Why so many temporal logics climb up the trees

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Many temporal logics were suggested as branching time specification formalisms during the last 20 years. These logics were compared against each other for their expressive power, model checking complexity and succinctness. Yet, unlike the case for linear time logics, no canonical temporal logic of branching time was agreed upon. We offer an explanation for the multiplicity of temporal logics over branching time and provide an objective quantified ‘yardstick’ to measure these logics. We define an infinite hierarchy BTLk of temporal logics and prove its strictness. We show that CTL* has no finite base, and that almost all of its many sub-logics suggested in the literature are inside the second level of our hierarchy. We show that for every logic based on a finite set of modalities, the complexity of model checking is linear both in the size of structure and the size of formula.

Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 2000 - 25th International Symposium, MFCS 2000 , Proceedings
EditorsBranislav Rovan, Mogens Nielsen
PublisherSpringer Verlag
Number of pages11
ISBN (Print)3540679014
StatePublished - 2000
Event25th International Symposium on Mathematical Foundations of Computer Science, MFCS 2000 - Bratislava, Slovakia
Duration: 28 Aug 20001 Sep 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference25th International Symposium on Mathematical Foundations of Computer Science, MFCS 2000
City Bratislava


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