Quantales and temporal logics

  • We provide an algebraic semantics for the temporal logic CTL* and simplify it for its sublogics CTL and LTL. We abstractly represent state and path formulas over transition systems in Boolean left quantales. These are complete lattices with an operation of multiplication that is completely disjunctive in its left argument and isotone in its right argument. On these quantales, the semantics of CTL* formulas can be encoded via finite and infinite iteration operators, the CTL and LTL operators can be related to domain operators. This yields interesting new connections between representations as known from the modal "mü"-calculus and Kleene/"omega"-algebraic ones.

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Author:Bernhard MöllerGND, Peter HöfnerGND, Georg StruthGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/288
Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2006-06)
Publisher:Institut für Informatik, Universität Augsburg
Place of publication:Augsburg
Year of first Publication:2006
Publishing Institution:Universität Augsburg
Release Date:2006/07/25
GND-Keyword:Algebraische Struktur; Temporale Logik
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