In this paper we prove that the principles in the languagewith relation composition and dynamic implication, valid forall binary relations, are the same ones as the principlesvalid when we restrict ourselves to DPL-relations,i.e. relations generated from conditions (tests) and resettings.

In this paper a semantics for dynamic predicate logic is developed that uses sequence valued assignments. This semantics is compared with the usual relational semantics for dynamic predicate logic: it is shown that the most important intuitions of the usual semantics are preserved. Then it is shown that the refined semantics reflects out intuitions about information growth. Some other issues in dynamic semantics are formulated and discussed in terms of the new sequence semantics.

Preface This book is about semantics and logic. More specifically, it is about the semantics and logic of natural language; and, even more specifically than ...

This paper presents a sound and complete proof system for the first order fragment of Discourse Representation Theory. Since the inferences that human language users draw from the verbal input they receive for the most transcend the capacities of such a system, it can be no more than a basis on which more powerful systems, which are capable of producing those inferences, may then be built. Nevertheless, even within the general setting of first order logic the structure of the formulas (...) of DRS-languages, i.e. of the Discourse Representation Structures suggest for the components of such a system inference rules that differ somewhat from those usually found in proof systems for the first order predicate calculus and which are, we believe, more in keeping with inference patterns that are actually employed in common sense reasoning.This is why we have decided to publish the present exercise, in spite of the fact that it is not one for which a great deal of originality could be claimed. In fact, it could be argued that the problem addressed in this paper was solved when Gödel first established the completeness of the system of Principia Mathematica for first order logic. For the DRS-languages we consider here are straightforwardly intertranslatable with standard formulations of the predicate calculus; in fact the translations are so straightforward that any sound and complete proof system for first order logic can be used as a sound and complete proof system for DRSs: simply translate the DRSs into formulas of predicate logic and then proceed as usual. As a matter of fact, this is how one has chosen to proceed in some implementations of DRT, which involve inferencing as well as semantic representation; an example is the Lex system developed jointly by IBM and the University of Tübingen ). (shrink)

We consider algebras on binary relations with two main operators: relational composition and dynamic negation. Relational composition has its standard interpretation, while dynamic negation is an operator familiar to students of Dynamic Predicate Logic (DPL) (Groenendijk and Stokhof, 1991): given a relation R its dynamic negation R is a test that contains precisely those pairs (s,s) for which s is not in the domain of R. These two operators comprise precisely the propositional part of DPL.This paper contains a finite equational (...) axiomatization for these dynamic relation algebras. The completenessresult uses techniques from modal logic. We also lookat the variety generated by the class of dynamic relation algebras and note that there exist nonrepresentable algebras in this variety, ones which cannot be construedas spaces of relations. These results are also proved for an extension to a signature containing atomic tests and union. (shrink)

This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with the principle of compositionality, (...) a principle which, implicitly or explicitly, has dominated semantics since the days of Frege. Therefore the question naturally arises whether non-compositionality is in any way a necessary feature of discourse semantics. Since we subscribe to the interpretation of compositionality as constituting primarily a methodological principle, we consider this to be a methodological rather than an empirical question. As a consequence, the emphasis in the present paper lies on developing an alternative compositional semantics of discourse, which is empirically equivalent to its non-compositional brethren, but which differs from them in a principled methodological way. Hence, no attempts are made to improve on existing theories empirically. Nevertheless, as we indicate in section 5, the development of a compositional alternative may in the end have empirical consequences, too. First of all, it can be argued that the dynamic view on interpretation developed in this paper suggests natural and relatively easy to formulate extensions which enable one to deal with a wider range of phenomena than can be dealt with in existing theories. Moreover, the various approaches to the model-theoretic semantics of discourse that have been developed during the last decade, have constituted a ‘fresh start’ in the sense that much of what had been accomplished before was ignored, at least for a start. Of course, this is a justified strategy if one feels one is trying to develop a radically different approach to recalcitrant problems. However, there comes a time when such new approaches have to be compared with the older one, and when an assessment of the pros and cons of each has to be made. One of the main problems in semantics today, we feel, is that a semantic theory such as Montague grammar, and an approach like Kamp’s discourse representation theory, are hard to compare, let alone that it is possible to unify their insights and results.. (shrink)

In this paper we describe a framework for the construction of entities that can serve as interpretations of arbitrary contiguous chunks of text. An important part of the paper is devoted to describing stacking cells, or the proposed meanings for bracket-structures.