Incremental dynamics

Journal of Logic, Language and Information 10 (3):319-351 (2001)
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Abstract

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.

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Jan Van Eijck
University of Amsterdam

References found in this work

Dynamic Predicate Logic.Jeroen Groenendijk & Martin Stokhof - 1991 - Linguistics and Philosophy 14 (1):39-100.
A Theory of Truth and Semantic Representation.Hans Kamp - 1981 - In P. Portner & B. H. Partee (eds.), Formal Semantics - the Essential Readings. Blackwell. pp. 189--222.
Background.[author unknown] - 2004 - The Chesterton Review 30 (3-4):411-413.
Variables Explained Away.W. V. Quine - 1967 - Journal of Symbolic Logic 32 (1):112-112.

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