
and still needs to be integrated with that on the logi- 
cal form of action sentences. Ironically, the conclusion 
that Moore arrived at, ten years ago, is still valid today 
\[14\]: "If real progress is to be made on understanding 
the logical form of natural-language utterances, it must 
be studied in a unified way and treated as an important 
research problem in its own right." In ray talk, I will 
present an initial attempt to do so. 

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