PRESUPPOSITION AND IMPLICATURE IN MODEL-THEORETIC PRAGMATICS 
Douglas B. Moran 
Oregon State University 
Model-theoretic pragmatics is an attempt to provide a 
formal description of the pragmatics of natural language 
as effects arising from using model-theoretic semantics 
in a dynamic environment. The pragmatic phenomena 
considered here have been variously labeled 
~resupposition \[I\] and eonven¢ional implicature \[6\]. 
The models used in traditional model-theoretic semantics 
provide a complete and static representation of knowledge 
about the world, llowever, this is not the environment 
in which language is used. Language is used in a 
dynamic environment - the participants have incomplete 
knowledge of the world and the understanding of a 
sentence can add to the knowledge of the listener. A 
formalism which allows models to contain incomplete 
knowledge and to which knowledge can be added has been 
developed \[2, 3, 12\]. 
In model-theoretic semantics, the relationships between 
words is not inherent in the structure of the model. 
These relationships between words are given by logical 
formulas, called meaning postulazes. In traditional 
model-theoretic semantics (with static models), these 
meaning postulates can be evaluated when the model is 
chosen to insure that it is a Peasonable model for the 
language. In dynamic model-theoretic semantics, these 
relationships must be verified as information is added 
to the model to insure that the new information does not 
violate any of these relationships. This verification 
process may cause the addition of more information to 
the model. 
The processing of the formula representing a sentence 
adds to the dynamic model the information given as the 
assertion of the sentence - the pr~maz~j information of 
the sentence - if it is not already in the model. The 
addition of this primary information can cause - through 
the verification of a meaning postulate - the addition 
of 8econ~x~ information. This secondary information 
is not part of the assertion 0£ the sentence, but is 
needed in the processing of the assertion. This 
characterization of secondary information is very similar 
to the classical definition of presupposition \[I\]. 
This approach displays different behavior for the three 
different cases of information contained in the model. 
In the first case, neither the assertion nor the pre- 
suppositions and implicatures are known. The attempt 
to add the assertion activates the verification of the 
meaning postulates giving the presuppositions and 
implicatures, thus causing that secondary information to 
be added to the model as a prerequisite to the addition 
of the primary information. In the second case, the 
presuppositions and implicatures are known (either true 
or false) and the assertion is unknown. The attempt to 
add the primary information again activates the 
verification of the meaning postulates. However, in 
this case, the presuppositions and implicatures are 
simply being checked - the verification process is not 
interrupted to add this secondary information to the 
model. This case corresponds to what Grice and others 
have termed to be a well-structured conversation. In 
the third case, the assertion of the sentence is known 
to be true or false. Since no new information needs to 
be added to the model to process the semantic represen- 
tation of the sentence, the verification of meaning 
postulates is not activated. The presuppositions and 
implicatures need not be verified because they had to 
have been verified before the assertion of the sentence 
or its negation could have been entered into the model. 
The presuppositions and implicatures of subordinate 
clauses do not necessarily become presuppositions and 
implicatures of the whole sentence. The problem of 
when and how such presuppositions become those of the 
matrix sentence is known as the pPoSeotion problem \[13\]. 
The system described here provides a simple and motivated 
solution to the projection problem. The models used in 
this system are partial models; a clause which has a 
presupposition or implicature which is not true has an 
undefinable denotation. An intensional logic \[ii\] is 
used to provide the semantic representations of sentences 
and the intensionality establishes transparent and opaque 
contexts (hoLg8 and plug8 \[7\]) which determine whether or 
not an undefinable value indicating the failure of a 
presupposition for a subordinate clause can propagate 
and force the matrix sentence to have an undefinable 
value. In the case where the presuppositions and 
implicatures are projected up from the subordinate clause 
to the matrix sentence, undefinable values are allowed to 
propagate, and thus a failure of a projected pre- 
supposition or implicature affects not only the sub- 
ordinate clause in which it originates, but also the 
matrix sentence. 
The determination of the projection characteristics is 
claimed to be an integral part of the meanings of words 
and not a separable feature. 
There are two other major attempts to handle pre- 
suppositions and implicatures in a model-theoretic 
framework. Karttunen and Peters \[g, 9, 10\] produce a 
formula giving the conventional implicatures of a 
sentence from its syntactic structure. Gazdar \[4, S\] 
accumulates sets of propositions, cancelling out those 
which are incompatible. Moran \[12\] compares the 
approach taken here to that of Karttunen and Peters and 
shows how this approach is simpler and better motivated. 
Gazdar's system is broader, but this approach is shown 
to correctly handle sentences which are incorrectly 
handled by Gazdar, and ways are suggested to expand the 
coverage of this system. 
REFERENCES 
\[I\] G. Frege (1892), "On sense and reference", in 
P. Geach and M. Black (eds.) (1966), Translations 
from the Philosophical Writings of Gottlob Frege, 
Blackwell, Oxford, 56-78. 
\[2\] J. Friedman, D. Moran, and D. ~arren (1978), 
"Explicit finite intensional models for PTQ", 
American Journal of Computational Linguistics, 
microfiche 74, 23-96. 
\[3\] J. Friedman, D. Moran and D. Warren (1979), 
"Dynamic Interpretations", Computer Studies in 
Pormal Linguistics N-16, Department of Computer 
and Communication Sciences, The University of 
Michigan; earlier version presented to the October 
1978 Sloan Foundation Workshop on Formal Semantics 
at Stanford University. 
\[4\] G. Gazdar (1979), Pragmatics: Implicature r 
Presupposition~ and Logical Form, Academic Press, 
New York. 
\[5\] G. Gazdar (1979), "A solution to the projection 
problem", in Oh and Dinneen (eds.), 57-89. 
\[6\] H. Grice (1975), "Logic and conversation", in 
P. Cole and J. Morgan (eds.) Syntax and Semantics 
3: Speech Acts, Academic Press, New York, 41-58. 
107 
\[73 L. Karttunen (1973), "Presuppositions of 
compound sentences", Linguistic Inquiry, ~, 
169-193. 
\[83 L. Karttunen and 5. Peters (1975\], "Conventional 
implicature in Montague GraEmar", Berhelev 
Linguistic Societ\[, !, 266-278. 
\[93 L. Karttunen and S. Peters (1976), "What indirect 
questions conventionally implicate", Chica~o 
Linguistic 5ocietz, 12, 351-568. 
\[I03 h. Karttunen and 5. Peters (1979), "Conventional 
implicatures", in Oh and Dinneen (eds.), 1-56. 
\[ii\] ~. Montague (1975~, "The proper treatment of 
quantification in ordinary £nglish", in J. 
Hintikka, J. Moravcsik and P. Suppes \[eds.) 
Approaches to Natural Language, D. Reidel, 
Dordrecht, 221-242; reprinted in R. Montague 
(1974), Formal Philosoph\[: Selected Papers of 
Richard Monta~ue, edited and with an introduction 
by Richmond Thomason, Yale University Press, 
247-270. 
\[123 D. Moran (1980), Model-Theoretic Pra~quatics: 
D~namic Models and an Application to Presupposition 
and lmplicature, unpublished Ph.D. dissertation, 
Department of Computer and Communication Sciences, 
The University of Michigan. 
\[133 J. Morgan (1969), "On the treatment of 
presupposition in transformational grammar", 
Chicago Linguistic Society, ~, 167-177. 
\[143 C. Oh and D. Dinneen (eds.), Syntax and Semantics 
Ii: Presupposition, Academic Press, New York. 
108 
