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 language be 
computationally plausible? Or, to put it another way, 
is the view of linguistic meaning as a relation between 
expressions of a natural language and things (objects, 
properties, etc.) in the world, as opposed to a 
relation between expressions and procedures in the head. 
consistent with a computational approach to 
understanding natural language? The model theorist must 
either claim that the answer is yes, or be willing to 
admit that humans transcend the computatlonally feasible 
in their use of language? 
Until recently the only model theory of natural language 
that was at all well developed was Montague Grammar. 
Unfortunately, it was based on the primitive notion of 
"possible world" and so was not a realist theory, unless 
you are prepared to grant that all possible worlds are 
real. Montague Grammar is also computatlonally 
intractable, for reasons to be discussed below. 
John Perry and I have developed a somewhat different 
approach to the model theory of natural language, a 
theor~ we call "Situation Semantics". Since one of my 
own motivations in the early days of this project was to 
use the insights of generalized racurslon theory to find 
a eomputatlonally plausible alternative to Montague 
Grammar, it seems fitting to give a progress report 
here. 
I. MODEL-THEORETIC SEMANTICS "VERSUS" 
PROCEDURAL SEMANTICS 
First, however, l can't resist putting my two cents 
worth into this continuing discussion. Procedural 
semantics starts from the observation that there is 
something computational about our understanding of 
natural language. This is obviously correct. Where 
some go astray, though, is in trying to identify the 
meaning of an expression with some sort of program run 
in the head. But programs are the sorts of things to 
HAVE meanings, not to BE meanings. A meaningful program 
sets up some sort of relationship between things - 
perhaps a function from numbers to numbers, perhaps 
something much more sophisticated. But it is that 
relation which is its meaning, not some other program. 
The situation is analogous in the case of natural 
language. It is the relationships between things in the 
world that a language allows us to express that make a 
language meaningful. It is these relationships that are 
identified with the meanings of the expressions in model 
theory. The meaningful expressions are procedures that 
define these relations that are their meanings° At 
least this is the view that Perry and I take in 
situation semantics. 
With its emphasis on situations and events, situation 
semantics shares some perspectives with work in 
artificial intelligence on representing knowledge and 
action (e.g., McCarthy and Hayes, 1969), but it differs 
in some crucial respects. It is a mathematical theory 
of linguistic meaning, one that replaces the view of the 
connection between language and the world at the heart 
of Tarski-style model theory with one much more like 
that found in J.L. A-stln's "Truth". For another, it 
takes seriously the syntactic structures of natural 
language, directly interpreting them without assuming an 
intermediary level of "logical form". 
2. A COMPUTATION OBSTRUCTION AT THE CORE OF 
~IRST-ORDER LOGIC 
The standard model-theory for first-order logic, and 
with it the derivative model-theory of indices 
("possible worlds") used in Montague GrA~r is based on 
Frege'a supposition that the reference of a sentence 
could only be taken as a truth value; that all else 
specific to the sentence is lost at the level of 
reference. As Quine has seen most clearly, the 
resulting view of semantics is one where to speak of a 
part of the world, as in (1). is to speak of the whole 
world and of all things in the world. 
(I) The dog with the red collar 
belongs to my son. 
There is a philosophical position that grows out of this 
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 
involves a universal quantification over all objects in 
the domain of discourse is doom"d by facts of ordinary 
discourse, e.g., the fact that I can make a statement 
llke (I) in a situation to describe another situation 
without making any statement at all about other dogs 
that come up later in a conversation, let alone about 
the dogs of Tibet. 
Logicians have been all too ready to dismiss such 
philosophical scruples as irrelevant to our task-- 
especially shortsighted since the same problem is well 
known to have been an obstacle in developing recurslon 
theory, both ordinary recur sion theory and the 
generalizations to other domains like the functions of 
finite type. 
We forget that only in 1938, several years after his 
initial work in recurslon theory, did K/eene introduce 
the class of PARTIAL recurslve functions in order to 
prove the famous Zecurslon Theorem. We tend to overlook 
the significance of this move, from total to partial 
functions, until its importance is brought into focus in 
other contexts. This is Just what happened when Kleene 
developed his recurslon theory for functions of finite 
type. His initial formulation restricted attention to 
total functlons, total functions of total functlons, 
etc. Two very important principles fail in the 
resulting theory - the Substitution Theorem and the 
First Recurslon Theorem. 
This theory has been raworked by Platek (1963), 
Moschovakls (1975), and by Kleene (1978, 1980) using 
109 
partial functions, partial functions of partial 
functions, etc., as the objects over which computations 
take place, imposing (in one way or another) the 
following constraint on all objects F of the theory: 
Persistence of Computations: If s 
is a partial function and F(s) is 
defined then F(s') m F(s) for every 
extension s" of a. 
In other words, it should not be possible to invalidate 
s computation that F(s) - a by simply adding further 
information to s. To put it yet another way, 
computations involving partial functions s should only 
be able to use positive information about s, not 
information of the form that s is undefined at this or 
that argument. To put it yet another way, F should be 
continuous in the topology of partial information. 
Computatlonally, we are always dealing with partial 
information and must insure persistence (continuity) of 
computations from it. But thls is just what blocks a 
straightforward implementation of the standard model- 
theory--the whollstic view of the world which it is 
committed to, based on Frege's initial supposition. 
When one shifts from flrst-order model-theory to the 
index or "possible world" se~antics used in ~ionta~e's 
semantics for natural language, the whollstlc view must 
be carried to heroic lengths. For index semantics must 
embrace (as David Lewis does) the claim that talk about 
a particular actual situation talks indirectly not Just 
about everything which actually exists, but about all 
possible objects and all possible worlds. And It is 
just thls point that raises serious difficulties for 
Joyce Friedman and her co-workers in their attempt to 
implement ~iontague Grammar in a working system (Friedman 
and Warren, 1978). 
The problem is that the basic formalization of possible 
world semantics is incompatible wlth the limitations 
imposed on us by partial information. Let me illustrate 
the problem thec arises in a very simple instance. In 
possible world semantics, the meaning of a word llke 
"talk' is a total function from the set I of ALL 
possible worlds to the set of ALL TOTAL functions from 
the set A of ALL possible individuals to the truth 
values 0, i. The intuition is that b talks in 'world" i 
if 
meaning('talk')(1)(d) - i. 
It is built into the formalism that each world contains 
TOTAL information about the extensions of all words and 
expressions of the language. The meaning of an adverb 
llke "rapidly" is a total function from such functions 
(from I into Fun(A,2)) to other such functions. Simple 
arithmetic shows that even if there are only I0 
individuals and 5 possible worlds, there are 
(iexpSO)exp(iexpSO) such functions and the specification 
of even one is completely out of the question. 
The same sorts of problems come up when one wants Co 
study the actual model-theory that goes wlth MontaEue 
Semantics, as in Gallin's book. When one specifies the 
notion of a Henkln model of intenslonal logic, it must 
be done in a totally "impredlcatlve" way, since what 
constitutes an object at any one type depends on what 
the objects are of other types. 
For some time I toyed with the idea of giving a 
semantics for Hontasue's logic via partial functions but 
attempts convinced me that the basic intuition behind 
possible worlds is really inconsistent wlth the 
constraints placed on us by partial information. At the 
same tlme work on the semantics of perception statements 
led me away from possible worlds, while reinforcing my 
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. 
3. ACTUAL sITUATIONS AND SITUATION-TYPES 
The world we perceive a-~ talk about consists not just 
of objects, nor even of just objects, properties and 
relations, hut of objects having properties and standing 
in various relations to one another; that is, we 
perceive and talk about various types of situations from 
the perspective of other situations. 
In situation semantics the meanlng of a sentence is a 
relation between various types of situations, types of 
discourse situations on the one har~ and types of 
"subject matter" sltuatio~s on the other. We represent 
various types of situations abstractly as PARTIAL 
functions from relations and objects to 0 and I. For 
example, the type 
s(belong, Jackie, Jonny) = 1 
s(dog, Jackie) " l 
s(smart, Jackle) = 0 
represents a number of true facts about my son, Jonny, 
and his dog. (It is important to realize that s is 
taken to be a function from objects, properties and 
relations to 0,I, not from words to 0,Io) 
A typical sltuatlon--type representing a discourse 
situation might be given by 
d(speak, Bill) = I 
d(father, Bill, Alfred) - i 
d(dog, Jackle) " I 
representing the type of discourse situation where Bill, 
the father of Alfred, is speaking and where there is a 
single dog, Jackie, present. The meaning of 
(2) The dog belongs to my son 
is a relation (or ,-tlti-valued function) R between 
various types of discourse situations a~d other types of 
situations. Applied to the d above R will have various 
values R(d) including s" given below, but not including 
the s from above: 
s'(belong, Jackie, Alfred) m 1 
s'(tall, Alfred) = i. 
Thus if Bill were to use this sentence in a situation of 
type d, and if s, not s', represents the true state of 
affairs, then what Bill said would be false. Lf s" 
represents the true state of affairs, then what he said 
would be true. 
Expressions of a language heve a fixed llngulstlc 
meanlng, Indepe-~enC of the discourse situation. The 
same sentence (2) can be used in different types of 
discourse situations to express different propositions. 
Thus, we can treat the linguistic meaning of an 
expression as a function from discourse si~uatlon types 
to other complexes of objects a -a properties. 
Application of thlS function to a partioular discourse 
situation type we call the interpretation of the 
expression. In particular, the interpretation of a 
sentence llke (2) in a discourse situation type llke d 
iS a set of various situation types, including s* shove, 
but not including s. This set of types is called the 
proposition expressed by (2). 
Various syntactic categories of natural language will 
have various sorts of interpretations. Verb phrases, 
e.g., will be interpreted by relations between objects 
and situation types. Definite descriptions will he 
interpreted as functions from situation types to 
individuals. The difference between referential and 
attributive uses of definite descriptions will 
correspond to different ways of using such a function, 
evaluation at s particular accessible situation, or to 
constrain other types within its domain. 
ii0 
4. A FRAGMENT OF ENGLISH INVOLVING DEFINITE AND 
INDEFINITE DESCRIPTIONS 
At my talk I will illustrate the ideas discussed above 
by presenting a grammar and formal semantics for a 
fragment of English that embodies definite an d 
indefinite descriptions, restrictive and nonrestrictive 
relative clauses, and indexlcals llke "I", "you", "this" 
and "that". The aim is to have a semantic account that 
does not go through any sort of flrst-order "logical 
form", but operates off of the syntactic rules of 
English. The fragment incorporates both referential and 
attributive uses of descriptions. 
The basic idea is that descriptions are interpreted as 
functions from situation types to individuals, 
restrictive relative clauses are interpreted as 
functions from situation types to sub-types, and the 
interpretation of the whole is to be the composition of 
the functions interpreting the parts. Thus, the 
interpretations of "the", "dog", and "that talks" are 
given by the following three functions, respectively: 
f(X) = the unique element of X if there 
is one, 
- undefined, otherwise. 
g(s) - the set of a such that s(dos, a)-I 
h(s) - the "restriction' of s to the set of 
a such that s(talk,a)-l. 
The interpretation of "the dog that talks" is Just the 
composition of these three functions. 
From a logical point of view, this is quite interesting. 
In first-order logic, the meaning of "the dog that 
talks' has to be built up from the meanings of 'the' and 
'dog that talks', not from the meanings of "the dog* and 
'that talks'. However, in situation semantics, since 
composition of functions is associative, we can combine 
the meanings of these expressions either way: f.(g.h) - 
(f.g).h. Thus, our semantic analysis is compatible with 
both of the syntactic structures argued for in the 
linguistic literature, the Det-Nom analysis and the NP-R 
analysis. One point that comes up in Situation 
Semantics that might interest people st this meeting Is 
the reinterpretaclon of composltlonality that it forces 
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 scope 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. 
REFERENCES 
I. J.L. Austin, "Truth", Philosophical Papers, Oxford, 
1961, 117-134. 
2. J. Barvise, "Scenes and other situations", J. of 
Philosophy, to appear, 1981. 
3. J. Barwise end J. Perry, "Semantic innocence and 
uncoap rom/s t~, situations", Midwest Studies in 
Philosophy V~I, to appear 1981. 
4. J. Barvise and J. Perry, Situation Se.~,ntics: A 
Mathematical Theory of Lin6uistic Meaning, book in 
preparation. 
5. J. Friedman and V.S. Warren, "A parsln8 ,us,hod for 
Hontague Grammars," IAnsulstlcs and Philosophy, 
2 (1978), 347-372. 
6. S.C. Kleene, "Recurslve functionals and quantlflers 
of finite type revisited I", Generalized gecurslon 
Theory 1__I, North Holland, 1978, 185-222; and part 
II in The Kleene S~nposium, North Holland, 1980, 1- 
31. 
7. J. McCarthy, "Programs with common sense". Semantic 
Inforwa. tlon Processing, (Minsky, ed.), M.I.T., 
1968, 403-418. 
8. R. Moo,ague, "Universal Grammar", Theorla, 36 
(1970), 373-398. 
9. Y.N. Moschovakls, "On the basic notions in the 
theory of induction", Logic, Foundations of 
Methe,aatice and Co~utabllit~" Theory, (Butts and 
Hintikka, ed), Reid, l, 1976, 207-236. 
I0. J. Perry, "Perception, action and the structure of 
bellevlng", to appear. 
II. R. Platek, "Foundations of Recursloo Theory", Ph.D. 
Thesis, Stanford University, 1963. 
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