Dynamic Predicate Logic (DPL) is a variant of Predicate Logic introduced by Groenendijk and Stokhof. One rationale behind the introduction of DPL is that it is closer to Natural Language than ordinary Predicate Logic in the way it treats scope.In this paper I develop some variants of DPL that can more easily approximate Natural Language in some further aspects. Specifically I add flexibility in the treatment of polarity and and some further flexibility in the treatment of scope.I develop a framework (...) that is intended to encourage further experimentation with alternative variants of DPL. In this framework the new meanings are, roughly,indexed sets of old meanings. The indices can be viewed as "files'' or "storage devices.''Each such file supports a separate "information stream.''The interaction of the new meanings is "programmed'' with the help of certain monoids acting on the indices. The construction of the new meanings can be viewed as an application of the Grothendieck Construction to monoids. (shrink)

We consider the variety of Dynamic Relation Algebras V(DRA). We show that the monoid of an algebra in this variety determines dynamic negation uniquely.

A new system of dynamic logic is introduced and motivated, witha novel approach to variable binding for incremental interpretation. Thesystem is shown to be equivalent to first order logic and complete.The new logic combines the dynamic binding idea from DynamicPredicate Logic with De Bruijn style variable free indexing. Quantifiersbind the next available variable register; the indexing mechanismguarantees that active registers are never overwritten by newquantifiers actions. Apart from its interest in its own right, theresulting system has certain advantages over Dynamic (...) Predicate Logic orDiscourse Representation Theory. It comes with a more well behaved(i.e., transitive) consequence relation, it gives a more explicitaccount of how anaphoric context grows as text gets processed, and ityields new insight into the dynamics of anaphoric linking in reasoning.Incremental dynamics also points to a new way of handling contextdynamically in Montague grammar. (shrink)

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.

This paper provides several examples of how modal logic can be used in studying the XML document navigation language XPath. More specifically, we derive complete axiomatizations, computational complexity and expressive power results for XPath fragments from known results for corresponding logics. A secondary aim of the paper is to introduce XPath in a way that makes it accessible to an audience of modal logicians.