Modal Kleene algebra and partial correctness

  • We enrich Kleene algebra by domain and codomain operators. These abstractions of relational notions give rise to four modal operators. The boxes and diamonds enjoy various symmetries via Galois connections and dualities. Lifting modal statements to modal operator semirings yields a further abstraction and thus a more elegant and concise “statefree” reasoning about modalities. We use this modal Kleene algebra for calculating soundness and completeness proofs for propositional Hoare logic. While our soundness proof is more direct than related ones, our algebraic completeness proof seems entirely novel. It uses a modal symmetry that relates the wlp predicate transformer with partial correctness assertions and that is beyond the expressibility of formalisms like propositional dynamic logic.

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Author:Bernhard MöllerGND, Georg StruthGND
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Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2003-08)
Publisher:Institut für Informatik, Universität Augsburg
Place of publication:Augsburg
Year of first Publication:2003
Publishing Institution:Universität Augsburg
Release Date:2006/06/20
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