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.

The development of the dynamic semantics of natural languagehas put issues of variable control on the agenda of formal semantics. Inthis paper we regard variables as names for stacks of values and makeexplicit several control actions as push and pop actions on stacks. Weapply this idea both to static and dynamic languages and compare theirfinite variable hierarchies, i.e., the relation between the number ofvariable stacks that is available and the expressivity of the language.This can be compared in natural languages with (...) relating the number ofpronouns available to the expressivity of the language.The results are obtained using techniques from static and dynamic modeltheory: model theoretic games, transition systems and bisimulation. (shrink)

This paper is concerned with the structure of texts in which aproof is presented. Some parts of such a text are assumptions, otherparts are conclusions. We show how the structural organisation of thetext into assumptions and conclusions helps to check the validity of theproof. Then we go on to use the structural information for theformulation of proof rules, i.e., rules for the (re-)construction ofproof texts. The running example is intuitionistic propositional logicwith connectives , and. We give new proofs of some (...) familiar results aboutthe proof theory of this logic to indicate how the new techniques workout. (shrink)

Dans le cadre de nos recherches sur la correspondance de Descartes, nous avons découvert une lettre inédite du philosophe. La lettre, qui se trouve à la Staatsbibliothek zu Berlin, Preußischer Kulturbesitz, est addressee à Joachim de Wicquefort, datée de Leyde, le 2 octobre 1640. Dans sa lettre Descartes réclame, par l' intermédiaire de Wicquefort, la traduction latine de ses Meteores, qui avait été remis au professeur de philosophie d'Amsterdam, Caspar Barlaeus. Elle précède de trois jours la lettre, déjà connue, à (...) Wicquefort sur le même sujet. L'importance de notre lettre est qu'elle confirme certaines hypothèses concernant l'édition latine du Discours, et le projet abandonné de la publication des objections faites au Discours et aux Essais et des réponses du philosophe. (shrink)

We consider substitutions in order sensitive situations, having in the back of our minds the case of dynamic predicate logic (DPL) with a stack semantics. We start from the semantic intuition that substitutions are move instructions on stacks: the syntactic operation [y/x] is matched by the instruction to move the value of the y-stack to the x-stack. We can describe these actions in the positive fragment of DPLE. Hence this fragment counts as a logic for DPL-substitutions. We give a calculus (...) for the fragment and prove soundness and completeness. (shrink)

An axiomatization is presented of the denotational semantics for first order language of Apt [1]. The goal is to obtain a rational reconstruction of the intuitions underlying this semantics. The axiomatization combines ideas about four valued logic with facts about substitutions. Soundness and completeness of the axiomatization are established. From the completeness proof a decision procedure is obtained that shows how four valued logic and order sensitivity of substitution together add up in a natural way to the denotational semantics for (...) the language of first order logic as proposed by Apt. (shrink)

Topic of this paper is the way in which the structure of events features in discourse. We focus on the structure as introduced by verbs that express some sense of progress. First it is shown by means of examples that this structure is anaphorically available in discourse. Then we go on to discuss the different ways in which the same event may be structured within one discourse situation. We give formal representations of the crucial examples in many-sorted dynamic logic.

In this paper we discuss the treatment of variables in dynamic semantics. Referent systems are introduced as a flexible mechanism for working with variables. In a referent system we carefully distinguish the variables themselves both from the machinery by which we manipulate them - their names - and from the information that we store in them - their values. It is shown that the referent systems provide a natural basis for dynamic semantics. The semantics with referent systems is compared with (...) the familiar formalisms in dynamic semantics, DRT and DPL. (shrink)