research-article

Refinement modal logic

Authors:

Laura Bozzelli,

Hans van Ditmarsch,

Sophie PinchinatAuthors Info & Claims

Information and Computation, Volume 239, Issue C

Pages 303 - 339

https://doi.org/10.1016/j.ic.2014.07.013

Published: 01 December 2014 Publication History

Abstract

In this paper we present refinement modal logic. A refinement is like a bisimulation, except that from the three relational requirements only 'atoms' and 'back' need to be satisfied. Our logic contains a new operator in addition to the standard box modalities for each agent. The operator acts as a quantifier over the set of all refinements of a given model. As a variation on a bisimulation quantifier, this refinement operator or refinement quantifier can be seen as quantifying over a variable not occurring in the formula bound by it. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second-order quantification. We present a sound and complete axiomatization of multi-agent refinement modal logic. We also present an extension of the logic to the modal µ-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be seen as a set of actions), and to dynamic epistemic logic. We further give detailed results on the complexity of satisfiability, and on succinctness.

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Ågotnes TGalimullin R(2023)Quantifying over information change with common knowledgeAutonomous Agents and Multi-Agent Systems10.1007/s10458-023-09601-037:1Online publication date: 8-Mar-2023
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cover image Information and Computation

Information and Computation Volume 239, Issue C

December 2014

376 pages

ISSN:0890-5401

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Copyright © Elsevier Inc.

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Academic Press, Inc.

United States

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Published: 01 December 2014

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