First Order Common Knowledge Logics

Author: Wolter F.¹

Source: Studia Logica, Volume 65, Number 2, July 2000 , pp. 249-271(23)

Publisher: Springer

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Abstract:

In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties of "quantifying into" epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies.

Keywords: Epistemic Logic; Game theory; Axiomatizability; Common knowledge

Language: English

Document Type: Regular paper

Affiliations: 1: Institut für Informatik Universität Leipzig Augustus-Platz 10-11 04109 Leipzig, Germany wolter@informatik.uni-leipzig.de

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