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International Conference on Relational Methods in Computer Science

RelMiCS 2008: Relations and Kleene Algebra in Computer Science pp 320–336Cite as

Knowledge and Games in Modal Semirings

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4988))

Abstract

Algebraic logic compacts many small steps of general logical derivation into large steps of equational reasoning. We illustrate this by representing epistemic logic and game logic in modal semirings and modal Kleene algebras. For epistemics we treat the classical wise men puzzle and show how to handle knowledge update and revision algebraically. For games, we generalise the well-known connection between game logic and dynamic logic to modal semirings and link it to predicate transformer semantics, in particular to demonic refinement algebra. The study provides evidence that modal semirings will be able to handle a wide variety of (multi-)modal logics in a uniform algebraic fashion well suited to machine assistance.

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Authors and Affiliations

  1. Institut für Informatik, Universität Augsburg, D-86135, Augsburg, Germany

    Bernhard Möller

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  1. Bernhard Möller
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Rudolf Berghammer Bernhard Möller Georg Struth

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Möller, B. (2008). Knowledge and Games in Modal Semirings. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_24

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  • DOI: https://doi.org/10.1007/978-3-540-78913-0_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78912-3

  • Online ISBN: 978-3-540-78913-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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