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EVERYONE KNOWS THAT SOMEONE KNOWS: QUANTIFIERS OVER EPISTEMIC AGENTS

Published online by Cambridge University Press:  09 January 2019

PAVEL NAUMOV  and
JIA TAO
PAVEL NAUMOV*
Affiliation:
Department of Mathematical Sciences, Claremont McKenna College
JIA TAO*
Affiliation:
Department of Computer Science, Lafayette College
*
*DEPARTMENT OF MATHEMATICAL SCIENCES CLAREMONT MCKENNA COLLEGE CLAREMONT, CA 91711, USA E-mail: pnaumov@cmc.edu
†DEPARTMENT OF COMPUTER SCIENCE LAFAYETTE COLLEGE EASTON, PA 18042, USA E-mail: taoj@lafayette.edu
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Abstract

Modal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of distributed knowledge in multiagent systems has also been previously studied. This article proposes a version of S5-like epistemic logic of distributed knowledge with quantifiers ranging over the set of agents, and proves its soundness and completeness with respect to a Kripke semantics.

Keywords

03A99epistemic logicquantifiersagentsBarcan formuladistributed knowledge
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 2 , June 2019 , pp. 255 - 270
Copyright
Copyright © Association for Symbolic Logic 2019 

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