Knowledge and games in modal semirings

  • 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 some classical examples like the wise men and muddy children puzzles; we also 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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Author:Bernhard MöllerGND
Frontdoor URL
Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2007-03)
Publisher:Institut für Informatik, Universität Augsburg
Place of publication:Augsburg
Year of first Publication:2007
Publishing Institution:Universität Augsburg
Release Date:2007/02/28
GND-Keyword:Kleene-Algebra; Halbring; Spiel
Institutes:Fakultät für Angewandte Informatik
Fakultät für Angewandte Informatik / Institut für Informatik
Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik