LP-1998-08: Incremental Dynamics

LP-1998-08: van Eijck, Jan (1998) Incremental Dynamics. [Report]

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An incremental semantics for a logic with dynamic binding is developed on the
basis of a variable free notation for dynamic logic that 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 indexing mechanism guarantees that active registers are never
overwritten by new quantifier actions. The resulting system is analysed and
applied to a new rational reconstruction of discourse representation theory.
It is argued that the present system of incremental dynamic logic 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, incremental interpretation, monotonic
semantics, anaphora and context.

Submitted for publication in the Journal of Logic, Language and Information.

Item Type: Report
Report Nr: LP-1998-08
Series Name: Logic, Philosophy and Linguistics (LP)
Year: 1998
Date Deposited: 12 Oct 2016 14:40
Last Modified: 12 Oct 2016 14:40
URI: https://eprints.illc.uva.nl/id/eprint/1268

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