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Home , Situation semantics

SOME COMPUTATIONAL ASPECTS OF SITUATION S~21ANTICS

Jon Barwise

Philosophy Department Stanford Unlverslty~ Stanford, California

Departments of Mathematics and Computer Science University of Wisconsin, Madison, Wisconsin

Can a realist model theory of natural be in some crucial respects. It is a mathematical theory computationally plausible? Or, to put it another way, of linguistic , one that replaces the view of the is the view of linguistic meaning as a relation between connection between language and the world at the heart expressions of a natural language and things (objects, of Tarski-style model theory with one much more like properties, etc.) in the world, as opposed to a that found in J.L. A-stln's "Truth". For another, it relation between expressions and procedures in the head. takes seriously the syntactic structures of natural consistent with a computational approach to language, directly interpreting them without assuming an understanding natural language? The model theorist must intermediary level of "". either claim that the answer is yes, or be willing to admit that humans transcend the computatlonally feasible 2. A COMPUTATION OBSTRUCTION AT THE CORE OF in their use of language? ~IRST-ORDER LOGIC Until recently the only model theory of natural language The standard model-theory for first-order logic, and that was at all well developed was . with it the derivative model-theory of indices Unfortunately, it was based on the primitive notion of ("possible worlds") used in Montague GrA~r is based on "" and so was not a realist theory, unless Frege'a supposition that the of a you are prepared to grant that all possible worlds are could only be taken as a truth value; that all else real. Montague Grammar is also computatlonally specific to the sentence is lost at the level of intractable, for reasons to be discussed below. reference. As Quine has seen most clearly, the resulting view of is one where to speak of a John Perry and I have developed a somewhat different part of the world, as in (1). is to speak of the whole approach to the model theory of natural language, a world and of all things in the world. theor~ we call "Situation Semantics". Since one of my own motivations in the early days of this project was to (I) The dog with the red collar use the insights of generalized racurslon theory to find belongs to my son. a eomputatlonally plausible alternative to Montague There is a philosophical position that grows out of this Grammar, it seems fitting to give a progress report here. view of logic, but it is not a practlc~l one for those who would implement the resulting model-theory as a theory of natural language. Any treatment of (I) that I. MODEL-THEORETIC SEMANTICS "VERSUS" involves a universal quantification over all objects in PROCEDURAL SEMANTICS the domain of is doom"d by facts of ordinary discourse, e.g., the fact that I can make a First, however, l can't resist putting my two cents worth into this continuing discussion. Procedural llke (I) in a situation to describe another situation semantics starts from the observation that there is without making any statement at all about other dogs that come up later in a conversation, let alone about something computational about our understanding of the dogs of Tibet. natural language. This is obviously correct. Where some go astray, though, is in trying to identify the Logicians have been all too ready to dismiss such meaning of an expression with some sort of program run philosophical scruples as irrelevant to our task-- in the head. But programs are the sorts of things to especially shortsighted since the same problem is well HAVE meanings, not to BE meanings. A meaningful program known to have been an obstacle in developing recurslon sets up some sort of relationship between things - theory, both ordinary recur sion theory and the perhaps a function from numbers to numbers, perhaps generalizations to other domains like the functions of something much more sophisticated. But it is that finite type. relation which is its meaning, not some other program. We forget that only in 1938, several years after his The situation is analogous in the case of natural initial work in recurslon theory, did K/eene introduce language. It is the relationships between things in the the of PARTIAL recurslve functions in order to world that a language allows us to express that make a prove the famous Zecurslon Theorem. We tend to overlook language meaningful. It is these relationships that are the significance of this move, from total to partial identified with the meanings of the expressions in model functions, until its importance is brought into in theory. The meaningful expressions are procedures that other contexts. This is Just what happened when Kleene define these relations that are their meanings° At developed his recurslon theory for functions of finite least this is the view that Perry and I take in type. His initial formulation restricted attention to situation semantics. total functlons, total functions of total functlons, etc. Two very important principles fail in the resulting theory - the Substitution Theorem and the With its emphasis on situations and events, situation First Recurslon Theorem. semantics shares some perspectives with work in artificial intelligence on representing knowledge and This theory has been raworked by Platek (1963), action (e.g., McCarthy and Hayes, 1969), but it differs Moschovakls (1975), and by Kleene (1978, 1980) using

109 partial functions, partial functions of partial 3. ACTUAL sITUATIONS AND SITUATION-TYPES functions, etc., as the objects over which computations about take place, imposing (in one way or another) the The world we perceive a-~ talk consists not just of objects, nor even of just objects, properties and following constraint on all objects F of the theory: relations, hut of objects having properties and standing Persistence of Computations: If s in various relations to one another; that is, we is a partial function and F(s) is perceive and talk about various types of situations from defined then F(s') m F(s) for every the perspective of other situations. s" of a. In situation semantics the meanlng of a sentence is a In other words, it should not be possible to invalidate relation between various types of situations, types of s computation that F(s) - a by simply adding further discourse situations on the one har~ and types of information to s. To put it yet another way, "subject matter" sltuatio~s on the other. We represent computations involving partial functions s should only various types of situations abstractly as PARTIAL be able to use positive information about s, not functions from relations and objects to 0 and I. For information of the form that s is undefined at this or example, the type that argument. To put it yet another way, F should be s(belong, Jackie, Jonny) = 1 continuous in the topology of partial information. s(dog, Jackie) " l Computatlonally, we are always dealing with partial s(smart, Jackle) = 0 information and must insure persistence (continuity) of represents a number of true facts about my son, Jonny, computations from it. But thls is just what blocks a and his dog. (It is important to realize that s is straightforward implementation of the standard model- taken to be a function from objects, properties and theory--the whollstic view of the world which it is relations to 0,I, not from words to 0,Io) committed to, based on Frege's initial supposition. A typical sltuatlon--type representing a discourse When one shifts from flrst-order model-theory to the situation might be given by index or "possible world" se~antics used in ~ionta~e's semantics for natural language, the whollstlc view must d(speak, Bill) = I be carried to heroic lengths. For index semantics must d(father, Bill, Alfred) - i embrace (as David Lewis does) the claim that talk about d(dog, Jackle) " I a particular actual situation talks indirectly not Just about everything which actually exists, but about all representing the type of discourse situation where Bill, the father of Alfred, is speaking and where there is a possible objects and all possible worlds. And It is single dog, Jackie, present. The meaning of just thls point that raises serious difficulties for Joyce Friedman and her co-workers in their attempt to (2) The dog belongs to my son implement ~iontague Grammar in a working system (Friedman and Warren, 1978). is a relation (or ,-tlti-valued function) R between various types of discourse situations a~d other types of The problem is that the basic formalization of possible situations. Applied to the d above R will have various world semantics is incompatible wlth the limitations values R(d) including s" given below, but not including imposed on us by partial information. Let me illustrate the s from above: the problem thec arises in a very simple instance. In s'(belong, Jackie, Alfred) m 1 possible world semantics, the meaning of a word llke s'(tall, Alfred) = i. "talk' is a total function from the set I of ALL possible worlds to the set of ALL TOTAL functions from Thus if Bill were to use this sentence in a situation of the set A of ALL possible individuals to the truth type d, and if s, not s', represents the true state of values 0, i. The intuition is that b talks in 'world" i affairs, then what Bill said would be false. Lf s" if represents the true state of affairs, then what he said would be true. meaning('talk')(1)(d) - i. Expressions of a language heve a fixed llngulstlc It is built into the formalism that each world contains meanlng, Indepe-~enC of the discourse situation. The TOTAL information about the extensions of all words and same sentence (2) can be used in different types of expressions of the language. The meaning of an adverb discourse situations to express different . llke "rapidly" is a total function from such functions Thus, we can treat the linguistic meaning of an (from I into Fun(A,2)) to other such functions. Simple expression as a function from discourse si~uatlon types arithmetic shows that even if there are only I0 to other complexes of objects a -a properties. individuals and 5 possible worlds, there are Application of thlS function to a partioular discourse (iexpSO)exp(iexpSO) such functions and the specification situation type we call the interpretation of the of even one is completely out of the question. expression. In particular, the interpretation of a The same sorts of problems come up when one wants Co sentence llke (2) in a discourse situation type llke d study the actual model-theory that goes wlth MontaEue iS a set of various situation types, including s* shove, Semantics, as in Gallin's book. When one specifies the but not including s. This set of types is called the notion of a Henkln model of intenslonal logic, it must expressed by (2). be done in a totally "impredlcatlve" way, since what Various syntactic categories of natural language will constitutes an object at any one type depends on what have various sorts interpretations. Verb phrases, the objects are of other types. of e.g., will be interpreted by relations between objects For some time I toyed with the idea of giving a and situation types. Definite descriptions will he semantics for Hontasue's logic via partial functions but interpreted as functions from situation types to attempts convinced me that the basic intuition behind individuals. The between referential and possible worlds is really inconsistent wlth the attributive uses of definite descriptions will constraints placed on us by partial information. At the correspond to different ways of using such a function, same tlme work on the semantics of perception statements evaluation at s particular accessible situation, or to led me away from possible worlds, while reinforcing my constrain other types within its domain. conviction that it was crucial to represent partial information about the world around us, information present in the perception of the scenes before us and of the situations in which we find ourselves all the time.

ii0 4. A FRAGMENT OF ENGLISH INVOLVING DEFINITE AND INDEFINITE DESCRIPTIONS I At my talk will illustrate the ideas discussed above I. J.L. Austin, "Truth", Philosophical Papers, Oxford, by presenting a grammar and formal semantics for a 1961, 117-134. fragment of English that embodies definite and indefinite descriptions, restrictive and nonrestrictive 2. J. Barvise, "Scenes and other situations", J. of relative clauses, and indexlcals llke "I", "you", "this" Philosophy, to appear, 1981. and "that". The aim is to have a semantic account that does not go through any sort of flrst-order "logical 3. J. Barwise end J. Perry, "Semantic innocence and form", but operates off of the syntactic rules of uncoap rom/s t~, situations", Midwest Studies in English. The fragment incorporates both referential and Philosophy V~I, to appear 1981. attributive uses of descriptions. The basic idea is that descriptions are interpreted as 4. J. Barvise and J. Perry, Situation Se.~,ntics: A functions from situation types to individuals, Mathematical Theory of Lin6uistic Meaning, book in restrictive relative clauses are interpreted as preparation. functions from situation types to sub-types, and the interpretation of the whole is to be the composition of 5. J. Friedman and V.S. Warren, "A parsln8 ,us,hod for the functions interpreting the parts. Thus, the Hontague Grammars," IAnsulstlcs and Philosophy, interpretations of "the", "dog", and "that talks" are 2 (1978), 347-372. given by the following three functions, respectively: 6. S.C. Kleene, "Recurslve functionals and quantlflers f(X) = the unique element of X if there of finite type revisited I", Generalized gecurslon is one, Theory 1__I, North Holland, 1978, 185-222; and part - undefined, otherwise. II in The Kleene S~nposium, North Holland, 1980, 1- g(s) - the set of a such that s(dos, a)-I 31. h(s) - the "restriction' of s to the set of a such that s(talk,a)-l. 7. J. McCarthy, "Programs with common sense". Semantic The interpretation of "the dog that talks" is Just the Inforwa. tlon Processing, (Minsky, ed.), M.I.T., composition of these three functions. 1968, 403-418. From a logical point of view, this is quite interesting. 8. R. Moo,ague, "Universal Grammar", Theorla, 36 In first-order logic, the meaning of "the dog that (1970), 373-398. talks' has to be built up from the meanings of 'the' and 'dog that talks', not from the meanings of "the dog* and 9. Y.N. Moschovakls, "On the basic notions in the 'that talks'. However, in situation semantics, since theory of induction", Logic, Foundations of is composition of functions associative, we can combine Methe,aatice and Co~utabllit~" Theory, (Butts and the meanings of these expressions either way: f.(g.h) - Hintikka, ed), Reid, l, 1976, 207-236. (f.g).h. Thus, our is compatible with both of the syntactic structures argued for in the I0. J. Perry, "Perception, action and the structure of linguistic literature, the Det-Nom analysis and the NP-R bellevlng", to appear. analysis. One point that comes up in Situation Semantics that might interest people st this meeting Is II. R. Platek, "Foundations of Recursloo Theory", Ph.D. the reinterpretaclon of composltlonality that it forces Thesis, Stanford University, 1963. on one, more of a top-down than a bottom-up composltionallty. This makes it much more computatlonally tractible, since it allows us to work with much smaller amount of information. Unfortunately, a full discussion of this point is beyond the of such a small paper. Another important point not discussed is the constraint placed by the requirement of persistence discussed in section 2. It forces us to introduce space-time locations for the analysis of attrlbutive uses of definlte descriptions, locations that are also needed for the semantics of tense, aspect and noun phrases like "every man', "neither dog', and the Ilk,.

5. CONCLUSION The main point of this paper has been to alert the readers to a perspective in the model theory of natural language which they might well find interesting and useful. Indeed, they may well find that it is one that they have in many ways adopted already for other reasons.

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