Modal and temporal operators on partial orders

  • We generalize the operators of classical linear time temporal logic to partial orders, such as the ones used in domain theory. This relates denotaional semantics and temporal logic. We put this into the general perspective of modal logic. Box and diamond are viewed as standard modalities, which gives "half" of the standard axioms of LTL. Moreover, we show that the next-time operator can be defined as a combination of two modalities. We show the role of the standard LTL axioms in narrowing the underlying partial orders to linear ones generated by the immediate-successor relation. We distinguish between modal and temporal validity of formulas and investigate their relation.

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Author:Bernhard MöllerGND
Frontdoor URL
Parent Title (English):Programming languages and fundamentals of programming
Publisher:Inst. für Informatik und Praktische Mathematik
Place of publication:Kiel
Editor:Rudolf Berghammer
Type:Part of a Book
Year of first Publication:1997
Release Date:2017/07/21
First Page:1
Last Page:11
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