Situations, Language and Logic

194 Pages·1987·10.724 MB·

by  Jens Erik Fenstad, Per-Kristian Halvorsen, Tore Langholm, Johan Van Benthem (auth.)

SITUATIONS, LANGUAGE AND LOGIC
STUDIES IN LINGUISTICS AND PHILOSOPHY
formerly Synthese Language Library
Managing Editors:
ROBIN COOPER, University of Wisconsin
ELISABET ENGDAHL, University of Wisconsin
RICHARD GRANDY, Rice University
Editorial Board:
EMMON BACH, University of Massachusetts at Amherst
JON BARWISE, CSLI, Stanford
JOHAN VA N BENTHEM, Mathematics Institute,
University of Amsterdam
DAVID DOWTY, Ohio State University, Columbus
GERALD GAZDAR, University of Sussex, Brighton
EWA N KLEIN, University of Edinburgh
BILL LAD USA W, University of California at Santa Cruz
SCOTT SOAMES, Princeton University
HENRY THOMPSON, University of Edinburgh
VOLUME 34
SITUATIONS, LANGUAGE
AND LOGIC
by
JENS ERIK FENSTA D
Department of Mathematics, Oslo University, Norway
PER-KRISTIAN HALVORSEN
Intelligent Systems Laboratory, Xerox Palo Alto Research Center
and CSLI, Stanford, U.S.A.
TORELANGHOLM
Department of Philosophy, Stanford University, U.S.A.
and
JOHAN V AN BENTHEM
Department of Mathematics, University of Amsterdam, The Netherlands
D. REIDEL PUBLISHING COMPANY
.....
A MEMBER OF THE KLUWER " ACADEMIC PUBLISHERS GROUP
DORDRECHT/BOSTON/LANCASTER/TOKYO
or
Libory Congress Cataloging in hbHcation Data
Situations, language, and logic / Jens Erik Fenstad ... ret al.].
p. em - (Studies in linguistics and philosophy; v. 34)
Bibliography: p.
Includes index.
ISBN-13:978-l-55608-049-4 e-ISBN-13:978-94-009-1335-6
DOl: 10.1007/978-94-009-1335-6
1. Content (Linguistics) 2. Semantics. I. Fenstad, Jens Erik.
II. Series.
P325.5.C65S58 1987
415-dc19 87-22305
CIP
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© 1987 by D. Reidel Publishing Company, Dordrecht, Holland
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TABLE OF CONTENTS
PREFACE Vll
I. INTRODUCTION 1
1. From linguistic form to situation schemata 1
2. Interpreting situation schemata 6
3. The logical point of view 10
II. FROM LINGUISTIC FORM TO SITUATION
SCHEMATA 12
1. Levels of linguistic form determining meaning 12
2. Motivation for the use of constraints 17
3. The modularization of the mapping from form to meaning 19
4. Situation schemata 21
5. The algorithm from linguistic form to situation schemata 30
III. INTERPRETING SITUATION SCHEMATA 52
1. The art of interpretation 54
2. The inductive definition of the meaning relation 68
3. A remark on the general format of situation schemata 76
4. Generalizing generalized quantifiers 77
vi TABLE OF CONTENTS
IV. A LOGICAL PERSPECTIVE 82
1. The mechanics of interpretation 82
2. A hierarchy of formal languages 87
2.1. Propositional logic 87
2.2. Predicate logic 94
2.3. Tense logic 97
2.4. Temporal predicate logic 105
2.5. Situated temporal predicate logic 106
3. Mathematical study of some formal languages 107
3.1. Definition of structure 107
3.2. The system La 109
3.3. Modal operators 122
4. On the model theoretic interpretation of situation schemata 127
4.1. The basic correspondence 127
4.2. The correspondence extended 129
V. CONCLUSIONS 131
APPENDICES
A. Prepositional Phrases in Situation Schemata 133
by Erik Colban
B. A Lyndon type interpretation theorem
for many-sorted first-order logic 157
C. Proof of the relative saturation lemma 164
REFERENCES 177
INDEX 182
PREFACE
This monograph grew out of research at Xerox PARC and the Center for
the Study of Language and Information (CSLI) during the first year of
CSLI's existence. The Center was created as a meeting place for people
from many different research traditions and there was much interest in
seeing how the various approaches could be joined in a common effort
to understand the complexity of language and information. CSLI was
thus an ideal environment for our group and our enterprise.
Our original goal was to see how a well-developed linguistic the
ory, such as lexical-functional grammar, could be joined with the ideas
emerging from research in situation semantics in a manner which would
measure up to the technical standards set by Montague grammar. The
outcome was our notion of situation schemata and the extension of
constraint-based grammar formalisms to deal with semantic as well as
syntactic information.
As our work progressed we widened our approach. We decided to
also include a detailed study of the logic of situation theory, and to
investigate how this logical theory is related to the relational theory of
meaning developed in situation semantics.
We are pleased that the first version of this work (Fenstad et al. 1985)
has been used as a basis for further studies at a number of different
sites. We include here a sample of such work in Appendix A where Erik
Colban of the Mathematics Department, University of Oslo, presents his
analysis of locative prepositional phrases. We believe that his analysis is
an illustration of the openness and extendability of our basic approach.
This book is a research monograph reporting on work in progress. We
have restricted ourselves to basic facts of language and logic, and our
aim has been to give a precise technical account of how to join linguistic
form and semantic structure. We hope that the techniques for linguistic
description which we illustrate here can be of wide applicability.
vii
viii PREFACE
We are indebted to CSLI and the Xerox Palo Alto Research Cen
ter for the support of our research. We are grateful for the assistance
in the preparation of the manuscript which we received from Dikran
Karagueuzian and Lynn Ruggles at CSLI, and Denise Pawson at Xe
rox PARCo We also wish to thank Mr. Martin Scrivener of D. Reidel
Publishing Company for his valuable advice.
CHAPTER I
INTRODUCTION
In this monograph our aim is to give an overall framework for relating
the linguistic form of utterances and their semantic interpretation which
is based on the idea of constraint propagation. In Chapter II we present
an algorithm which converts linguistic form into a format, which we
call a situation schema, better suited for semantic interpretation. In
Chapter III we spell out the meaning relation, i.e. the interpretation of
the situation schemata into a system of situation semantics. In Chapter
IV we investigate the structure of the semantic interpretation through a
hierarchy of many-sorted formal languages.
1 FROM LINGUISTIC FORM TO SITUATION SCHEMATA
The informational content of an utterance is determined not only by its
linguistic form (i.e. its phonology, morphology and syntax), but also
by a number of contextual factors. The interpretation of the utterance
must satisfy all the constraints imposed by all the relevant aspects of the
larger "utterance situation." Each semantically relevant aspect provides
us with important, though partial, information about the interpretation
of the utterance. There seems to be no firm empirical evidence that one
component of linguistic form has primacy over the others in determining
the interpretation, nor that the interpretation of the utterance proceeds
in any particular order (e.g. the one suggested by the syntactic surface
structure) .
With this in mind we have chosen to represent the constraints which
are imposed on the interpretation of the utterance by contextual and
linguistic constituents of the utterance situation through a cumulative
(or monotonic) system of constraint equations (Kay 1979; Kaplan and
Bresnan 1982; Halvorsen 1983). Each equation makes a statement about
properties of the interpretation, and the problem of systematically de-
1
2 CHAPTER I
termining the interpretation becomes the problem of finding a solution
to the constraint equations (Robinson 1965). The constraints flowing
from various aspects of the utterance situation, whether contextual or
formal, are all taken to be represented in the same equational form,
which simplifies the integration of constraints from various levels.
In part one we are primarily concerned with the constraints derived
from the linguistic form; in part two we discuss how larger aspects of
the utterance situation constrain the meaning relation.
Our proposal contrasts with the traditional point of view that the
meaning of larger phrases is determined through functional composition
of word meanings where the control structure for the function com
position is given exclusively by the syntactic structure of the phrase
(Montague 1970). It is not our purpose to argue at length the deficien
cies of the traditional point of view. But it does not seem to be the
best interpretation strategy to "force" the full informational content of
the utterance and the context through the syntactic tree to arrive at
the meaning content. 1 Even restricting ourselves to linguistic form, syn
tax is not the obvious repository for information regarding the semantic
impact of intonation or for resolving questions of scope or anaphoric ref
erence. These points become even more pronounced for languages with
free word order. In such languages, the syntactically motivated surface
constituent structure is flat and lacking in the hierarchical organization
required for the "logical syntax."
Taking certain liberties with traditional boundaries and hierarchies
between linguistic modules does not imply disrespect. Obviously, there
are natural syntactic and morphological (as well as other) clusters of con
straint equations, and all the usual insights about the internal structure
and interconnections of these components remain. Moreover, liberties
should not degenerate into license. If a system of cumulative constraint
equations is to acquire descriptive and theoretical "bite", we shall even-
10f course, by "packaging" enough contextual and interpretative factors
into denotations, the letter of the compositionality principle can usually be
obeyed after all, but often-in the process-its spirit has departed. Gawron
(1986) suggests that the "descriptive content" of an utterance is determined
exclusively by the syntactic analysis of the utterance, while its meaning de
pends on other factors as well. Our interpretations are largely coextensive with
Gawron's "descriptive content," but we prefer a less syntax oriented approach
(see Chapter III for supporting arguments).