LP-1997-10: Dynamic Reasoning Without Variables

LP-1997-10: van Eijck, Jan (1997) Dynamic Reasoning Without Variables. [Report]

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A variable free notation for dynamic logic is proposed which takes its cue from De Bruijn's variable free notation for lambda calculus. De Bruijn indexing replaces variables by indices which indicate the distance to their binders. We propose to use reverse De Bruijn indexing, which works almost the same, only now the indices refer to the depth of the binding operator in the formula. The resulting system is analysed at length and applied to a new rational reconstruction of discourse representation theory. It is argued that the present system of dynamic logic without variables provides an explicit account of anaphoric context and yields new insight into the dynamics of anaphoric linking in reasoning. A calculus for dynamic reasoning with anaphora is presented and its soundness and completeness are established. Keywords and Phrases: dynamic semantics of natural language, complete calculus for dynamic reasoning with anaphora, anaphora and context.

Item Type: Report
Report Nr: LP-1997-10
Series Name: Logic, Philosophy and Linguistics (LP)
Year: 1997
Date Deposited: 12 Oct 2016 14:40
Last Modified: 12 Oct 2016 14:40
URI: https://eprints.illc.uva.nl/id/eprint/1260

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