Abstract
We give the first single-pass (“on the fly”) tableau decision procedure for computational tree logic (CTL). Our method extends Schwendimann’s single-pass decision procedure for propositional linear temporal logic (PLTL) but the extension is non-trivial because of the interactions between the branching inherent in CTL-models, which is missing in PLTL-models, and the “or” branching inherent in tableau search. Our method extends to many other fix-point logics like propositional dynamic logic (PDL) and the logic of common knowledge (LCK).
The decision problem for CTL is known to be EXPTIME-complete, but our procedure requires 2EXPTIME in the worst case. A similar phenomenon occurs in extremely efficient practical single-pass tableau algorithms for very expressive description logics with EXPTIME-complete decision problems because the 2EXPTIME worst-case behaviour rarely arises. Our method is amenable to the numerous optimisation methods invented for these description logics and has been implemented in the Tableau Work Bench ( twb.rsise.anu.edu.au ) without these extensive optimisations. Its one-pass nature also makes it amenable to parallel proof-search on multiple processors.
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Abate, P., Goré, R., Widmann, F. (2007). One-Pass Tableaux for Computation Tree Logic. In: Dershowitz, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2007. Lecture Notes in Computer Science(), vol 4790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75560-9_5
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DOI: https://doi.org/10.1007/978-3-540-75560-9_5
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