PROBLEMS IN LOGICAL FORM 
Robert C. Moore 
SRI International, Menlo Park, CA 94025 
I INTRODUCTION 
Decomposition of the problem of "language 
understanding" into manageable subproblems has always 
posed a major challenge to the development theories of, 
and systems for, natural-language processing. More or 
less distinct components are conventionally proposed for 
handling syntax, semantics, pragmatics, and inference. 
While disagreement exists as to what phenomena properly 
belong in each area, and how much or what kinds of 
interaction there are among these components, there is 
fairly widespread concurrence as to the overall 
organization of linguistic processing. 
Central to this approach is the idea that the 
processing of an utterance involves producing an 
expression or structure that is in some sense a 
representation of the literal meaning of the utterance. 
It is often maintained that understanding what an 
utterance literally means consists in being able to 
recover this representation. In philosophy and 
linguistics this sort of representation is usually said 
to display the~ form of an utterance, so we will 
refer (somewhat loosely-~-- to the representations 
themselves as "logical forms," 
This paper surveys what we at SRI view as some of 
the key problems encountered in defining a system of 
representation for the logical forms of English 
sentences, and suggests possible approaches to their 
solution. We will first look at some general issues 
related to the notion of logical form, and then discuss 
a number of problems associated with the way information 
involving certain key concepts is expressed in English. 
Although our main concern here is with theoretical 
issues rather than with system performance, this paper 
is not merely speculative. The DIALOGIC system 
currently under development in the SKI Artificial 
Intelligence Center parses English sentences and 
translates them into logical forms embodying many of the 
ideas presented here. 
II THE NATURE OF LOGICAL FORM 
pieces of the logical form of the utterance that 
constitute referring expressions. Having logical forms 
be semantically compositional is the ultimate expression 
of this kind of decomposability, as it renders ev,ery 
well-formed subexpression a locus of meanlng--and 
therefore a potential locus of meanlng-dependent 
processing. This is probably a more telling argument 
for semantic composltlonality in designing language- 
processing systems than in analyzing human language, but 
it can be reasonably argued that such design principles 
must be followed by any system, whether natural or 
artificial, that has to adapt to a complex environment 
(see \[Simon, 1969\], especially Chapter 4). I 
Logical form, therefore, is proposed as a level of 
representation distinct from surface-syntactlc form, 
because there is apparently no direct way to 
semantically interpret natural language sentences in a 
compositional fashion. Some linguists and philosophers 
have challenged this assumption \[Montague, 1974a\] 
\[Barwlse and Cooper, 1981\], but the complexity of their 
proposed systems and the limited range of syntactic 
forms they consider leave serlous doubt that the 
logical-form level can be completely bypassed. 2 
Beyond being co~positiouel, it is desirable--though 
perhaps not essential--that the meaning of a logical 
form also be independent of the context in which the 
associated utterance occurs. (The meaning of an 
expression in natural language, of course, is often 
context-dependent.) A language-processing system must 
eventually produce a context-independent representation 
of what the speaker means by an utterance because the 
content of the utterance will normally be subjected to 
further processln E after the original context has been 
lost. In the many cases in which the speaker's intended 
meaning is simply the literal meaning, a context- 
independent logical form would give us the 
representation we need. There is little doubt that some 
representation of this sort is required. For example, 
much of our general knowledge of the world is derived 
from simple assertions of fact in natural language, but 
our situation would be hopeless if, for every fact we 
knew, we had to remember the context in which it was 
obtained before we could use it appropriately. Imagine 
trying to decide what to do with a tax refund by having 
to recall whether the topic of conversation was rivers 
or financial institutions the first time one heard that 
banks were good places in which to keep money. 
The first question to ask is, why even have a level 
of logical form? After all, sentences of natural 
languages are themselves conveyers of meaning; that is 
what natural languages are for. The reason for having 
logical foznns is to present the literal meanings of 
sentences more perspicuously than do the sentences 
themselves. It is sometimes said that natural-language 
sentences do not '~ear their meanings on their sleeves"; 
logical forms are intended to do exactly that. 
From this perspective, the main desideratum for a 
system of logical form is that its semantics be 
compositional. That is, the meaning of a complex 
expression should depend only on the meaning of its 
subexpresslons. This is needed for meanlnE-dependent 
cou~utational processes to cope with logical forms of 
arbitrary complexity. If there is to be any hope of 
maintaining an intellectual grasp of what these 
processes are doing, they must be decomposable into 
smaller and smaller meanlng-dependent subprocesses 
operating on smaller and smaller meaningful pieces of a 
logical form. For instance, if identifying the entities 
referred to by an utterance is a subprocess of inferring 
the speaker's intentions, there must be identifiable 
As this example suggests, context independence is 
closely related to the resolution of ambiguity. For any 
given ambiguity, it is possible to find a case in which 
the information needed tO resolve it is derived from the 
context of an utterance. Therefore, if the meanlnEs of 
logical forms are to be context-lndependent, the system 
of logical forms must provide distinct, unambiguous 
representations for all possible readings of an 
ambiguous utterance. The question remains whether 
logical form should also provide ambiguous 
representations to handle cases in which the 
dlsamblguatlng information is obtained later or is 
simply general world knowledge. The pros and cons of 
such an approach are far from clear, so we will 
generally assume only unembIEuous logical forms. 
Although it is sometimes assumed that a context- 
independent representation of the literal meaning of a 
sentence can be derived by using syntactic and semantic 
knowledge only, some pragmatic factors must also be 
taken into account. To take a concrete example, suppose 
the request "Please llst the Nobel Prize winners in 
physics," is followed by the question '~dho are the 
Americans?" The phrase "the Americans" in the second 
utterance should almost certainly be interpreted as 
117 
referring to American winners of the Nobel Prize in 
physics, rather than all inhabitants or citizens of the 
United States, as It might be understood in isolation. 
If the logical form of the utterance is to reflect the 
intended interpretation, processes that are normally 
assigned to praSmatlcs must be used to derive it. 
One could attempt to avoid thls consequence by 
representing "the Americans" at the level of logical 
form as literally meaning all Americans, and have later 
pragmatic processing restrict the interpretation co 
American winners of the Nobel Prize in physics. There 
are other cases, however, for which thls sort of move is 
not available. Consider more carefully the adjective 
"American." American people could be either inhabitants 
or citizens of the United States; American cars could be 
either manufactured or driven in the United States; 
American food could be food produced or consumed in or 
prepared in a style indigenous Co the United States. In 
short, the meaning of "American" seems to be no more 
than "bearing some contextually determined relation to 
the United States." Thus, there is n~o deflnlte context- 
independent mesnlng for sentences containing modifiers 
llke "American." The same is true for many uses of 
"have," "of," possessives, locative prepositions 
\[Herskovits, 1980\] and compound nominals. The only way 
to hold fast to the position that the construction of 
loglcal-form precedes all pragmatic processing seems to 
be to put in "dummy'* symbols for the unknown relations: 
This m@y in fact be very useful in building an actual 
system, ~ but It is hard to imagine that such a level of 
representation would bear much theoretical weight. 
We will chum assume that a theoretically 
interesting level of logical form will have resolved 
contextually dependent definite references, as well as 
the ocher "local" pragmatic lndeterminacies mentioned. 
An important consequence of this view is that sentences 
per se do not have logical forms~ only sentences in 
context ~.~-~f we speak loosely of the logical form of 
a sentence, this is how It should be interpreted. 
If we go thls far, why not say that all pragmaClc 
processing Cakes place before the logical form is 
constructed? That is, why make any distinction at all 
between what the speaker intends the hearer to infer 
from an utterance and what the utterance literally 
means? There are two answers co this. The first is 
that, while the pragmatic factors we have introduced 
into the derivation of logical form so far are rather 
narrowly circumscribed (e.g., resolving definitely 
determined noun phrases), the inference of speaker 
intentions is completely open-ended. The problem 
confronting the hearer is to answer the question, 'Why 
would the speaker say that in this situation?" 
Practically any relevant knowledge chat the speaker and 
hearer mutually possess \[Clark and Marshall, 1981\] 
\[Cohen and Perrault, 1981\] may be brought to bear in 
answering thls question. Prom a purely ~echodologica ! 
standpoint, then, one would hope to define some more 
restricted notion of meaning as an intermediate step in 
developing the broader theory. 
Even putting aside this methodological concern, it 
seems doubtful chat a theory of intended meaning can be 
co~trucCed without a concomitant thaor¥ of literal 
meaning, because the latter notion appears to play an 
explanatory role in the former theory. Specifically, 
the literal meaning of an utterance is one of chose 
things from which hearers infer speakers" intentions. 
For instance, in the appropriate context, "I'm getting 
cold" could be a request to close a window. The only 
way for the hearer to understand this as a request, 
however, is to recover the literal content of the 
utterance, i.e., that the speaker is getting cold, and 
to infer from this chat the speaker would llke him co do 
something about It. 
In summary, the notion of logical form we wish to 
capture is essentially that of a representation of the 
"literal meaning in context" of an utterance. To 
facilitate further processing, it is virtually essential 
that the meaning of Ioglcal-form expressions be 
compositional and, at the same time, it is highly 
desirable that they be conCext-lndependenc. The latter 
condition requires that a system of logical form furnish 
distinct representations for the dlfferenc readings of 
ambiguous natural-language expressions. It also 
requires chat some limited amount of prag~atlc 
processing be involved in producing those 
representations. Finally, we note that not all 
pragmatic factors in the use of language can be 
reflected in the logical form of an utterance, because 
some of those factors are dependent on information that 
the logical form itself provides. 
III FORM AND CONTENT IN KNOWLEDGE P.EP&ESENTJtTION 
Developing a theory of the loglcal form of English 
sentences is as much an exercise in knowledge 
representation as in linguistics, but ic differs from 
most work in arclficlal intelligence on knowledge 
representation in one key respect. Knowledge 
representation schemes are usually intended by their 
designers to be as general as possible and to avoid 
com~aitment to any particular concepts. The essential 
problem for a theory of logical form, however, is co 
represent specific concepts chat natural languages have 
special features for expressing information about. 
Concepts that fall in chls category include: 
* Events, actions, and procesmes 
* Time and space 
* Collective entities and substances 
* Propositional attitudes and modalltles. 
A theory of logical form of natural-language 
expressions, therefore, is primarily concerned with the 
content rather than the form of representation. Logic, 
semantic networks, frames, scripts, and production 
systems are all different forms of representation. But 
to say merely that one has adopted one of these forms is 
to say nothing about content, i.e., what is represented. 
The representation used in this paper, of course, takes 
a particular form (higher-order logic with intensional 
operators) but relatively little will be said about 
developing or refining chat form. Rather, we will be 
concerned with the question of what particular 
predicates, functions, operators, and the like are 
needed to represent the content of English expressions 
involving concepts in the areas listed above. This 
project might thus be better described as knowledge 
encodln 6 to distinguish It from knowledge 
representation, as it is usually understood in 
arclflcial intelligence. 
IV A FRAMEWORK FOR LOGICAL FORM 
As mentioned previously, the basic fr-mework we 
will use to represent the logical form of English 
sentences is higher-order logic (i.d., higher-order 
predicate calculus), augmented by intensional operators. 
At a purely notational level, all well-formed 
expressions will be in "Cambridge Polish" form, as in 
the programming language LZSP; thus, the logical form of 
"John likes Mary" will be simply (LIKE JOHN MARY). 
Despite our firm belief in the principle of semantic 
compositionaltt7, we will not attempt co give a formal 
semantics for the logical forms we propose. Hence, our 
I18 • 
adherence Co that principle is a good-falth intention 
rather than a demsnstrated fact. It should be noted, 
though, that virtually all the kinds of lo~tcal 
constructs used here are drawn from more formal work of 
logicians and philosophers in which rigorous semantic 
treatments are provided. 
The only place in which our logical language 
differs sigulflcancly from more familiar syscezs is In 
the treatment of quantiflers. Normally the English 
determiners "every" and "some" are translated as logical 
quantlfiers that bind a single variable in an arbitrary 
formula. This requires using an appropriate logical 
connective co combine the contents of the noun phrase 
governed by the determiner with the contents of the rest 
of the sentence. Thus '~very P is q" becomes 
(EVERY X (IMPLIES (P X) (q X))), 
and "Some P is Q'* becomes 
(SOME X (AND (e X) (q X))) 
It seems somewhat inelegant to have to use different 
connectives to Join (P X) and (~ X) in the two cases, 
but semantically it works. 
In an extremely interesting paper, Barwise and 
Cooper \[1981\] point out (and, in fact, prove) that there 
are :any determiners in English for which this approach 
does not work. The transformations employed in standard 
logic co handle "every" and "some" depend on the fact 
that any statement about every P or some P is logically 
equivalent to a statement about everything or something; 
for example, "Some P is Q" is equivalent to "Something 
is P and Q." What Barwlse and Cooper show is that there 
is no such transformation for determiners like "msst" or 
"more than half." That iS, statements about most P's or 
more than half the P's cannot be rephrased as statements 
about most things or more than half of all things. 
Barvise and Cooper incorporate this insight into a 
rather elaborate system modeled after Montague's, so 
that, among other things, they can assign a denotation 
to arbitrary noun phrases out of context. Adopting a 
more conservative modification of standard logical 
notation, we will simply insist that all quantified 
formulas have an additional element expressing the 
restriction of the quantifier. '~ost P's are Q" will 
thus be represented by 
(HOST X (F X) (q X)). 
Following thls convention gives us a uniform treatment 
for determined noun phrases: 
"Most men are mortal" 
"Some man is mortal" 
"Every man Is mortal" 
"The man iS mortal" 
"Three men are mortal" 
Note that we treat 
(MOST X (4 X) (MORTAL X)) 
(SOME X (MAN X) (MORTAL X)) 
(EVERY X (MAN X) (MORTAL X)) 
(THE X (MAN X) (MORTAL X)) 
(3 x (HA. X) (MORTJU. X)) 
"the" as a quantifier, on a par 
wlth "some" and "every." "The" is often treated 
formally as an operator chat produces a complex singular 
term, but thls has the disadvantage of not indicating 
clearly the scope of the expression. 
A final point about our basic framework Is that 
most common nouns will be interpreted as relations 
rather than functions in logical form. That is, even If 
we know that a person has only one height, we will 
represent "John's height is 6 feet" as 
(HEIGE'£ JOHN (FEET 6)) 
rather than 
(EQ (HEIGHT JOHN) (FEET 6)) 5 
There are two reasons for this: one is the desire for 
"syntactic uniformity; the other is co have a variable 
available for use in complex predicates. Consider 
"John's height is more than 5 feet and less than 6 
feet." If height is a relation, we can say 
(THE L (HEIGHT JOHN L) 
(AND (GT L (FEET 5)) 
(LT L (FEET 6)))), 
whereas, if length is a function, we would say 
(AND (GT (HEIGHT JOHN) (FT 5)) 
(LT (HEIGHT JOHN) (FT 6))) 
The second variant may look simpler, but it has the 
disadvantage that (HEIGHT JOHN) appears twice. This is 
not only syntactically unmotivated, since "John's 
height" occurs only once in the original English but, 
what is worse, it may lead Co redundant prucasslns later 
on. Let us suppose Chat we want to test whether the 
assertion is true and that determining John's height 
requires some expensive operation, such as accessing an 
external database. To avoid doing the computation 
twice, the evaluation procedure must be much more 
complex if the second representation is used rather than 
the first. 
V EVENTS, ACTIONS, AND PROCESSES 
The source of many problems in this area is the 
question of whether the treatment of sentences that 
describe events ("John is going to New York") should 
differ in any fundamental way from that of sentences 
chat describe static situations (*'John is tn New York"). 
In a very influential paper, Davidson \[ 1967\] argues 
that, while simple predicate/argument notation, such as 
(LOC JOHN mY), may be adequate for the latter, event 
sentences require explicit reference to the event as an 
object. Davldson's proposal would have us represent 
"John is going to New York" as if It were somsthing like 
"There is an event wh/~h Is a going of John co New 
York": 
(soME E (EVENT E) (GO E JOHN mY)) 
Davidson's arguments for this analysis are that (1) many 
adverbial modifiers such as "quickly" are best regarded 
as predicates of the events and that 42) it is possible 
co refer to the event explicitly in subsequent 
discourse. ("John is going co New York. Th...~e trip will 
take four hours.") 
The problem wlth Davidson's proposal is that for 
sentences in which these phenomena do not arise, the 
representation becomes unnecessarily complex. We 
therefore suggest introducing an event abstraction 
operator, EVABS, chat will allow us to introduce event 
variables when we need them: 
(P Xl ... X.) <-> 
(SOME E (EVENT E) ((gVABS F) E xl ... xn)) 
In simple cases we can use the more straightforward 
form. The logical form of "John is kissing Mary" would 
simply be (KISS JOHN MARY). The logical form of "John 
is gently kissing Mary," however, would be 
(SOME Z (EVENT E) 
(AND ((EWSS KZSS) Z JoHN ~Y) 
(GENTLE E)))) 
119 
If we let EVABS apply to complex predicates 
(represented by LAMBDA expressions), we can handle other 
problems as well. Consider the sentence "Being a parent 
caused John's nervous breakdown." "Parent" Is a 
relational noun; thus, if John is a parent, he must he 
the parent of someone, but if John has several children 
we don't want to he forced into asserting chat beinS the 
parent of any particular one of them caused the 
breakdown. If we had PARENTI as the monadic properry of 
bein S a parent, however, we could say 
(SOME E (EVENT E) 
(Am) ((EVABS PARENTL) E JOHN) 
(CAUSE E "John's nervous breakdown"))) 
We don't need tO introduce PARENTI explicitly, however, 
if we simply substitute for It the expression, 
(LAMBDA X (SOME Y (PERSON Y) (PARENT X Y))), 
which would give us 
(SOME E (EVENT E) 
(AND ((EVANS (LAMBDA X (SOME Y (PERSON Y) 
(PARZNT x z)))) Z 
JOHN) 
(CAUSE E "John's nervous breakdown"))) 
Another important question is whether actions---chat 
is, events wlth agents--should be treated differently 
from events without agents and, if so, should the agent 
be specially indicated? The point is that, if John 
kissed Mary, that £s somethln S he did, but not 
necessarily something sh....~e did. Zt is not clear whether 
this distinction should be represented at the level of 
logical form or is rather an inference based on world 
knowledge.. 
Finally, most AS work on actions and events assumes 
that they can be decomposed into discrete steps, and 
that their effects can be defined in terms of S final 
state. Neither of these assumptions is appropriate for 
continuous processes; e.g., "The flow of water continued 
to flood the basement." What the logical form for such 
statements should look like seems co be a completely 
open question. 6 
VI TIME AND SPACE 
We believe that information about time is best 
represented primarily by sencential operators, so that 
the logical form of a sentence like "John is in New York 
at 2:00" would be somethln S likm 
(AT 2:00 (LOt JOHN NY)). There are two main reasons for 
following chls approach. First, current time can be 
indicated simply by the lack of any operator; e,g. , 
"John owns Fido" becomes simply (OWNS JOHN FIDO)o This 
is especially advantageous in baslcsily static dowalns 
in which tlme plays a minimal role, so we do not have to 
put someChln S into the logical form of a sentence chat 
will be systemetically ignored by lower-level 
processing. The other advantage of this approach is 
that temporal operators can apply Co a whole sentence, 
rather than Just to a verb. For instance, in the 
preferred reading of "The President ha8 lived in the 
White House since 1800," the referent of "the President" 
changes with the time contexts involved in evaluatin S 
the truth of the sentence. The other reading can be 
obtained by allowing the quanclfier "the" in "the 
President" to assume a wider scope than that of the 
temporal operator. 
Although we do not strongly dlstlnsulsh action 
verbs from stative verbs semantically, there are 
120 
syntactic distinctions that -.,st be taken into account 
before tense can be mapped into time correctly. Stative 
verbs express present time by means of the simple 
present tense, while action verbs use the present 
progressive. Compare: 
John kisses Mary (normally habitual) 
John is kissln 8 Mary (normally present time) 
John owns Pido (normally present time) 
John is owning Fido (unacceptable) 
This is why (KISS JOHN MARY) represents "John is klsslns 
Mary," rather than "John kisses Mary," which would 
nor~slly receive a dispositional or habitual 
interpretation. 
What temporal operators will be needed? We will 
use the operator AT to assert that a certain condition 
holds at a certain time. PAST and FUTURE will be 
predicates on points in time. Sinq~le past tense 
statements with sCaCive verbs, such a8 "John was in New 
York," could mean either that John was in New York at 
some unspecified time In the past or at a coutexcua/ly 
specific time in the past: 
(SOME T (PAST T) (AT T (LOt JOHN NY))) 
(TME T (PAST T) (AT T (LOC JOHN NY))) 
(For the second expression to be an "official" lo~tcal- 
form representation, the incomplete definite reference 
would have to be resolved.) Simple future-tense 
statements with sCaCive verbs are parallel, with PUTI~ 
replacing PAST. Explicit temporal modifiers are 
generally treated as additional restrictions on the time 
referred to. "John was in New York on Tuesday" aright be 
(on at least one interpretation): 
(SOME T (AND (PAST T) (DURING T TUESDAY)) 
(AT ~ (C0C JoHN ~)))) 
For action verbs we get representations of tkts 8oft for 
past and future progressive tenses; e.g., "John was 
kissing Mary" becomes 
(THE T (PAST T) (AT T (KISS JOHN ~.lY))) 
When we use event abstraction to introduce 
individual events, the interactions with time become 
somewhat tricky. Since (KISS JOHN MAEY) means "John is 
(presently) klns£ns Mary," so must 
(SOME E (EVENT E) ((EVABS KZSS) E JOHN MAEY)) 
Since logically this formal expression means something 
llke "There is (presently) an event which is a kissing 
of Mary by John," we will interpret the prnd£caCe EVENT 
as being true at s particular time of the events in 
progress at that time. To tie all this together, "John 
was kissing Mary gently '' would be represmnced by 
(THE T (PAST T) 
(AT T 
(soME E (EVY~T E) 
(AND ((EVABS KISS) ~. JoHN MAltY) 
(GENTLE E))))) 
Tha major unsolved problem relecing to time se ams 
to be recouc-tlius statemancs chat refer co points in 
time with those that refer co intervals--for instance, 
"The colpany earned $5 m4111on in March." This 
csrtainIy does not moan that st every point in time 
during March the company earned $5 auLlliou. One could 
invent a repreesucaciou for sentences about intervals 
with no particular reletiou Co the representation for 
sentences about points, but then we would have the 
difficult task of constantly having to decide which 
representation is approp rlace. This Is further 
complicated by the fact that the same event, e. S. the 
American Rmvolutlon, could be viewed as dofin/J~ either 
a point in time or an interval, depending on the time 
scale being considered. 7 ("At the time of the American 
Revolution, France was a--'monarchy," compared wlth 
"During the American Revolution, England suffered a 
decllne in trade.") One would hope that there exist 
systematic relationships between statements about points 
in time and statements about intervals that can be 
exploited in developin B a logical form for tensed 
sentences. There is a substantial literature in 
philosophical logic devoted to "tense logic" \[Rescher 
and Urquhart, 1971\] \[McCawley, 1981\], but almost all of 
thls work see s: to be concerned wlth evaluating the 
truth of sentences at points, which, as we have seen, 
cannot be immediately extended to handle sentences about 
intervals. 
We include space under the same heading as tlme 
because a major question about space Is the extent to 
which Its treatment should parallel that of time. From 
an objective standpoint, it is often convenient to view 
physical space and time together as a four-dlmenslonal 
Euclidean space. Furthermore, there are natural- 
language constructions that seem best interpreted as 
asserting that a certain condition holds in a particular 
place ("In California it is legal to make a right turn 
on a red light"), Just as time expressions often assert 
that a condition holds at a particular time. The 
question is how far this analogy between space and time 
can be pushed. 
VlI COLLECTIVE ENTITIES AND SUBSTANCES 
Most representation schemes are designed to express 
information about such discrete, well-individuated 
objects as people, chairs, or books. Not all objects 
are so distinct, however; collections and substances 
seem to pose special difficulties, Collections are 
often indicated by conjoined noun phrases. If we say 
"Newell and Simon wrote Human Problem Solving," we do 
not mean that they each did it individually (cf. 
"Newell and Simon have PhDs."), rather we mean that they 
did it as a unit. Furthermore, if we want the treatment 
of this sentence to be parallel to chat of "~ulne wrote 
Word and Object," we need an explicit representation of 
the unit "Newell and Simon," so that It can play the 
same role the individual "~ulne" plays in the latter 
sentence. These considerations create difficulties in 
sentence interpretation because of the possibility of 
ambiguities between collective and distributed readings. 
Thus, "Newell and Simon have written many papers," might 
mean that individually each has written many papers or 
that they have jointly coauthored many papers. The 
problems associated with conjoined noun phrases also 
arise with plural noun phrases and singular noun phrases 
that are inherently collective. "John, Bill, Joe, and 
Sam," "the Jones boys," and "the Jones String Quartet" 
may all refer to the same collective entity, so that an 
adequate logical-form representation needs to treat them 
as much alike as possible. These iss,--S are treated in 
detail by Webber \[1978\]. 
The most obvious approach to handling collective 
entities is to treat them as sets, but standard set 
theory does not provide quite the right logic. The 
interpretation of "and" in "the Jones boys and the Smith 
girls" would be the union of two sets, but in "John and 
Mary" the interpretation would be constructing a set out 
of two individuals. Also, the distinction made in set 
theory between an individual, on one hand, and the 
singleton sat containing the individual, on the other, 
semas totally artificial in thls context. We need a 
"flatter" kind of structure than is provided by standard 
set theory. The usual formal treatment of strings is a 
useful model; there is no distinction made between a 
character and a string Just one character lens; 
moreover, string concatenation applies equally to 
strings of one character or more than one. Collective 
entities have these features in common with strings, but 
share with sets the properties of being uoordered and 
not having repeated elements. 
The set theory we propose has a set formation 
operator COMB Chat takes any number of arguments. The 
arguments of COMB may be individuals or sets of 
individuals, and the value of COMB is the set chat 
contains all the individual arguments and all the 
elements of the set arguments; thus, 
(COMB A iS C} D {E F C}) = {A S C D E F G} 
(The notation using braces is NOT part of the logical- 
form language; this example is Just an attempt to 
illustrate what COMB means in terms of more conventional 
concepts.) If A is an individual, (COMB A) is elmply A. 
We need one other special operator to handle 
definitely determined plural noun phrases, e.g., "the 
American ships." The problem is that in context this 
may refer to some particular set of American ships; 
hence, we need to recognize it as a definite reference 
that has to be resolved. Following Weber \[1978\], We 
will use the notation (SET X P) to express a predicate 
on sets that is satisfied by any set, all of whose 
members satisfy (LAMBDA X P). Then "the P's" would be 
the contextually determined set, all of whose members 
are P's: 
(THE S ((SET X (P X)) S) ...) 
It might seem that, to properly capture the meaning 
of plurals, we would have to limit the extension of 
(SET X P) to sets of two or more elements. This is not 
always appropriate, however. Although "There are ships 
in the Med," might seex to mean "The set of ships in the 
Med has at least two members," the question "Are there 
any ships in the Med?" does not mean "Does the set of 
ships in the Mad have at least two members?" The answer 
to the former question is yes, even if there is only one 
ship in the Mediterranean. This suggests Chat any 
presupposition the plural carries to the effect that 
more than one object is involved may be a matter of 
Gricean lmplicature ("If he knew there was only one, why 
didn't he say so?") rather than semantics. Similarly, 
the plural marking on verbs seams to be Just a syntactic 
reflex, rather than any sort of plural operator. On the 
latter approach we would have to take "Who killed Cock 
Robin?" as amblBuous between a singular and plural 
reading, since sinBular and plural verb forms would be 
semantically distinct. 
To illustrate the use of our notation, we will 
represent "Every one of the men who defeated Hannibal 
was brave." Since no one defeated Hannibal 
individually, this mast be attributed to a collection of 
men: 
(soHE T (PAST T) 
(AT T 
(EVERY X (THE S (AND ((SET Y (MAN Y)) S) 
(DEFEAT S HANNIBAL)) 
(MzMB x s)) 
(EEAVE x) ))) 
Note Chat we can replace the plural noun phrase "the men 
who defeated Hannibal" by the singular collective noun 
phrase, "the Roman army," as in "Everyone in the Romeo 
army was brave": 
(SOME T (PAST T) 
(AT T 
(EVERY X (THE S (AND (ARMY S) (ROMAN S)) 
(Mz~ x s)) 
(BRAVE X)))) 
121 
The only change In the logical form of'the sentence is 
chat IX QUESTIONS AND IMFERATIVE3 
(AND ((SET Y (MAN Y)) S) (DEFEAT S ~NIBAL)) 
is replaced by (AND (ARMY S) (RO~.~N S)). 
Collective entities are not the only objects that 
are difficult to represent. Artificial intelligence 
representation schemes have notoriously shied away from 
mass quencitie• and substances. (\[Hayes, 1978\] Is a 
notable exception.) In a sentence like "All Eastern 
coal contains soma sulfur," it see,." tb•\[ "coal" and 
"sulfur" refer to properties of samples or pieces of 
"stuff." We might paraphrase thls sentence as "All 
pieces of stuff that are Eastern coal contain soue stuff 
that Is sulfur." If we take this approach, then, In 
interpreting a sentence like "The Universe Ireland Is 
carrying |00,000 barrels of Saudi light crude," we need 
co indicate that the "piece of stuff" being described is 
the maximal "piece" of Saudl light crude the shlp is 
carrying. In other cases, substances seem to be more 
llke abstract individuals, e.g., "Copper is the twenty- 
ninth element in the periodic table." Nouns that refer 
Co substances can also function as do plural noun 
phrases in their ~eneric use: "Copper is \[antelopes are\] 
abundant in the American southwest." 
Vlll PROPOSITIONAL ATTITUDES AND MODALITIES 
Propositional attitudes and modalities are 
discussed together, because they are both normally 
treated as intensional sentential operators. For 
instance, to represent "John believes Chat the Fox is in 
Naples," we would have an operator BELIEVE that takes 
"John" as its first argunmnt and the representation of 
"The Fox is in Naples" as Its second argument. 
S£,,tlarly, to represent '*the Fox might be in Naples," we 
could apply an" operator POSSIBLE to the representation 
of "The Fox is in Naples." This approach works 
particularly well on a number of problems involving 
quanCifiers. For example, "John believes someone is in 
the basement s' possesses an ambiguity that is revealed by 
the two par•phrases, "John believes there is someone in 
the basement" and "There is someone John believes Co be 
in the basement." As chess paraphrases suggest, thls 
distinction is represented by different relative scopes 
of the belief operator and the existential quantifier 
introduced by the indefinite pronoun "someone": 
(BELIEVE JOHN (SOME X (PERSON X) (LOC X BASEMENT))) 
(SOME X (PERSON X) (BELIEVE JOHN (LOC X ~N~S~IENT))) 
This approach works very well up to a point, but 
there •re cases It does not handle. For exanple, 
sometimes verbs like "believe" do not take a sentenc• a• 
• n •rs~menc, but rather a description of a sentence, 
e.g., "John believes Goldbach's conjecture." TF we were 
to make "believe" a predicate rather than a sentence 
operator to handle this type of ~m?le, the elegant 
semantics chat has been worked ouC for "quanc£fylng In" 
would completely break down. Another alternative is to 
introduce a predicate TIUE co map s descriptio n of a 
sentence into • sentence that necessarily has the smse 
truth value. Than "John believes Coldbach's conjecture" 
is treated •s If It were "John belleves of Coldbach's 
conjecture that It is true." This is dlsc£nSulshed in 
ch~ usual way from "John believes that Coldbach's 
--~-c~nJecture (whatever It may be) is true" by reversing 
the scope of the description "Goldbach's conjecture" and 
the operator "believe." 
The only types of utterances we have tried Co 
represent in logical form to this point are assertions, 
but of course there are other speech acts as well. The 
only two ve will consider •re questions and imperatives 
(commands). Since performatives (promises, bets, 
declarations, etc.) have the •ate syntactic form •s 
assertions, it appears that they raise no new problems. 
We will also concern ourselves only wich the literal 
speech act expressed by an utterance. Dealing wlth 
indirect speech acts does noc seem to change the range 
of representations needed; sometimes, for example, we 
may simply need to represent what is literally an 
assertion as somachlng lnc•nded as a command. 
For question•, we would like to have a uniform 
treatment of both the yes/no and WH forms. The simplest 
approach is co regard the semantic content of a WH 
question to be a predicate whose extension is being 
sought. This does noc address the issue of what is a 
satisfactory answer to • question, but we regard that as 
part of the theory of speech acts proper, rather than a 
question of logical form. We will introduce the 
operator WHAT for constructlng complex set descriptions, 
which, for the sake of uniformity, we will give the same 
four-part structure ve u•e for quantlflers. The 
represent•tlon of '~hat American ships are in the Med?" 
would roughly be as follows: 
(WHAT X (AND (SHIP X) ~.MERICAN X)) 
(LOC x ~zD)) 
WHAT is conveniently mnemonic, since we can represent 
"who" as (WHAT X (PERSON X) .... ), "when" as 
(WHAT X (TZHZ X) .... ), and so forth. "How many" 
questions will be treated a• questioning the quantifier. 
'~lov many men •re mortal?" would be represented a• 
(WHAT N (Nb~mZR N) 
(N X (MAN X) (MOZTAL X))) 
Yes/no questions can be handled •s • degenerate 
case of WH questions by treating a proposition •s a O- 
ary predicate. Since the exC•ueion of •n n-sty 
predicate is a set of n-tuples, the extension of a 
proposition would be a set of 0-~uples. There is only 
one 0-tuple, the e~ty topis, so there •re only two 
po•slble s•ts of O-~uple•. Th•se are the singleto~ set 
containing the empty topis, and the empty set, which we 
can identify wlth the truth values TRUE and FALSE. The 
logical form of a yes/no question wlth Che proposition P 
as its S'mantic content would be (WHAT () TEUE P), or 
more simply P. 
With regard to imperatives, It is less clear what 
type of semantic object Chair content should be. We 
might propose that It l• a proposition, but ve then have 
Co account for the fact that not •ll propositions are 
acceptable as commands. For instance, John cannot be 
commanded "Bill go to New York." The respon•e that a 
person can only be "commanded somechlng" he has control 
over is not adequate, because any proposition can be 
converted into a command by the verb "sake"--e.g., "Make 
Bill So Co New York." 
The awkwerdnas• of the phrasing "command someone 
somathlng" suggests another approach. One cmmands 
sos'one Co d.~o something, and the thinks that are done 
are actions. If actions are treated as objects, we can 
d•flne a relation DO chat map• •n agent sad an action 
into a proposition (See \[Moore, 1980\]). "John is going 
Co New York" would then be represented by 
(DO JO~h~ (GO ~f)). Actions are nov available to be the 
semantic content of imperatives. The problem with this 
approach is that we now have to pack into actions all 
the semantic complexities Chat can •rise in commsnds- 
122 
for instance, adverbial modifiers, which we have treated 
above as predicates on events ("Co quickly"), 
quantiflers ("Go to every room in the house"), and 
negation ("Don't go"). 
A third approach, which we feel is actually the 
most promising, is to treat the semantic content of an 
imperative as being a unary predlcace. The force of an 
imperative 18 that the person to whom the command is 
directed is supposed to satisfy the predlcaCe. 
According to this theory the role of "make" is clear--it 
converts any proposition into a unary predicate. If the 
assertion "John Is making glll go Co NOw York" is 
represented as (MAKE JOHN (GO BILL MY)), we can form a 
unary predicate by LAMBDA abstraction: 
(LAMBDA X (MAKE X (GO gILL mY)), 
which would be the semantic content of the command "Make 
Bill go to New York." 
This approach does away wlth the problem concerning 
adverbial modifiers or quantlflers In commands; they can 
simply be part of the proposition from which the 
predicate is formed. A final piece of evidence favoring 
thls approach over a theory based on the notion of 
action is that some imperatives have nothing at all to 
do wlth actions directly. The semantic content of 
commands llke "Be good" or "Don't be a fool" really does 
seem to consist exclusively of a predicate. 
X CONCLUSION 
In a paper that covers such a wide range of 
disparate topics, it is hard to reach any sweeping 
general conclusions, but perhaps a few remarks about the 
nature and current status of the research program are in 
order. First, it should be clear from the issues 
discussed that at least as many problems remain in the 
quest for logical form as have already been resolved. 
Considering the amount of effort that has been expended 
upon natural-language semantics, this is somewhat 
surprising. The reason may be that relatlvely few 
researchers have worked in thls area for its own sake. 
Davldeon's ideas on action sentences, for instance, 
raised some very interesting points about logical form-- 
but the major debate Ic provoked in the philosophical 
llcerature was about the metaphysics of the concept of 
action, noc about the semantics of action sentences. 
Even when semantics is a major concern, as in the work 
of Montague, the emphasis is often on showing chat 
relatively well-understood subareas of semantics (e.g., 
quantificaclon) can be done in a parClcular way, rather 
than on attempting to take on really new problems. 
An additional difficulty is that so much work has 
been done in a fragmentary fashion. It is clear that 
the concept of action is closely related to the concept 
of time, but it is hard to find any work on either 
concept that takes the other one seriously. To build a 
language-processlng system or a theory of language 
processing, however, requires an integrated theory of 
logical form, not Just a set of incompatible fragmentary 
theories. Our conclusion, then, is chac 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. 
ACKNOWLEDGEMENTS 
The ideas in this paper are the collective result 
of the efforts of a large number of people at SRI, 
particularly Barbara Grosz, SCan Rosenscheln, and Gary 
dendrix. Jane Robinson, Jerry Hobbs, Paul Martin, and 
Norman Haas are chiefly responsible for the 
implementaClon of the DIALOGIC system, building on 
earlier systems co which Ann Robinson and Bill Paxcon 
made major contributions. This research was supported 
by the Defense Advanced Research Projects Agency under 
Contracts N00039-80-C-0645 and N00039-80-C-0575 with the 
Naval Electronic Systems Command. 
NOTES 
I Although our immediate aim is to construct a theory of 
natural-language processing rather than truth- 
conditional semantics, It is worth noting that a system 
of logical form wlth a well-deflned semantics 
constitutes a bridge between the two projects. If we 
have a processing theory that associates English 
sentences with their logical forms, and if those loKical 
forms have a truth-~ondltional semantics, then we will 
have specified the semantics of the English sentences as 
well. 
2 In other papers (e.g., \[Montague, 1974b\]), Montague 
himself uses an intenslonal logic in exactly the role we 
propose for logical form--and for much the same reason: 
'We could ... introduce the semantics of our fraKment 
\[of English\] directly; but It Is probably mere 
perspicuous to proceed indirectly by (I) setting up a 
certain simple artificial language, that of tensed 
Intenslonal logic, (2) giving the semantics of that 
language, and (3) interpreting English indirectly by 
showing in a rigorous way how to translate it into the 
artificial language. This Is the procedure we shall 
adopt;..." \[Montague, 1974b, p.256\]. 
3 The DIALOGIC system does build such a representation, 
or at least components of one, as an intermediate step 
in deriving the logical form of a sentence. 
4 This suggests chac our logical forms are 
representations of what David Kaplan, in his famous 
unpublished paper on demonstratives \[Kaplan, 1977\], 
calls the content of a sentence, as opposed to Its 
character. Kaplan introduces the content/character 
distinction to sort out puzzles connected wlth the use 
of demonstratives and Indaxlcals. He notes that there 
are at least two different notions of "the meaning of a 
sentence" that conflict when indexical expressions are 
used. If A says to B, "I am hungry," and g says to A, 
"~ am hungry," they have used the same words, but in one 
sense they mean different things. After all, it may be 
the case that what A said is true and what B said is 
false. If A says to g, "~ am hungry," and B says to A, 
"You are hungry," they have used different words, but 
mean the same thing, that A is hungry. This notion of 
"meaning different things" or "meaning the same thing" 
is one kind of meaning, which Kaplan calls "content." 
There Is another sense, though, In which A and g both 
use the words "I am hungry" with the same meanlng, 
namely, that the same rules apply to determine, in 
context, what content is expressed. For thls notion of 
meaning, Kaplan uses the term "character." Kaplan's 
notion, therefore, is that the rules of the language 
determine the character of a sentence--whlch, in turn, 
together wlth the context of utterance, determines the 
content. If ~ broaden the scope of Kaplan's theory to 
include the local pragmatic indetermlnacles we have 
discussed, it seems Chec the way they depend on context 
would also be part of the character of a sentence and 
Chat our logical form is thus a representation of the 
content of the sentence-ln-context. 
5 It should be obvious from the example that nouns 
referring to unlCs of measure--e.g., "feet"--are an 
exception co the general rule. We treat types of 
quanCitles, such as distance, weight, volume, time 
123 
duracioo, etc., as basic conceptual categories. 
Following Hayes \[1979\], unlCs such as feet, pounds, 
gallons, and hours are considered to be functions from 
numbers,to quantities. Thus (FEET 3) and (YARDS l) 
denote the same distance. Halations llke length, 
weight, size, and duration hold between an entity and a 
quantity of an appropriate type. Where a word llke 
"welghc" serves in English to refer co both the relaClon 
and the quantity, we must be careful Co dlsClngulsh 
between chem. To see the dlscincCion, note Chac length, 
beam, and draft are all relaclons between a ship and a 
quanClcy of the same type, discance. We treat 
comparatives llke "greater than" as molcidomain 
relaclons, working with any two quanciCles of the same 
type (or wich pure numbers, for chac matter). 
6 Hendrix \[1973\], Rieger \[1975\], Hayes \[1978\], and 
McDermott \[1981\] have all dealt with conClnuous 
processes co some extent, buc none of them has 
considered specifically how language expresses 
information about processes. 
7 This point was impressed upon me by Pat Hayes. 
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