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Abstract: We introduce a simple game theoretic approach to satisfiability checking of temporal logic, for LTL and CTL, which has the same complexity as using automata. The mechanisms involved are both explicit and transparent, and underpin a novel approach to developing complete axiom systems for temporal logic. The axiom systems are naturally factored into what happens locally and what happens in the limit. The completeness proofs utilise the game theoretic construction for satisfiability: if a finite... (Update)
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...This approach was first used in [6] to solve the model checking problem for the temporal logics LTL and CTL # in a game based way. In [7] it is shown how this technique solved satisfiability for the temporal logics LTL and CTL, and at the same time led to simple completeness...
.... [Sti95] as well as CTL # [LS00, VB00] The latter work has led to game based satisfiability checkers for temporal and dynamic logics [LS01a, LS01b] which easily yield complete axiom systems. There it is shown that games neatly relate satisfiability and consistency of a formula...
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BibTeX entry: (Update)
M. Lange and C. Stirling. Focus games for satisfiability and completeness of temporal logic. Submitted, 2001. http://citeseer.ist.psu.edu/lange01focus.html More
@inproceedings{ lange01focus,
author = "Martin Lange and Colin Stirling",
title = "Focus Games for Satisfiability and Completeness of Temporal Logic",
booktitle = "Proceedings of the 16th Annual {IEEE} Symposium on Logic in Computer Science, {LICS'01}",
publisher = "IEEE Computer Society Press",
address = "Boston, MA, USA",
year = "2001",
url = "citeseer.ist.psu.edu/lange01focus.html" }
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128 An automata-theoretic approach to linear temporal logic - Vardi - 1996
114 Logics of Time and Computation (context) - Goldblatt - 1992
86 An automata-theoretic approach to branching-time model check.. - Kupferman, Vardi et al. - 2000
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49 Model Theory (context) - Hodges - 1993
20 Completeness of Kozen's axiomatisation of the propositional .. - Walukiewicz - 2000
19 Efficient on-the-fly model checking for CTL - Bhat, Cleaveland et al. - 1995
14 A note on model checking the modal nu-calculus (context) - Winskel - 1991
9 Efficient model checking via the equational -calculus (context) - Bhat, Cleaveland - 1996
7 Propositional temporal logics: decidability and completeness (context) - Lichtenstein, Pnueli - 2000
7 and Stockmeyer (context) - Chandra, Kozen - 1981
3 An axiomatisation of full computation tree logic (context) - Reynolds - 2000
2 and Stirling (context) - Lange - 2000
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