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Home , Logical form

PROBLEMS IN Robert C. Moore SRI International, Menlo Park, CA 94025

pieces of the logical form of the utterance that I INTRODUCTION constitute referring expressions. Having logical forms be semantically compositional is the ultimate expression of this kind of decomposability, as it renders ev,ery Decomposition of the problem of " well-formed subexpression a locus of meanlng--and understanding" into manageable subproblems has always therefore a potential locus of meanlng-dependent posed a major challenge to the development theories of, processing. This is probably a more telling and systems for, natural-language processing. More or for semantic composltlonality in designing language- less distinct components are conventionally proposed for processing systems than in analyzing human language, but handling , , , and . it can be reasonably argued that such design principles While disagreement exists as to what phenomena properly must be followed by any system, whether natural or belong in each area, and how much or what kinds of artificial, that has to adapt to a complex environment interaction there are among these components, there is (see [Simon, 1969], especially Chapter 4). I fairly widespread concurrence as to the overall Logical form, therefore, is proposed as a level of organization of linguistic processing. representation distinct from surface-syntactlc form, because there is apparently no direct way to Central to this approach is the idea that the semantically interpret natural language sentences in a processing of an utterance involves producing an compositional fashion. Some linguists and philosophers expression or structure that is in some sense a have challenged this assumption [Montague, 1974a] representation of the literal of the utterance. [Barwlse and Cooper, 1981], but the complexity of their It is often maintained that understanding what an proposed systems and the limited range of syntactic utterance literally means consists in being able to forms they consider leave serlous doubt that the recover this representation. In philosophy and logical-form level can be completely bypassed. 2 this sort of representation is usually said to display the~ form of an utterance, so we will Beyond being co~positiouel, it is desirable--though refer (somewhat loosely-~-- to the representations perhaps not essential--that the meaning of a logical themselves as "logical forms," form also be independent of the context in which the associated utterance occurs. (The meaning of an This paper surveys what we at SRI view as some of expression in natural language, of course, is often the key problems encountered in defining a system of context-dependent.) A language-processing system must representation for the logical forms of English eventually produce a context-independent representation sentences, and suggests possible approaches to their of what the speaker means by an utterance because the solution. We will first look at some general issues content of the utterance will normally be subjected to related to the notion of logical form, and then discuss further processlnE after the original context has been a number of problems associated with the way information lost. In the many cases in which the speaker's intended involving certain key is expressed in English. meaning is simply the literal meaning, a context- Although our main concern here is with theoretical independent logical form would give us the issues rather than with system performance, this paper representation we need. There is little doubt that some is not merely speculative. The DIALOGIC system representation of this sort is required. For example, currently under development in the SKI Artificial much of our general knowledge of the world is derived Intelligence Center parses English sentences and from simple assertions of fact in natural language, but translates them into logical forms embodying many of the our situation would be hopeless if, for every fact we ideas presented here. 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 II THE NATURE OF LOGICAL FORM banks were good places in which to keep money.

As this example suggests, context independence is The first question to ask is, why even have a level closely related to the resolution of . For any of logical form? After all, sentences of natural given ambiguity, it is possible to find a case in which are themselves conveyers of meaning; that is the information needed tO resolve it is derived from the what natural languages are for. The for having context of an utterance. Therefore, if the meanlnEs of logical foznns is to present the literal meanings of logical forms are to be context-lndependent, the system sentences more perspicuously than do the sentences of logical forms must provide distinct, unambiguous themselves. It is sometimes said that natural-language representations for all possible readings of an sentences do not '~ear their meanings on their sleeves"; ambiguous utterance. The question remains whether logical forms are intended to do exactly that. logical form should also provide ambiguous representations to handle cases in which the From this perspective, the main desideratum for a dlsamblguatlng information is obtained later or is system of logical form is that its semantics be simply general world knowledge. The pros and cons of compositional. That is, the meaning of a complex such an approach are far from clear, so we will expression should depend only on the meaning of its generally assume only unembIEuous logical forms. subexpresslons. This is needed for meanlnE-dependent cou~utational processes to cope with logical forms of Although it is sometimes assumed that a context- arbitrary complexity. If there is to be any hope of independent representation of the literal meaning of a maintaining an intellectual grasp of what these can be derived by using syntactic and semantic processes are doing, they must be decomposable into knowledge only, some pragmatic factors must also be smaller and smaller meanlng-dependent subprocesses taken into account. To take a concrete example, suppose operating on smaller and smaller meaningful pieces of a the request "Please llst the Nobel Prize winners in logical form. For instance, if identifying the entities physics," is followed by the question '~dho are the referred to by an utterance is a subprocess of inferring Americans?" The phrase "the Americans" in the second the speaker's intentions, there must be identifiable utterance should almost certainly be interpreted as

117 referring to American winners of the Nobel Prize in In summary, the notion of logical form we wish to physics, rather than all inhabitants or citizens of the capture is essentially that of a representation of the United States, as It might be understood in isolation. "literal meaning in context" of an utterance. To If the logical form of the utterance is to reflect the facilitate further processing, it is virtually essential intended interpretation, processes that are normally that the meaning of Ioglcal-form expressions be assigned to praSmatlcs must be used to derive it. compositional and, at the same time, it is highly desirable that they be conCext-lndependenc. The latter One could attempt to avoid thls consequence by condition requires that a system of logical form furnish representing "the Americans" at the level of logical distinct representations for the dlfferenc readings of form as literally meaning all Americans, and have later ambiguous natural-language expressions. It also pragmatic processing restrict the interpretation co requires chat some limited amount of prag~atlc American winners of the Nobel Prize in physics. There processing be involved in producing those are other cases, however, for which thls sort of move is representations. Finally, we note that not all not available. Consider more carefully the adjective pragmatic factors in the use of language can be "American." American people could be either inhabitants reflected in the logical form of an utterance, because or citizens of the United States; American cars could be some of those factors are dependent on information that either manufactured or driven in the United States; the logical form itself provides. 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- III FORM AND CONTENT IN KNOWLEDGE P.EP&ESENTJtTION independent mesnlng for sentences containing modifiers llke "American." The same is true for many uses of "have," "of," possessives, locative prepositions Developing a theory of the loglcal form of English [Herskovits, 1980] and compound nominals. The only way sentences is as much an exercise in knowledge to hold fast to the position that the construction of representation as in linguistics, but ic differs from loglcal-form precedes all pragmatic processing seems to most work in arclficlal intelligence on knowledge be to put in "dummy'* for the unknown relations: representation in one key respect. Knowledge This m@y in fact be very useful in building an actual representation schemes are usually intended by their system, ~ but It is hard to imagine that such a level of designers to be as general as possible and to avoid representation would bear much theoretical weight. com~aitment to any particular concepts. The essential problem for a theory of logical form, however, is co We will chum assume that a theoretically represent specific concepts chat natural languages have interesting level of logical form will have resolved special features for expressing information about. contextually dependent definite , as well as Concepts that fall in chls category include: the ocher "local" pragmatic lndeterminacies mentioned. An important consequence of this view is that sentences * Events, actions, and procesmes per se do not have logical forms~ only sentences in * Time and space context ~.~-~f we speak loosely of the logical form of * Collective entities and substances a sentence, this is how It should be interpreted. * Propositional attitudes and modalltles.

If we go thls far, why not say that all pragmaClc A theory of logical form of natural-language processing Cakes place before the logical form is expressions, therefore, is primarily concerned with the constructed? That is, why make any distinction at all content rather than the form of representation. , between what the speaker intends the hearer to infer semantic networks, frames, scripts, and production from an utterance and what the utterance literally systems are all different forms of representation. But means? There are two answers co this. The first is to say merely that one has adopted one of these forms is that, while the pragmatic factors we have introduced to say nothing about content, i.e., what is represented. into the derivation of logical form so far are rather The representation used in this paper, of course, takes narrowly circumscribed (e.g., resolving definitely a particular form (higher-order logic with intensional determined noun phrases), the inference of speaker operators) but relatively little will be said about intentions is completely open-ended. The problem developing or refining chat form. Rather, we will be confronting the hearer is to answer the question, 'Why concerned with the question of what particular would the speaker say that in this situation?" predicates, functions, operators, and the like are Practically any relevant knowledge chat the speaker and needed to represent the content of English expressions hearer mutually possess [Clark and Marshall, 1981] involving concepts in the areas listed above. This [Cohen and Perrault, 1981] may be brought to bear in project might thus be better described as knowledge answering thls question. Prom a purely ~echodologica ! encodln 6 to distinguish It from knowledge standpoint, then, one would hope to define some more representation, as it is usually understood in restricted notion of meaning as an intermediate step in arclflcial intelligence. 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 IV A FRAMEWORK FOR LOGICAL FORM 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 As mentioned previously, the basic fr-mework we things from which hearers infer speakers" intentions. will use to represent the logical form of English For instance, in the appropriate context, "I'm getting sentences is higher-order logic (i.d., higher-order cold" could be a request to close a window. The only predicate calculus), augmented by intensional operators. way for the hearer to understand this as a request, At a purely notational level, all well-formed however, is to recover the literal content of the expressions will be in "Cambridge Polish" form, as in utterance, i.e., that the speaker is getting cold, and the programming language LZSP; thus, the logical form of to infer from this chat the speaker would llke him co do "John likes Mary" will be simply (LIKE JOHN MARY). something about It. 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 (EQ (HEIGHT JOHN) (FEET 6)) 5 rather than a demsnstrated fact. It should be noted, though, that virtually all the kinds of lo~tcal There are two for this: one is the desire for constructs used here are drawn from more formal work of "syntactic uniformity; the other is co have a variable logicians and philosophers in which rigorous semantic available for use in complex predicates. Consider treatments are provided. "John's height is more than 5 feet and less than 6 feet." If height is a relation, we can say The only place in which our logical language differs sigulflcancly from more familiar syscezs is In (THE L (HEIGHT JOHN L) the treatment of quantiflers. Normally the English (AND (GT L (FEET 5)) determiners "every" and "some" are translated as logical (LT L (FEET 6)))), quantlfiers that bind a single variable in an arbitrary formula. This requires using an appropriate logical whereas, if length is a function, we would say connective co combine the contents of the noun phrase governed by the determiner with the contents of the rest (AND (GT (HEIGHT JOHN) (FT 5)) of the sentence. Thus '~very P is q" becomes (LT (HEIGHT JOHN) (FT 6)))

(EVERY X (IMPLIES (P X) (q X))), The second variant may look simpler, but it has the disadvantage that (HEIGHT JOHN) appears twice. This is and "Some P is Q'* becomes not only syntactically unmotivated, since "John's height" occurs only once in the original English but, (SOME X (AND (e X) (q X))) what is worse, it may lead Co redundant prucasslns later on. Let us suppose Chat we want to test whether the It seems somewhat inelegant to have to use different assertion is true and that determining John's height connectives to Join (P X) and (~ X) in the two cases, requires some expensive operation, such as accessing an but semantically it works. external database. To avoid doing the computation twice, the evaluation procedure must be much more In an extremely interesting paper, Barwise and complex if the second representation is used rather than Cooper [1981] point out (and, in fact, prove) that there the first. 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 about every P or some P is logically equivalent to a statement about everything or something; V EVENTS, ACTIONS, AND PROCESSES 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 The source of many problems in this area is the "more than half." That iS, statements about most P's or question of whether the treatment of sentences that more than half the P's cannot be rephrased as statements describe events ("John is going to New York") should about most things or more than half of all things. differ in any fundamental way from that of sentences chat describe static situations (*'John is tn New York"). Barvise and Cooper incorporate this insight into a In a very influential paper, Davidson [ 1967] argues rather elaborate system modeled after Montague's, so that, while simple predicate/argument notation, such as that, among other things, they can assign a denotation (LOC JOHN mY), may be adequate for the latter, event to arbitrary noun phrases out of context. Adopting a sentences require explicit to the event as an more conservative modification of standard logical object. Davldson's proposal would have us represent notation, we will simply insist that all quantified "John is going to New York" as if It were somsthing like formulas have an additional element expressing the "There is an event wh/~h Is a going of John co New restriction of the quantifier. '~ost P's are Q" will York": thus be represented by (soME E (EVENT E) (GO E JOHN mY)) (HOST X (F X) (q X)). Davidson's for this analysis are that (1) many Following thls convention gives us a uniform treatment adverbial modifiers such as "quickly" are best regarded for determined noun phrases: as predicates of the events and that 42) it is possible co refer to the event explicitly in subsequent "Most men are mortal" (MOST X (4 X) (MORTAL X)) discourse. ("John is going co New York. Th...~etrip will "Some man is mortal" (SOME X (MAN X) (MORTAL X)) take four hours.") "Every man Is mortal" (EVERY X (MAN X) (MORTAL X)) "The man iS mortal" (THE X (MAN X) (MORTAL X)) The problem wlth Davidson's proposal is that for "Three men are mortal" (3 x (HA. X) (MORTJU. X)) sentences in which these phenomena do not arise, the representation becomes unnecessarily complex. We Note that we treat "the" as a quantifier, on a par therefore suggest introducing an event abstraction wlth "some" and "every." "The" is often treated operator, EVABS, chat will allow us to introduce event formally as an operator chat produces a complex singular variables when we need them: term, but thls has the disadvantage of not indicating clearly the scope of the expression. (P Xl ... X.) <-> (SOME E (EVENT E) ((gVABS F) E xl ... xn)) A final point about our basic framework Is that most common nouns will be interpreted as relations In simple cases we can use the more straightforward rather than functions in logical form. That is, even If form. The logical form of "John is kissing Mary" would we know that a person has only one height, we will simply be (KISS JOHN MARY). The logical form of "John represent "John's height is 6 feet" as is gently kissing Mary," however, would be

(HEIGE'£ JOHN (FEET 6)) (SOME Z (EVENT E) (AND ((EWSS KZSS) Z JoHN ~Y) rather than (GENTLE E))))

119 If we let EVABS apply to complex predicates syntactic distinctions that -.,st be taken into account (represented by LAMBDA expressions), we can handle other before tense can be mapped into time correctly. Stative problems as well. Consider the sentence "Being a parent verbs express present time by means of the simple caused John's nervous breakdown." "Parent" Is a present tense, while action verbs use the present relational noun; thus, if John is a parent, he must he progressive. Compare: the parent of someone, but if John has several children we don't want to he forced into asserting chat beinS the John kisses Mary (normally habitual) parent of any particular one of them caused the John is kissln 8 Mary (normally present time) breakdown. If we had PARENTI as the monadic properry of John owns Pido (normally present time) bein S a parent, however, we could say John is owning Fido (unacceptable) (SOME E (EVENT E) This is why (KISS JOHN MARY) represents "John is klsslns (Am) ((EVABS PARENTL) E JOHN) Mary," rather than "John kisses Mary," which would (CAUSE E "John's nervous breakdown"))) nor~slly receive a dispositional or habitual interpretation. We don't need tO introduce PARENTI explicitly, however, if we simply substitute for It the expression, What temporal operators will be needed? We will use the operator AT to assert that a certain condition (LAMBDA X (SOME Y (PERSON Y) (PARENT X Y))), holds at a certain time. PAST and FUTURE will be predicates on points in time. Sinq~le past tense which would give us statements with sCaCive verbs, such a8 "John was in New York," could mean either that John was in New York at (SOME E (EVENT E) some unspecified time In the past or at a coutexcua/ly (AND ((EVANS (LAMBDA X (SOME Y (PERSON Y) specific time in the past: (PARZNT x z)))) Z (SOME T (PAST T) (AT T (LOt JOHN NY))) JOHN) (TME T (PAST T) (AT T (LOC JOHN NY))) (CAUSE E "John's nervous breakdown"))) (For the second expression to be an "official" lo~tcal- Another important question is whether actions---chat form representation, the incomplete definite reference is, events wlth agents--should be treated differently would have to be resolved.) Simple future-tense from events without agents and, if so, should the agent statements with sCaCive verbs are parallel, with PUTI~ be specially indicated? The point is that, if John replacing PAST. Explicit temporal modifiers are kissed Mary, that £s somethlnS he did, but not generally treated as additional restrictions on the time necessarily something sh....~e did. Zt is not clear whether referred to. "John was in New York on Tuesday" aright be this distinction should be represented at the level of (on at least one interpretation): logical form or is rather an inference based on world knowledge.. (SOME T (AND (PAST T) (DURING T TUESDAY)) (AT ~ (C0C JoHN ~)))) Finally, most AS work on actions and events assumes that they can be decomposed into discrete steps, and For action verbs we get representations of tkts 8oft for that their effects can be defined in terms of S final past and future progressive tenses; e.g., "John was state. Neither of these assumptions is appropriate for kissing Mary" becomes continuous processes; e.g., "The flow of water continued to flood the basement." What the logical form for such (THE T (PAST T) (AT T (KISS JOHN ~.lY))) statements should look like seems co be a completely open question. 6 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

VI TIME AND SPACE (SOME E (EVENT E) ((EVABS KZSS) E JOHN MAEY))

Since logically this formal expression means something We believe that information about time is best llke "There is (presently) an event which is a kissing represented primarily by sencential operators, so that of Mary by John," we will interpret the prnd£caCe EVENT the logical form of a sentence like "John is in New York as being true at s particular time of the events in at 2:00" would be somethln S likm progress at that time. To tie all this together, "John (AT 2:00 (LOt JOHN NY)). There are two main reasons for was kissing Mary gently '' would be represmnced by following chls approach. First, current time can be indicated simply by the lack of any operator; e,g. , (THE T (PAST T) "John owns Fido" becomes simply (OWNS JOHN FIDO)o This (AT T is especially advantageous in baslcsily static dowalns (soME E (EVY~T E) in which tlme plays a minimal role, so we do not have to (AND ((EVABS KISS) ~. JoHN MAltY) put someChln S into the logical form of a sentence chat (GENTLE E))))) will be systemetically ignored by lower-level processing. The other advantage of this approach is Tha major unsolved problem relecing to time se ams that temporal operators can apply Co a whole sentence, to be recouc-tlius statemancs chat refer co points in rather than Just to a verb. For instance, in the time with those that refer co intervals--for instance, preferred reading of "The President ha8 lived in the "The colpany earned $5 m4111on in March." This White House since 1800," the referent of "the President" csrtainIy does not moan that st every point in time changes with the time contexts involved in evaluatin S during March the company earned $5 auLlliou. One could the of the sentence. The other reading can be invent a repreesucaciou for sentences about intervals obtained by allowing the quanclfier "the" in "the with no particular reletiou Co the representation for President" to assume a wider scope than that of the sentences about points, but then we would have the temporal operator. difficult task of constantly having to decide which representation is approp rlace. This Is further Although we do not strongly dlstlnsulsh action complicated by the fact that the same event, e. S. the verbs from stative verbs semantically, there are American Rmvolutlon, could be viewed as dofin/J~ either

120 a point in time or an interval, depending on the time moreover, string concatenation applies equally to scale being considered. 7 ("At the time of the American strings of one character or more than one. Collective Revolution, France was a--'monarchy," compared wlth entities have these features in common with strings, but "During the American Revolution, England suffered a share with sets the properties of being uoordered and decllne in trade.") One would hope that there exist not having repeated elements. systematic relationships between statements about points in time and statements about intervals that can be The theory we propose has a set formation exploited in developin B a logical form for tensed operator COMB Chat takes any number of arguments. The sentences. There is a substantial literature in arguments of COMB may be individuals or sets of devoted to "tense logic" [Rescher individuals, and the value of COMB is the set chat and Urquhart, 1971] [McCawley, 1981], but almost all of contains all the individual arguments and all the thls work see s: to be concerned wlth evaluating the elements of the set arguments; thus, truth of sentences at points, which, as we have seen, cannot be immediately extended to handle sentences about (COMB A iS C} D {E F C}) = {A S C D E F G} intervals. (The notation using braces is NOT part of the logical- We include space under the same heading as tlme form language; this example is Just an attempt to because a major question about space Is the extent to illustrate what COMB means in terms of more conventional which Its treatment should parallel that of time. From concepts.) If A is an individual, (COMB A) is elmply A. an objective standpoint, it is often convenient to view physical space and time together as a four-dlmenslonal We need one other special operator to handle Euclidean space. Furthermore, there are natural- definitely determined plural noun phrases, e.g., "the language constructions that seem best interpreted as American ships." The problem is that in context this asserting that a certain condition holds in a particular may refer to some particular set of American ships; place ("In California it is legal to make a right turn hence, we need to recognize it as a definite reference on a red light"), Just as time expressions often assert that has to be resolved. Following Weber [1978], We that a condition holds at a particular time. The will use the notation (SET X P) to express a predicate question is how far this analogy between space and time on sets that is satisfied by any set, all of whose can be pushed. 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) ...) VlI COLLECTIVE ENTITIES AND SUBSTANCES It might seem that, to properly capture the meaning of plurals, we would have to limit the extension of Most representation schemes are designed to express (SET X P) to sets of two or more elements. This is not information about such discrete, well-individuated always appropriate, however. Although "There are ships objects as people, chairs, or books. Not all objects in the Med," might seex to mean "The set of ships in the are so distinct, however; collections and substances Med has at least two members," the question "Are there seem to pose special difficulties, Collections are any ships in the Med?" does not mean "Does the set of often indicated by conjoined noun phrases. If we say ships in the Mad have at least two members?" The answer "Newell and Simon wrote Human Problem Solving," we do to the former question is yes, even if there is only one not mean that they each did it individually (cf. ship in the Mediterranean. This suggests Chat any "Newell and Simon have PhDs."), rather we mean that they the plural carries to the effect that did it as a unit. Furthermore, if we want the treatment more than one object is involved may be a matter of of this sentence to be parallel to chat of "~ulne wrote Gricean lmplicature ("If he knew there was only one, why Word and Object," we need an explicit representation of didn't he say so?") rather than semantics. Similarly, the unit "Newell and Simon," so that It can play the the plural marking on verbs seams to be Just a syntactic same role the individual "~ulne" plays in the latter reflex, rather than any sort of plural operator. On the sentence. These considerations create difficulties in latter approach we would have to take "Who killed Cock sentence interpretation because of the possibility of Robin?" as amblBuous between a singular and plural between collective and distributed readings. reading, since sinBular and plural verb forms would be Thus, "Newell and Simon have written many papers," might semantically distinct. mean that individually each has written many papers or that they have jointly coauthored many papers. The To illustrate the use of our notation, we will problems associated with conjoined noun phrases also represent "Every one of the men who defeated Hannibal arise with plural noun phrases and singular noun phrases was brave." Since no one defeated Hannibal that are inherently collective. "John, Bill, Joe, and individually, this mast be attributed to a collection of Sam," "the Jones boys," and "the Jones String Quartet" men: may all refer to the same collective entity, so that an adequate logical-form representation needs to treat them (soHE T (PAST T) as much alike as possible. These iss,--S are treated in (AT T detail by Webber [1978]. (EVERY X (THE S (AND ((SET Y (MAN Y)) S) (DEFEAT S HANNIBAL)) The most obvious approach to handling collective (MzMB x s)) entities is to treat them as sets, but standard set (EEAVE x) ))) theory does not provide quite the right logic. The interpretation of "and" in "the Jones boys and the Smith Note Chat we can replace the plural noun phrase "the men girls" would be the union of two sets, but in "John and who defeated Hannibal" by the singular collective noun Mary" the interpretation would be constructing a set out phrase, "the Roman army," as in "Everyone in the Romeo of two individuals. Also, the distinction made in set army was brave": theory between an individual, on one hand, and the singleton sat containing the individual, on the other, (SOME T (PAST T) semas totally artificial in thls context. We need a (AT T "flatter" kind of structure than is provided by standard (EVERY X (THE S (AND (ARMY S) (ROMAN S)) . The usual formal treatment of strings is a (Mz~ x s)) useful model; there is no distinction made between a (BRAVE X)))) character and a string Just one character lens;

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)) The only types of utterances we have tried Co is replaced by (AND (ARMY S) (RO~.~N S)). represent in logical form to this point are assertions, but of course there are other speech acts as well. The Collective entities are not the only objects that only two ve will consider •re questions and imperatives are difficult to represent. Artificial intelligence (commands). Since performatives (promises, bets, representation schemes have notoriously shied away from declarations, etc.) have the •ate syntactic form •s mass quencitie• and substances. ([Hayes, 1978] Is a assertions, it appears that they raise no new problems. notable exception.) In a sentence like "All Eastern We will also concern ourselves only wich the literal coal contains soma sulfur," it see,." tb•[ "coal" and expressed by an utterance. Dealing wlth "sulfur" refer to properties of samples or pieces of indirect speech acts does noc seem to change the range "stuff." We might paraphrase thls sentence as "All of representations needed; sometimes, for example, we pieces of stuff that are Eastern coal contain soue stuff may simply need to represent what is literally an that Is sulfur." If we take this approach, then, In assertion as somachlng lnc•nded as a command. interpreting a sentence like "The Universe Ireland Is carrying |00,000 barrels of Saudi light crude," we need For question•, we would like to have a uniform co indicate that the "piece of stuff" being described is treatment of both the yes/no and WH forms. The simplest the maximal "piece" of Saudl light crude the shlp is approach is co regard the semantic content of a WH carrying. In other cases, substances seem to be more question to be a predicate whose extension is being llke abstract individuals, e.g., "Copper is the twenty- sought. This does noc address the issue of what is a ninth element in the periodic table." Nouns that refer satisfactory answer to • question, but we regard that as Co substances can also function as do plural noun part of the theory of speech acts proper, rather than a phrases in their ~eneric use: "Copper is [antelopes are] question of logical form. We will introduce the abundant in the American southwest." operator WHAT for constructlng complex set , 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: Vlll PROPOSITIONAL ATTITUDES AND MODALITIES (WHAT X (AND (SHIP X) ~.MERICAN X)) (LOC x ~zD)) Propositional attitudes and modalities are discussed together, because they are both normally WHAT is conveniently mnemonic, since we can represent treated as intensional sentential operators. For "who" as (WHAT X (PERSON X) .... ), "when" as instance, to represent "John believes Chat the Fox is in (WHAT X (TZHZ X) .... ), and so forth. "How many" Naples," we would have an operator BELIEVE that takes questions will be treated a• questioning the quantifier. "John" as its first argunmnt and the representation of '~lov many men •re mortal?" would be represented a• "The Fox is in Naples" as Its second argument. S£,,tlarly, to represent '*the Fox might be in Naples," we (WHAT N (Nb~mZR N) could apply an" operator POSSIBLE to the representation (N X (MAN X) (MOZTAL X))) of "The Fox is in Naples." This approach works particularly well on a number of problems involving Yes/no questions can be handled •s • degenerate quanCifiers. For example, "John believes someone is in case of WH questions by treating a •s a O- the basement s' possesses an ambiguity that is revealed by ary predicate. Since the exC•ueion of •n n-sty the two par•phrases, "John believes there is someone in predicate is a set of n-tuples, the extension of a the basement" and "There is someone John believes Co be proposition would be a set of 0-~uples. There is only in the basement." As chess paraphrases suggest, thls one 0-tuple, the e~ty topis, so there •re only two distinction is represented by different relative scopes po•slble s•ts of O-~uple•. Th•se are the singleto~ set of the belief operator and the existential quantifier containing the empty topis, and the empty set, which we introduced by the indefinite pronoun "someone": can identify wlth the truth values TRUE and FALSE. The logical form of a yes/no question wlth Che proposition P (BELIEVE JOHN (SOME X (PERSON X) (LOC X BASEMENT))) as its S'mantic content would be (WHAT () TEUE P), or more simply P. (SOME X (PERSON X) (BELIEVE JOHN (LOC X ~N~S~IENT))) With regard to imperatives, It is less clear what This approach works very well up to a point, but type of semantic object Chair content should be. We there •re cases It does not handle. For exanple, might propose that It l• a proposition, but ve then have sometimes verbs like "believe" do not take a sentenc• a• Co account for the fact that not •ll are • n •rs~menc, but rather a of a sentence, acceptable as commands. For instance, John cannot be e.g., "John believes Goldbach's conjecture." TF we were commanded "Bill go to New York." The respon•e that a to make "believe" a predicate rather than a sentence person can only be "commanded somechlng" he has control operator to handle this type of ~m?le, the elegant over is not adequate, because any proposition can be semantics chat has been worked ouC for "quanc£fylng In" converted into a command by the verb "sake"--e.g., "Make would completely break down. Another alternative is to Bill So Co New York." introduce a predicate TIUE co map s descriptio n of a sentence into • sentence that necessarily has the smse The awkwerdnas• of the phrasing "command someone truth value. Than "John believes Coldbach's conjecture" somathlng" suggests another approach. One cmmands is treated •s If It were "John belleves of Coldbach's sos'one Co d.~o something, and the thinks that are done conjecture that It is true." This is dlsc£nSulshed in are actions. If actions are treated as objects, we can ch~ usual way from "John believes that Coldbach's d•flne a relation DO chat map• •n agent sad an action --~-c~nJecture (whatever It may be) is true" by reversing into a proposition (See [Moore, 1980]). "John is going the scope of the description "Goldbach's conjecture" and Co New York" would then be represented by the operator "believe." (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 particularly Barbara Grosz, SCan Rosenscheln, and Gary above as predicates on events ("Co quickly"), dendrix. Jane Robinson, Jerry Hobbs, Paul Martin, and quantiflers ("Go to every room in the house"), and Norman Haas are chiefly responsible for the negation ("Don't go"). implementaClon of the DIALOGIC system, building on earlier systems co which Ann Robinson and Bill Paxcon A third approach, which we feel is actually the made major contributions. This research was supported most promising, is to treat the semantic content of an by the Defense Advanced Research Projects Agency under imperative as being a unary predlcace. The force of an Contracts N00039-80-C-0645 and N00039-80-C-0575 with the imperative 18 that the person to whom the command is Naval Electronic Systems Command. 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 NOTES 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: I Although our immediate aim is to construct a theory of natural-language processing rather than truth- (LAMBDA X (MAKE X (GO gILL mY)), conditional semantics, It is worth noting that a system of logical form wlth a well-deflned semantics which would be the semantic content of the command "Make constitutes a bridge between the two projects. If we Bill go to New York." have a processing theory that associates English sentences with their logical forms, and if those loKical This approach does away wlth the problem concerning forms have a truth-~ondltional semantics, then we will adverbial modifiers or quantlflers In commands; they can have specified the semantics of the English sentences as simply be part of the proposition from which the well. predicate is formed. A final piece of evidence favoring thls approach over a theory based on the notion of 2 In other papers (e.g., [Montague, 1974b]), Montague action is that some imperatives have nothing at all to himself uses an intenslonal logic in exactly the role we do wlth actions directly. The semantic content of propose for logical form--and for much the same reason: commands llke "Be good" or "Don't be a fool" really does 'We could ... introduce the semantics of our fraKment seem to consist exclusively of a predicate. [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 X CONCLUSION showing in a rigorous way how to translate it into the artificial language. This Is the procedure we shall adopt;..." [Montague, 1974b, p.256]. In a paper that covers such a wide range of disparate topics, it is hard to reach any sweeping 3 The DIALOGIC system does build such a representation, general conclusions, but perhaps a few remarks about the or at least components of one, as an intermediate step nature and current status of the research program are in in deriving the logical form of a sentence. order. First, it should be clear from the issues discussed that at least as many problems remain in the 4 This suggests chac our logical forms are quest for logical form as have already been resolved. representations of what David Kaplan, in his famous Considering the amount of effort that has been expended unpublished paper on demonstratives [Kaplan, 1977], upon natural-language semantics, this is somewhat calls the content of a sentence, as opposed to Its surprising. The reason may be that relatlvely few character. Kaplan introduces the content/character researchers have worked in thls area for its own sake. distinction to sort out puzzles connected wlth the use Davldeon's ideas on action sentences, for instance, of demonstratives and Indaxlcals. He notes that there raised some very interesting points about logical form-- are at least two different notions of "the meaning of a but the major debate Ic provoked in the philosophical sentence" that conflict when indexical expressions are llcerature was about the metaphysics of the of used. If A says to B, "I am hungry," and g says to A, action, noc about the semantics of action sentences. "~ am hungry," they have used the same words, but in one Even when semantics is a major concern, as in the work sense they mean different things. After all, it may be of Montague, the emphasis is often on showing chat the case that what A said is true and what B said is relatively well-understood subareas of semantics (e.g., false. If A says to g, "~ am hungry," and B says to A, quantificaclon) can be done in a parClcular way, rather "You are hungry," they have used different words, but than on attempting to take on really new problems. mean the same thing, that A is hungry. This notion of "meaning different things" or "meaning the same thing" An additional difficulty is that so much work has is one kind of meaning, which Kaplan calls "content." been done in a fragmentary fashion. It is clear that There Is another sense, though, In which A and g both the concept of action is closely related to the concept use the words "I am hungry" with the same meanlng, of time, but it is hard to find any work on either namely, that the same rules apply to determine, in concept that takes the other one seriously. To build a context, what content is expressed. For thls notion of language-processlng system or a theory of language meaning, Kaplan uses the term "character." Kaplan's processing, however, requires an integrated theory of notion, therefore, is that the rules of the language logical form, not Just a set of incompatible fragmentary determine the character of a sentence--whlch, in turn, theories. Our conclusion, then, is chac if real together wlth the context of utterance, determines the progress is to be made on understanding the logical form content. If ~ broaden the scope of Kaplan's theory to of natural-language utterances, it must be studied in a include the local pragmatic indetermlnacles we have unified way and treated as an important research problem discussed, it seems Chec the way they depend on context in its own right. 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. ACKNOWLEDGEMENTS 5 It should be obvious from the example that nouns referring to unlCs of measure--e.g., "feet"--are an The ideas in this paper are the collective result exception co the general rule. We treat types of of the efforts of a large number of people at SRI, quanCitles, such as distance, weight, volume, time

123 duracioo, etc., as basic conceptual categories. Linaulsclcs , Universlcy of Pennsylvania, Following Hayes [1979], unlCs such as feet, pounds, Philadelphia, Pennsylvania, pp. i-5 (19-22 June gallons, and hours are considered to be functions from 1980). 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 Kaplan, D. [1977] "DemonsCratlves, An Essay on the quantity of an appropriate type. Where a word llke SemonCics, Logic, HeCaphysics and EpisCemology of "welghc" serves in English to refer co both the relaClon DemonsCratlves and OCher Indexlcals," unpublished and the quantity, we must be careful Co dlsClngulsh manuscrlpc (March 1977). 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 McCawley, J. D. [1981] Everything chac Llnsuiscs Have comparatives llke "greater than" as molcidomain AlwaTs Wanted co Know AbouC~bu...~CWere Ashamed relaclons, working with any two quanciCles of the same to Ask (UnlverslCy of Chicago Press, Chicago, type (or wich pure numbers, for chac matter). Illinois, 1981).

6 Hendrix [1973], Rieger [1975], Hayes [1978], and McDermott [1981] have all dealt with conClnuous MoDermocc, D. V. [1981] "A Temporal Logic for Reasoning processes co some extent, buc none of them has about Processes and Plans," keearch Keporc 196, considered specifically how language expresses Yale University, Department of CompuCer Science, information about processes. New Haven, Connecticut (March 1981).

7 This point was impressed upon me by Pat Hayes. Moncague, R. [1974a] "English as a ," in Formal Philosophy, Selected Papers of Richard MoncaSue, R. H. Thomason, ed., pp. 18~21 ('-~al~ REFERENCES University Press, New Haven, Connecticut, and London, England, 1974).

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