Abstract
We propose a tableau-based decision procedure for the full Alternating-time Temporal Logic \(\mathsf {ATL^*}\). We extend our procedure for \(\mathsf {ATL^{+}}\) in order to deal with nesting of temporal operators. As a side effect, we obtain a new and conceptually simple tableau method for \(\mathsf {CTL^*}\). The worst case complexity of our procedure is \(\mathrm {3EXPTIME} \), which is suboptimal compared to the \(\mathrm {2EXPTIME} \) complexity of the problem. However our method is human-readable and easily implementable. A web application and binaries for our procedure are available at http://atila.ibisc.univ-evry.fr/tableau_ATL_star/.
All proofs of lemmas, propositions and theorems, as well as complete examples can be found in the version with appendices at https://www.ibisc.univ-evry.fr/~adavid/fichiers/cade15_tableaux_atl_star_long.pdf.
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Acknowledgement
I would like to thank Serenella Cerrito and Valentin Goranko for their advices and proofreading. I also thank the anonymous referees for their helpful criticisms.
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David, A. (2015). Deciding \(\mathsf {ATL^*}\) Satisfiability by Tableaux . In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_14
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DOI: https://doi.org/10.1007/978-3-319-21401-6_14
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