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I~I~RODUCTION 
The problem of explicating the meaning of natural language discourse 
and how this meaning is obtained has been of central importance 
to the study of philosophy since the time of Aristotle. This 
problem has continued to perplex philosophers, linguists, 
psychologists, and other academicians right up to this very day, 
such perplexity manifesting itself in disputes such as nominalism 
vs. realism, behaviorism vs. mentalism, logical positivism vs. 
the "ordinary-language" approach, and structuralism vs. trans- 
formationalism. Basic to this perplexity has been the lack of an 
adequate set of tools with which to formalize meaning in natural 
language, resulting in a basic split between those who use exist- 
ing tools to produce formalizations that are oversimplified and 
inadequate and those who attempt to account for the full 
complexity of natural language but, in doing so, abandon any 
attempt at formalization. Clearly, any move toward providing a 
more powerful set of tools with which to formalize the semantics 
of natural languages will have implications that will reverberate 
through a variety of academic disciplines. 
A formalization of natural language semantics that is keyed to 
the computer will have a variety of very practical applications 
as well. Two decades of research in machine translation have 
failed to produce effective systems, chiefly because machines have 
not yet been able to duplicate the translator's function of 
understanding the material in the source language and then re- 
stating it in the target language. Once computers are capable 
of analyzing natural language to a depth where it becomes 
possible to mechanically determine equivalence of meaning in 
context of statements in two different languages, and capable of 
generating well-formed natural-language discourse from such an 
analysis, mechanical translation of scientific and other expository 
2 
text will be straightforward. Information storage and retrieval 
will also be much simpler once it is possible to store and 
retrieve information by means of statements, questions, and 
c~mmands in natural language--which requires, at least, that these 
natural-language inputs be interpretable as commands to the 
storage and retrieval mechanism. Computer-assisted instruction 
will not realize its full potential until student answers can 
be evaluated with respect to their meaningful content and this 
evaluation used to generate appropriate remedial instruction 
form a body of lesson information. And most importantly, a 
capability for meaningful analysis and generation of natural 
language will make computers accessible to people for an infinite 
variety of problem-solving applications in the way which is best 
Suited to them as human beings. 
The thesis of this paper is that, as a result of recent advances 
of the state of the art in linguistics, computation, and their 
interface, we are on the verge of being able to formalize the 
semantics of natural languages for the computer in a manner 
that will be philosophically interesting, linguistically and 
psychologically revealing, and computationally useful in the 
manners just suggested. Such a formalization, it shall be argued 
here, may be based on the notion that natural language is 
basically explicable as a method of programming a particular 
kind of computer--a computer with a relational associative 
memory structure that is purposive and goal-directed in its 
actions, in the manner of a human being. 
T~ PROBLEM 
A. Requirements for a Semantic Theory 
1. A Definition of Semantics 
The term semantics is generally used to denote the system of 
relations between the expressions of a language and their mean- 
ings--in contrast to synts~x, which describes the acceptable 
structural forms of linguistic expression, and pragmatics, which 
concerns itself with the effects of communications in a language 
upon the communicants. The term "meaning" here is to be analyzed 
in terms of its particular relevance to the act of communication. 
An act of communication includes a sender who encodes a message 
into a signal (usually a string of phonetic or alphanumeric 
symbols), a channel along which the signal is sent, and a receiver 
who decodes the signal into the original message and interprets 
the message. Meaning is the functional import of the message, 
which calls forth a re sponse--cognitive~ affective, and/or 
conative--from the receiver in the partfcular communication 
situation; it is a relation of the message to the receiver. Let 
us now make the simplifying assumption that this meaning is 
determined by the functional form of the message under some 
"standard" functional interpretation (this is basically an 
oversimplification, since the rules of functional interpretation, 
especially on the affective response dimension, will vary from 
receiver to receiver and even for the same receiver over time); 
we may then define semantics as the explication of the relation- 
ship between the surface forms of linguistic utterances (as 
spatial or temporal arrangements of morphological units, which 
are the minimal linguistic units that have a direct functional 
relationship to the determination of meaning) and the functional 
forms of the messages they express. For a semantics to be 
formalized, this relationship must be sufficiently well defined 
to enable the processes of encoding and decoding to at least 
be formally explicable in terms of it, if not totally formal- 
ized within it. 
2. The Semantics of Formalized Languages 
The most successful attempts to formalize semantics have been 
for the formalized languages of the deductive sciences. Tarski, 
in his classic paper \[43\]3 has set down a systematic method 
for formalizing the semantics of a formalized language, which 
is any language for which the set of meaningful sentences is 
defined by a formal syntactic grammar, all sentences are 
unambiguous, and there is a set of (syntactically defined) 
axioms and rules of inference from which theorems in the 
language may be derived. The method involves construction of a 
metalan~uage containing expressions and axioms of a general 
logical kind, translations of the expressions and axioms of the 
language L to be characterized, and expressions and axioms 
which define the syntax of L. The notions of satisfaction and 
truth for the language L, which together constitute a semantic 
description of L, can be defined in the metalanguage M as follows: 
Given a domain D of individuals, a "semantic interpretation 
function" ~ is defined in M which assigns to each individual 
constant and individual variable of L an individual of the domain 
R, to each function letter of L of degree n m 1 a function from 
D n (the set of all ordered n-tuples of elements of D ) intoD, to 
each predicate letter of L of degree n ~ 1 an n-ary relation on 
D (defined as a subset of Dn), and to each phrase-forming rule 
of L a function Ti, which determines the semantic interpretation 
of the phrase formed in terms of the semantic interpretations of 
the constituent phrases. An n-tuple (al,...,an> of individual 
constants then satisfies the sentential function F of n free 
variables whenever ¢ (F) \[~5 (al),... ~ ~5 (an) \] = T (truth). The 
notion of truth is defined as a special case of the notion of 
satisfaction for sentential functions of zero free variables 
l 
(i.e., sentences of L). Examples of the application of the Tarski 
approach are to be found in any standard logic textbook in the 
truth-table interpretations (standard and non-standard) of the 
propositional calculus and the standard set of semantical rules 
for the first-order predicate calculus. 
The Tarski approach runs into difficulty, however, in that it 
establishes only a single notion of truth, without reference 
to the different ways in which truth may be epistemologically 
established. This becomes critical when it comes to establishing 
rules of substitutability for "oblique" or "nonextensional" 
contexts such as quotation, indirect discourse, modal sentences, 
and belief sentences, in which the unrestricted substitutivity 
of equivalence does not preserve truth-value--one must here 
define types of equivalence stronger than identity of reference, 
which is the type of semantic equivalence defined in the Tarski 
approach. It was mainly to deal with this problem that Carnap 
\[9\] proposed a method of semantic analysis called "the method 
of extension and intension." In the framework of Tarski's formu- 
lation, the method can be stated as follows: Given a "model" 
of the language L, consisting of an individual domain D and a 
semantic interpretation function ~b for L over P, the extension 
of any well-formed expression E in L is defined as the set of 
values for E of all semantic interpretation functions #' over 
P which differ from # at most on their assignments to the 
free variables of E. Now if one considers the domain of possible 
models for L, the intension of any well-formed expression E in 
L may be defined as that function over models of L which yields 
as its value for any model the extension of E in that model. 
The notion of intension may be formalized by considering the 
metalanguage translations of well-formed expressions of L to be 
intensional structures for these expressions, which, since 
intensions are funcZions, will take the form of function defini- 
tions. The translations may be defined by a translation function 
e which assigns to each individual constant, function letter, and 
predicate letter of L an appropriate function letter of the 
metalanguage M, to each variable of L a variable of M ranging over 
functions on models of L which map into the appropriate extensional 
range, and to each phrase-forming rule of L a function-definition 
operator ~i (which could be functional composition, c~nplement, 
union, intersection, iteration, transitive closure, summation, 
minimalization, etc. ). Given this definition, one can recreate 
Tarski's definition of satisfaction and truth by noting that for 
any model  . of L the corresponding semantic interpretation 
i 
function ¢i is given by ¢i (E) = \[ e (E)\] (Mi). And one can define, 
along with the ordinary notion of (extensional) equivalence, 
the notions of L-equivalence and intensional isomorphism as 
equivalence of intension and intensional structure respective- 
ly--and show, as Carnap does in \[9\], how these stronger types of 
equivalence permit the establishment of suitable substitutability 
criteria for "oblique" contexts. 
To fit the semantics of formalized languages into our general 
definition of semantics, which presupposes use of the language 
for the purpose of communication, we must introduce one more 
thing into the metalanguage, namely, the performative operators 
of asserting, questioning, and ccmmmading. We posit that the 
language L is being used to communicate between two information 
and control systems A and B, both of which possess inccmplete 
and/or changing models of L 2 corresponding to knowledge of some 
environmental situation over which both A and B can exercise 
i 
2~ote that the reference to disparate models of L (the only 
situation in which communication would ma/~e sense in this 
context) and changing models of L necessitates the use, at 
least £mplicitly, of an intensional semantics. 
certain degrees of control. Then for any sentence $ of Lj an 
assertion '$.' from A to B carries the functional import of 
instructing B to modify its model so as to make S evaluate to 
truth, a ~uestion '$?' from A to B instructs B to evaluate S 
in its model and return the result to A, and a command 'S '' 
from A to B instructs B to modify its environment (if possible 
and if necessary) so that S ~-lll evaluate to truth in the model 
of the environment so changed. The metalanguage translations 
of the assertion, question, and command signs in L will be, of 
course, the corresponding performative operators. By identify- 
ing, now, the notion of message with metalanguage translation, 
the notion of arrangement of morphological units with syntactic 
description in the metalanguage, the notion of decoding with 
the translation function e, and the notion of encoding with the 
inverse of ~, we show how the semantics of formalized languages 
meets our general requirements for a formalization of semantics. 
3- Natural Language Semantics 
We may now arrive at a set of specific requirements for a formal 
theory of natural language semantics by examining the crucial 
differences that are kno~m to exist between natural languages 
and formalized languages and noting the revisions and extensions 
of the formalized-language paradigm that are required to take 
these differences into account. This approach is indicated by 
the fact that the semantics of formalized languages represents 
the most highly-developed point of departure frc~ which to 
undertake a formal description of the real-world phenomenon of 
natural language semantics, and thus, if it indeed contains the 
potential of producing a description that fits the phenomenon, 
brings one much closer to that description than if one were to 
start with only the general definition of semantics given at 
the beginning of this section. What, then, does this approach 
indicate for the features of a revised paradigm under which the 
known properties of natural language as an instrument of 
communication may be subsumed? 
Natural languages, first of all, are used for a vastly wider 
variety of communication acts than are formalized languages. The 
messages that are communicated in natural language relate to 
virtually every area of human activity and extend to nearly every 
purpose involving some kind of human interaction. As a result, 
there is a large inventory of different types of messages that 
are expressed in natural language, each in its own particular 
way or ways. 3 The three basic types of performative operators-- 
assertion, questioning, and commanding--are subject to modifi- 
c~ion as to the manner of the request conveyed by the message 
(which indicates, among other things, the speaker' s perceived 
or intended relation to the hearer 4) and to functional combination, 
as in the case of threatening and warning, both of which combine 
commanding with asserting. A formal theory of natural language 
semantics must explicate these dimensions of the performative and 
also the relation of the performative to the notions of speaker, 
hearer, and context of utterance. 
The explication of the non-performative parts of messages as 
intensional definitions requires some extension and elaboration 
3Austin \[1\] has compiled what is perhaps the most extensive and 
systematized inventory of these message types. 
4A very interesting discussion of this aspect of communication is 
contained in Watzlawick et al \[46\]. 
I 
in order to be applicable to natural language. First, people 
carry in their memories not one model but many, corresponding 
to the many different situations that they have knowledge of. 
Thus, a message must refer either to a specific model, to a 
specific range of models, or generically to all models in which 
the specified intensions have nonempty extensions. Restricting 
the range of applicable models is accomplished in natural language 
through presuppositions, which indicate prior conditions that 
must be satisfied in a model for a given message to be applicable 
to it. Indicating generic vs. model-specific information, as well 
as "given" (for locating the appropriate model) vs. "new" (for 
adding to the model) information in the model-specific case, is 
accomplished through the subject-predicate division and through 
an extensive assortment of quantifiers. Furthermore, as Morris 
\[31, 32\] has pointed out, natural-language expressions not only 
designate but also appraise and prescribe--thus, natural-language 
intensions may take on as extensions not only objects, sets, and 
relations, but also values and actions. Natural-language inten- 
sions may also take on as extensions other intensions, thus 
giving natural language a "recursiveness" of logical order and a 
self-referential capability (which leads, naturally, to the 
classical logical paradoxes). 
Intensional definitions are also more complex in their formal 
structure for natural languages than for formalized languages. 
Intensions may be defined by specifying the combination of tests 
and results that indicate which elements of any given model 
are to be included in their extensions--these tests may be on 
either "inherent" or "contextual" attributes of the element and 
the values of these attributes may be either countable sets or 
measurements on some continuous scale. For formalized languages, 
lO 
the identification function of an intension must distinguish 
clearly and unequivocally between exemplars and non-exemplars on 
the basis of a Boolean combination of the results fo the various 
tests. For natural languages, however, tests may be either 
criterial for identification of an exemplar or else have only a 
probabilistic bearing on identification; thus, the identification 
of exemplars of natural-language intensions is by no means 
clear-cut, but rather may resemble the assignment of degrees 
of confirmation to hypotheses (with a certain "level of confidence" 
being required for identification to take place). The use in 
English of generic determiners such as 'many', 'most', 'almost 
all', and 'few', and (corresponding) intensional adverbs such as 
'co~only', 'usually', 'characteristically', and 'seldom', is 
indicative of the probabilistic nature of intensional definitionS 
±n natural language. 5 
The morphological structure of natural languages is also consider- 
ably more complex than that of formalized languages, as has been 
well recognized by contemporary linguists. The simple phrase- 
structure grammars that suffice to describe the syntax of 
formalized languages simply do not work for natural languages; 
to dascribe the surface syntactic structure of a natural language 
requires a system, such as a relational phrase-structure 
grammar (Bellert, \[4\]) or a complex-feature-symbol grammar, with 
the power of expressing the various relations of grammatical 
agreement among constituents. If the language to be analyzed 
is spoken language, the arrangements of morphological units are 
5A full analysis of these generic determiners and adverbs, their 
logical interrelationships, and their relation to notions of 
probability is given in Celce and Schwarcz \[131. A capsule 
summa~j of this analysis is presented later in this paper. 
ll 
not simply linear strings of symbols (connected by whatever 
gra~natical relations) but are, rather, two-dimensional sequences 
consisting of both segmental and suprasegmental (stress, intona- 
tion, etc. ) morphemes. Furthermore, the exact correspondence 
between gra~aatical sentences and semantically-interpretable 
sentences that obtains in formalized languages does not hold for 
natural languages, which permit of both "grammatical nonsense" 
and syntactically deviant utterances that make perfect sense--the 
first phenomenon requires a semantic theory to posit nonsyntactic 
conditions for semantic acceptability; the second, a procedure 
for syntactic error correction in decoding. 
The above are only two of the phenomena that render explication of 
the process of encoding and decoding much more complex for natural 
languages than for formalized languages. In formalized languages 
all well-formed expressions are unambiguously interpretable in or 
out of context, their interpretations are determined in a 
straightforward compositional manner by function-definition 
operators in one-to-one correspondence With the syntactic 
formation rules of the language, and performatives are represented 
as single symbols preceding or following each sentence. For 
natural language none of these properties hold--indeed, semantic 
ambiguity and anomaly, discourse structure and other forms of 
context dependence, syntactic-semantic non-correspondence, idioms 
and figures of speech, and complex encodin~s of performatives 
are all common features of natural language. Their explication 
in a semantic theory requires, first, that the correspondence 
between syntactic form and semantic function be taken as many-to- 
many rather than as one-to-one; second, that intensional "well- 
formedness" relative to the particular domain of discourse and 
applicability to the model or range of models currently under 
12 
consideration be taken as criteria for semantic acceptability in 
a discourse context; and third, that the theory specify the various 
alternative encodings of a message rather than a single encod- 
ing. There is also a need to incorporate analogical processes 
into the explications of encoding and decoding in order to account 
for the metaphorical use of language. 
Finally, there are two inherent limitations that govern any attempt 
to formalize the semantics of natural languages: one formal, 
the other eplstemological. The formal limitation is a conse- 
quence of Tarski's theorem \[43\], which states that any consistent 
and complete semantic theory of a language must be formulated in 
a metalaugua~e of higher order than the lsmguage being described. 
But since the set of theorems of any deductive system must be 
recursively enumerable, and since there are subsets of natural 
languages sufficiently powerful to define any recursively enumer- 
able set, any formalization of natural language semantics using a 
deductive logic (including the logic of computation) as a meta- 
language will be incomplete in the sense that there will be 
questions about the language 6 that are theoretically unanswerable 
in the metalanguage (one could, however, go to inductive logics 
and probabilistic metatheories as the basis for a metalanguage ). 
The epistemological limitation derives from the fact that, while 
formalized languages are uniquely defined, no two speakers of a 
natural language have quite the same idea of what their language 
is. It is clearly impossible, then, to formulate a semantic 
theory that describes all the speakers of a natural language. 
6Including~ of course, any question as to the truth-value of a 
sentence expressing a logical paradox. 
I 
13 
Neither is it practicable to attempt an "ideal speaker-hearer" 
theory that purports to explain how native speakers of a language 
"generally" assign meanings to utterances and express meanings 
through utterances 3 since validation of such a theory would be next 
to impossible. A more appropriate goal, especially in light of 
the fact that the data for any semantic theory must ultimately 
derive from the use of the language for communication, is to 
construct a theory of a "typical speaker-hearer" of the language 
in question, whose validity would then derive from the ability of 
a physical realization of the theory (e.g., as a program running 
on a digital computer) to engage in successful purposive cCm~uni- 
7 cation with native speakers of the language. 
Let us enumerate, then, the requirements for a formal theory of 
natural language semantics that have been indicated here: 
1. The theory shall be couched in a formal metalanguage. 
2. The metalanguage shall contain models of possible discourse 
contexts, expressions representing extensions, expressions 
representing intensions, and axioms defining the relation of 
extension to intension for any given model. 
3. The metalanguage shall contain expressions representing the 
messages ecmm~nicated in the natural language, which will 
contain performatives specified as to type and manner, 
intensional definitions of both fixed and recursive logical 
order with criterial and/or noncriterial components on the 
descriptive, appraisive, and prescriptive dimensions, 
presuppositions, and both generic and specific quantifiers. 
7Further reasons for preferring the "typical speaker-hearer" model 
to the "ideal speaker-hearer" model are given in Schwarcz \[38\]. 
14 
4. The metalanguage shall contain axioms characterizing the 
functional import of messages, sufficient to define both 
extensional and intensional equivalence, entailment, and 
contradiction among messages up to the limits of theoret- 
ical decidability. 
5. The metalsm~uage shall contain expressions and axioms 
defining a "standard" syntax of the language at the level 
of surface arrangements of morphological units, in terms 
of both phrase structure and relations of grammatical 
agreement. 
6. The metalanguage shall contain axioms defining the possible 
encodings of any message in any discourse context to which 
it is applicable. 
7. The metalanguage shall contain axioms defining the possible 
decodings of arrangements of morphological units that are 
~¢ell-formed in the "standard" syntax or deviate from it 
by at most a tolerable degree and determining the inten- 
sional well-formedness and applicability to a given discourse 
context of these decodings. 
8. The theory, to be validated as a description of a "typical 
speaker-hearer" of the language under consideration, must 
support a physical embodiment that is capable of engagiD~ 
successfully in purposive corm~unication with native speakers 
of the lar~uage. 
B. Computational Avenues of Approach to a Semantic Theory 
Since language is an instrument of communication and communication 
is essentially purposive, any semantic theory that one develops 
for the computer will of necessity be based, unless one is simply 
engaged in an academic exercise, on the purpose for which one 
I 
wishes to communicate with the computer in natural language. In 
15 
this section several such purposes and the sorts of semantic theory 
they have led to or are likely to lead to will be described. 
The purpose of oldest vintage is, of course, translation by 
machine from one langua£~ to another. The problem here is, 
given a discourse in one language 3 to produce a discourse in a 
second language that has the same functional import with respect 
to a model of the domain of discourse as the first. Perhaps the 
reason that no efforts in this direction have achieved notable 
success to date is that the model of the domain of discourse and 
its functional interaction with the language have generally been 
ignored in the design of translation systems. The direction that 
will lead to a breakthrough here is that of developing domain- 
specifi___.____~e (rather thau langllage-specific) translation systems for 
well-understood and formally structurable domains of discourse such 
as physics and mathematics--once a fomnal model of the subject 
matter ~id a canonical procedural language for communicating with 
that model are defined, efforts can be directed toward specifying 
the decodings of as much of the relevant natural-language subsets 
as possible into the procedural language aud reasonable encodings 
of the procedural langaago into each of the natural languages. 
Data management and infor,~ation retrieval is another purpose of 
-widespread interest. The domains of discourse to which these 
systems may apply may be arbitrarily broad or narrow; whatever 
the case, the requirements for formal structurability and a 
formal procedural language for storing and retrieving information 
in the data base are present. If the system is to do deductive 
question answering (or ~hat Travis \[~5\] has called "analytic 
information retrieval"), the system must be able to store and 
utilize the logical relationships among concepts and facts. The 
16 
problem of specifying encodings and decodings here is simpler than 
for machine translation 3 since the user may make do with a fairly 
restricted natural-language subset for input, and natural-language 
output may be generated in a canonical form if it is in fact 
necessary at all. Thus it is possible here to get by with an 
oversimplified semantic theory, but for that very reason it can 
be expected that more progress can be made sooner with this than 
with any other approach (and this has, in fact, turned out to be 
the case). 
Another purpose is the use of natural language to interface ~r'±th 
pictorial information. Here the model is a set of logical state- 
ments describing the visual image, derived by the application of 
pattern-recognition operations to the visual image. The model, 
once derived, can then be either directly encoded into a set of 
natural-language sentences or else used as a data base for 
information retrieval. An alternative approach is to decode 
natural-language retrieval statements into search procedures on 
the visual image itself, performing the pattern-recognition 
operations, then, during the execution of these search procedures. 
If the visual image is what a robot sees in its environment, the 
robot may not or, Sy be asked about what it sees but also told to 
move about in its environment and to move parts of the environ- 
ment about~ thus 3 the intensional structure of the robot's 
message language will include a prescriptive as well as a 
descriptive dimension. As in the case of data management and 
information retrieval systems, the input language can be restricted 
and the output language can be minimal, thus obviating the need 
for sophisticated fornmlations of decoding and encoding. 
17 
The use of the computer to develop models of human thought 
processes is a purpose that can lend revealing insights into the 
nature of a semantic theory. Here one starts with hypotheses 
about the structure of human memory and the information 
processes that take place there, embeds these hypotheses in a 
computer program, and runs the program to determine the conse- 
quences of these hypotheses in terms of predictions of observable 
behavior. In terms of a semantic theory, the emphasis here is 
• likely to focus on models, messages, and the pragmatic functions 
of messages on models; only limited attention is likely to be 
paid to the syntactic structure of the language, and encoding 
and decoding are likely to be formulated in a rough-and-ready 
heuristic fashion rather than in a way motivated by linguistic 
considerations. 8 Nevertheless, such models are an excellent 
way to test the workability of semantic ideas, for the models' 
linguistic poverty is compensated for in experimentation by 
their designers' linguistic flexibility--and once the innards 
are working right, they may serve as a basis for a more 
linguistically sophisticated formulation of decoding and encoding. 
A purpose incorporating both analytic information retrieval 
and psychological modeling is computer-aided instruction with 
natural language. 9 The capabilities required here are to 
semantically analyze a student's natural-language response or 
question, to compare an analyzed response to a standard "correct 
response" to determine the logical difference if any, to generate 
remedial feedback in natural language by application of "tutorial 
decision rules" to the structure representing this difference, 
8The one exception is models of linguistic performance, as 
discussed in Sehwarez \[38\]; there, of course, linguistic 
considerations are paramount from the beginning. 
9This approach to CAI is described in Bennik, Sehwarcz, and 
Silberman \[6\]. 
18 
and to answer a student's analyzed question and generate a natural- 
lar~age reply. For natural-language CAT all the components of a 
semantic theory, except perhaps for encoding, must be developed 
to their full extent with respect to the subject areas to be 
taught. The linguistic requirements are not quite so severe as 
for machine translation, since the capability of dynamic inter- 
action enables students to put up with a certain amount of rigidity 
on the machine's part and since the machine will not be required 
to analyze or generate long coherent discourses, but the require- 
ment of thorough and complete logical analysis is more demanding 
here than in any other application of a semantic theory. 
Finally, there is the purpose of enabling people to program the 
computer in natural language. Messages here are statements in a 
general-purpose progrsm~ning language which includes capabilities 
for defining both macros and closed subroutines; they will thus 
have both descriptive and prescriptive dimensions. Nouns, verbs, 
and adjectives will be decoded into either data items (if proper 
names, numbers, or truth values), primitive functions, macros, 
or closed subroutines, conjunctions and prepositions will decode 
into operators for combining program steps, adverbs will decode 
into designations of program sequencing, and quantifiers will 
decode into specifications for iterative loops. The decoding 
process will likely be some form of syntax-directed compiling, 
which exactly fits the decoding paradigm for formalized-language 
semantics, except in that the procedure may allow for a small 
degree of ambiguity. Encoding will either be completely 
standardized or else be defined in terms of a sublanguage of out- 
put specifications that may be associated in an arbitrary 
manner with computational procedures. All this assumes, however, 
that natural language is being used to program the computer in 
35 
for small western cities?' produced a ten-item request 3 and the 
question 'For the smoggy high-income cities what is the age- 
income value-range?' produced twenty separate procedural requests. 
Although most of Kellogg's e~perimentation has been performed on 
a data base of census information, his system has also been 
successfully tier prostrated with airline-schedule and educational 
data bases. 
If Kellogg's system can be f~Atlted as a semantic theory~ other 
than in its lack of a nontrivial formulation of encoding, it is 
principally in its failure to deal with certain of the require- 
ments specific to the semantics of natural languages. Chief in 
importance among these are noneriterial attributes of intensions 
(except those quantified by 'some'), recursiveness of logical 
order, the appraisive dimension of language, discourse structure 
recognition, disambiguation by discourse context, and deviations 
from standard syntax.. 14 The logic of equivalence, entailment, and 
contradiction among messages, particularly on the intensional 
side, has also not been formalized to the extent that it could be. 
In all fairness, however, it must be pointed out that few if any 
of the other current approaches to semantics have dealt with 
any of these requirements (except the last 3 for predicate-calculus- 
based systems) in a formally satisfying way. Kellogg has 
succeeded in putting together the best of current knowledge in 
linguistics, fomal semantics, and systems programming to 
develop an eminently usable formalization of English semantics 
for the computer. 
Both the linguistic and the computational formalizations of 
natural language semantics, when looked at individually, can 
be seen to fall considerably short of the requirements for a 
i Thish last item# as well as undefined words and zemantic 
anomalies, is handled by Kellogg through appropriate feed- 
back messages to the user. 
36 
semantic theory that is adequate for natural languages. When 
taken collectively, however, they contribute an enormous reser- 
voir of ideas and experience upon which one may draw in under- 
taking the formulation of an adequate semantic theory. With 
the addition of recent advances in linguistic theory, programming 
languages, and artificial intelligence to this reservoir, ~ may 
draw from it the elements that will combine to make up an 
adequate approach. Let us now look at one possible such approach. 
AN OFERI~IONAL-MEANING APPROACH TO SEMANTICS 
A. Methodological Basis 
To arrive at a formal theory of natural language semantics, we 
must start from the set of requirements enumerated earlier-- 
particularly those concerning the relation of a message to its 
functional import. Intensions are the principal components of 
• messages, and they are classified according to their values along 
the descriptive, appraisive, and prescriptive dimensions. 
Prescriptive intensions have values which are actions of the 
communicating system, and therefore can be sensibly regarded 
only as pro~ for action. Appraisive intensions have 
values which are evaluations of one kind or another; the only 
sensible way to regard these, then, is as evaluation functions. 
Descriptive intensions have values which are objects, sets of 
objects, and relations among objects, where the objects may in 
turn be intensions. Here we adopt the operationist philosophy, 
in the formulation of Benjsmin \[5\], and assert that descriptive 
intensions are functional operations on a data space which 
yield elements of knowledge as their result. 
37 
It is clear, then, that the most natural representation of 
intensions is as programs is some programming language. Since 
intensions are functions on models, the operations that 
constitute them will be performed on structures that represent 
models--and since intensions may be values of intensions, the 
structure of programs must be of the same form as the 
structures of models. Furthermore, the progran~ning system which 
interprets the language must interpret it n0ndeterministically, 
for natural language may al~rays specify alternative definitions 
of a concept, or alternative procedures for evaluation, or 
alternative ways to perform an action; with respect to the 
first, it is a fund~nental premise of modern operationism that 
one can arrive at the same item of knowledge by means of 
different operational procedures, and that, in fact, the 
utility of a concept is largely as an expression of the 
generalization that a class of different operational procedures 
produce identical results. 15 Nondeterministic operation and 
the existence of evaluation functions characterizes a class of 
artificial-intelligence programs that have been written to do 
game playing, theorem proving, and general problem solving 2 
all of which are based on the paradigm method of goal-directed 
heuristic search. A programming system based on this method of 
program operation, similar to the one that Pople \[34\] has 
recently implemented, would thus be indicated as the basis for 
an operational formalization of natural language semantics. 
Let us now turn to a sketch of how the semantics of natural 
languages might be formalized within such a system. 
15This view is expressed clearly in Bridgman \[8\]. 
38 
B. Models and Messages 
There are two basic issues to be decided in the formulation of 
any model: what information is to be contained in the model, 
and in what form that information is to be represented. In 
the formulation of a message language for conT.municating with 
the model, it must furthermore be decided what computational 
processes are to be performed in the model. A semantic theory 
will rise or fsll on the basis of the extent of information that 
can be represented in the model, the extent of information 
processing that can be formulated in the message language, and 
the ease with which translation algorithms can be formulated 
between the message language and the corresponding natural 
language subset. 
Because of its close similarity to both formal logic and the 
attribute-value list structures and relational associative 
structures that have been employed in many artificial-intelli- 
gence programs, as well as its demonstrated advantages for 
linguistic formulations, the Fillmore case structure appears to 
be the most useful starting point for representing both models 
and messages. Additional specifications must be added in to 
represent the logical features which are lacking in Fillmore's 
formulation: logical connectives, quantification and quanti- 
ficational ordering~ other function-definition operators, the 
structure of the modality constituent, etc. The inventory of 
case relations must also be completely specified and, since 
case relations are all contextual, supplemented with a set of 
inherent relations that will enter into both extensional and 
intensional description--s~ne of which, like the "spatially 
contains' relation, will be converses of the case relations 
l 
themselves. 
39 
The formal content of both intensional and extensional description 
is still largely an open question, to which the various attempts 
to formalize nattu~al language semantics can only suggest methods 
for solution. At the lowest level of semantic description, the 
actions that an operational semantic model will be able to perform 
will be computer actions and not human actions, and the evaluations 
that it will be able to make will a//nost certainly be pragmatic 
evaluations rather than aesthetic evaluations (this iS not to 
assert, however, that no way will ever be found to program a 
computer to simulate a human being's appreciation of poetry, 
art, or musi&). It is the descriptive dimension that is most 
interesting, especially since both appraisive and prescriptive 
intersions -~xe instances of second-order (or higher) descriptive 
intersiors, with the consequence that the values and actions of 
humaa beings ma~, be described in an operational semantic frame- 
work, and perhaps as a consequence also modeled by analogy 
though not applied directly. On the descriptive dimension 
Benjamin \[5\] lists the following types of operations, which we 
shall characterize as intensions with corresponding extensions: 
l° 
2. 
Inters ion 
Discriminating 
Associating 
a. Co-occurrence 
b. Temporal succession 
c. Configurational 
Extension 
Deictic references (present 
events) 
Co-occurrence classes and 
relations 
Temporal and causal relations; 
durable objects and states 
Part-whole relations; Gestalts 
~0 
3. Generalizing 
4. Ordering 
5. Measuring 
6. Analogizing and 
disanalogizing 
Supersets and class-inclusion 
relations 
Partial and total orderings 
( including enumerations ) 
Numerical values 
Analogies, icons; models 
All these operations may be combined, of course, by function- 
definition operators in defining intensions. Models may be 
defined in this context in terms of situations, which are 
hierarchically structured configurations of events where the 
elements of each level of the hierarchy are connected by 
relations of co-occurrence and temporal succession, and different 
levels are connected by part-whole relations. With each node of 
a situational hierarchy will be associated that extensional 
information which applies (inherently or contextually) to all 
events below it. Some situations will be associated with goals 
of the communicating system, which are intensional descriptions 
for which the communicating system seeks to transform the situation 
in order to satisfy. These goals form the basis for the operation 
of programs in the system. 
The criteriality or noncriteriality of intensional attributes 
may be represented by associating with each attribution a 
quantifier; in an intensional definition these quantifiers 
represent levels of criteriality for attributions. In English 
and other natural languages there are five levels of criteriality 
for both positive and negative attributions that acquire lexical 
ek~pression~ these, as represented by generic determiners, adverbs 
of relative frequency and adjectives of possibility, are shown in the 
diagram below, along with their relations of implication and 
minLmal mutual contradiction, and their relation to the absolute 
41 
scale of probability (represented by the diagonal in the figure). 
almost all; 
characteris- 
some; many; most; .tically; all; 
sometimes; often; generally; almost always; 
possible likely probable certain certain 
/ < ,, < ,, < ,,5~L1 
I I • l 
' • , / ,," X x x ~ ~ , 
o.s<J,, > ,' > .' > , 
no; few; most + not; not nearly not all; 
never; seldom; generally + all; not always; 
impossi- unlikely not; often + not; not certain 
ble improbable not nearly 
certain 
With a bit of intuition, patience, and attention to the 
requirements of commutativity and associativity, one may also 
construct a heuristic "multiplication table" that will define 
products of these levels of possibility, to handle conjunc- 
tive and disjunctive attributions. 
The most general possible explication of messages, and probably 
the one that will prove to be necessary for a semantic theory, 
is that they be simply any programs in the system. Other than 
performative operations and intensional evaluation operations, 
the set of operations that constitute messages will include 
finding an instance of an intension, creating a new instance of 
an intension, finding or creating an intension similar to a 
given intension, inserting or deleting quantified relations 
42 
between extensions and/or intensions, comparing extensions or 
intensions for equality, inclusion, or mutual exclusiveness, 
adding or deleting intensional definitions, modifying inten- 
sional definitions, rearranging and otherwise modifying situation 
structures, numerical computations, and the logical operations 
indicated by the function-definition operators. The specific 
form of the language in which all these operations may best be 
combined into programs is yet to be determined, but it may well 
turn out to be similar to Woods' procedural language, in which 
the basic statement form is a quantified "pattern-operation" rule. 
C. Decoding and Encoding 
The process of decoding natural language consists of three stages: 
syntax recognition, semantic translation, and application to the 
model representing the current discourse context. Syntax 
recognition includes recognition of both phrase structure and 
relations of gra~natical ~em~nt among the two or more 
constituents that are combined by a syntactic rule. Syntactic 
error correction might be handled by a method akin to Chomsky's 
\[l~\] notion of "degrees of gr~ticalness": relaxation of 
first grammatical agreement and then syntactic categorization 
conditions could be allowed until a parsing leading to a 
semantically-acceptable decoding was obtained. Semantic 
translation of the cembination of constituents recognized into 
a functional form in the message language then proceeds by 
way of one or more interpretation functions associated with the 
rule of grammar. These interpretation functions will make 
tests for agreement among the inherent and contextual attributes 
of the intensions they combine; if any of these tests fails, 
metaphorical interpretation rules (which operate by analogizin~ 
43 
and disanalogizing) might be invoked to attempt to resolve the 
conflict through appropriate construal of one or more of the 
constituents before the interpretation is rejected entirely. In 
the final step, application to the model representing the discourse 
context, antecedents of anaphoric and elliptical expressions are 
found through appropriate intensional evaluation, and further 
disambiguation may be achieved in case one or more of the 
alternative decodings contains presuppositions that are not 
satisfied in the model. Here additional rules of application may 
need to be introduced to add information to the model that is 
required by a presupposition but with respect to which the model 
is nonc cmnittal. 
The problem of encoding is that of transforming a message into a 
well-formed surface syntactic structure through lexical substitu- 
tion and formation of syntactic constructions. Encoding may be 
formulated as a recursive top-down procedure, which operates from 
the outermost level of functional application in the message on 
inward to the point where each expression may be replaced by a 
lexical item, therea±%er "unwinding" its way back outward, 
applying syntactic encodings followed optionally by syntactic 
transformations to each functional composition encountered on 
the way. There will, of course, be alternative paths that may 
be followed in the encoding of a message, because of the 
possibilities of alternative lexical substitutions, applications 
of alternative encoding rules, and optional application of 
transformations. Some of these paths may block because syntactic 
conditions on the application or output of the encoding rules 
are not satisfied, others because certain "performance-oriented" 
constraints, such as constraints on the level of certain types 
of embedding, are not met in the resulting surface structure. 
~4 
The rules for lexical substitution can probably be formulated along 
the lines proposed by Gruber, those for encoding into nominal 
structures along lines suggested by Celce and Schwarcz \[ll, 12\], 
and those for encoding into clauses and sentences along the lines 
suggested by Fillmore. 
Both decoding and encoding may be formulated most neatly as non- 
deterministic procedures employing heuristic search and evaluation. 
The rules employed in both, furthermore, are of the pattern-opera- 
tion type, the syntactic structures they operate on are of the 
form of situation structures, and the semantic structures they 
operate on are, of course, components of models and messages. 
Therefore both procedures and rules for decoding and encoding 
should be formulatable, and perhaps formulatable most elegantly, 
in the message language, since it is a general-purpose programming 
language containing all these features. Such a formulation 
would have the further advantages of parsimony with respect to 
computer implementation of the semantic theory and easy modifi- 
ability through the ability to use natural-language statements 
to effect changes in these procedures and rules. 
D. Implications 
The approach described above, though it has not yet been imple- 
mented, can be regarded as a sincere attempt to meet the require- 
ments set forth for a formal theory of natural language semantics 
in the first part of this paper--an achievement that no other 
approach advanced to date can claim, despite the many valuable 
ideas these approaches have produced. Evaluation of this 
attempt as a semantic theory must, of course, await the 
satisfaction of the final requirement: that the proposed system, 
45 
when progrmmned, engage successfully in purposive co~unlcation 
with speakers of a natural language. Simply as an approach that 
holds the promise of adequacy as a semantic theory, h0wever , it 
can provide a unifying direction for research in a number of 
areas, including linguistics, lexicology, logic, theory of 
computing, and artificial intelligence. The unification of such 
a diversity of directions of exploration, along with the 
rigorous test that the approach implies for an operationist theory 
of knowledge and meaning, should render the approach an interest- 
ing and fruitful one for philosophical study and exploration. 
Adopting an approach such as this, or any approach satisfying 
the requirements for a semantic theory, as ~ metatheoretical 
basis would also help greatly to resolve the confusion that 
exists today in linguistic theory. This state of disarray is a 
result of the fact that, with a very few exceptions, linguists 
have basically ignored the fundamental fact of language as 
being a tool for communicating sc~ethin~ to somebody. They have 
almost without exception ignored the interface between language 
and the speaker's or hearer's model of the universe of discourse. 
Operating in this sort of vacuum, linguists are under too few 
empirical constraints to determine any theory of grammar, let 
alone one that is meaningful. Only a semantic metatheory that 
takes the con~nunicational significance of language explicitly 
into account can provide a satisfactorily sound basis for a 
theory of gra~nar. 
The exploration of the approach offered here would bear very 
much upon the interests of cognitive psychologists, too, in that 
it offers a unified framework for a theory of language and 
cognitive processing. The heuristic-search-and-evaluation mode 
~6 
of operation is the paradigm that has emerged from an extensive 
amount of empirical research on human thinking and problem 
solving; its successful extension to explicating the understand- 
ing and production of language would lend support to the view 
that the mechanisms employed in language processing are the 
same as those employed in human thinking in general. The specific 
forms of model and message structures would, conversely, provide 
a basis for a formal theory of cognition that would receive 
support from the linguistic side as well. 
Finally, the formulation of the approach as a general-purpose 
programming system implies that it would be usable, in principle 
at least, for any application of computers to linguistic and 
semantic information processing, including all the ones mentioned 
earlier in the paper. Availability of suitable computer hardvare 
and operating systems would, of course, be essential to any 
application of the approach on a realistic scale. A more demand- 
ing requirement, however, is that of encoding the definitions of 
the thousands of different words that make up any natural language 
into an appropriately structured lexicon. A standard dictionary 
is one possible source of this information, but it will obviously 
not contain enough to define every word of a language operationally. 
The work of Olney etal \[BBS should be very helpful, however, in 
determining what can be gleaned from a standard dictionary and 
whether this information can be appropriately supplemented to 
yield an adequate operational lexicon, or whether a major new 
lexicographic effort, more rigorous in its requirements than any 
that have gone before, will have to be undertaken. Nhatever the 
case, the operational lexicon, once created, would be usable for 
all varieties of applications--and its construction, as well as 
the programming of applications, would be made 'easier by the 
capability implied by this approach to program the system in a 
47 
natural language once it had been supplied with sufficient 
information to define the semantics of a suitable "base" 
subset of the language. 
This approach, of course, is only one of many that might be 
taken to formalizing the semantics of natural languages. Like 
all other approaches that have been attempted or proposed so 
far, it will surely reveal its limitations somewhere along 
the way. But at a time when linguistics, semantics, and 
computational linguistics are all anxiously searching for 
a paradigm to follow, this may well be a fruitful one to try. 
~8 
l° 
2. 
3. 
4. 
. 
6. 
7. 
8. 

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