Abstract
We extend Pratt’s worst-case optimal decision procedure for PDL to a richer logic with nominals, difference modalities, and inverse actions. We prove correctness and worst-case optimality. Our correctness proof is based on syntactic models called demos. The main theorem states that a formula is satisfiable if and only if it is contained in a demo. From this theorem the correctness of the decision procedure is easily obtained. Our development is modular and we extend it stepwise from modal logic with eventualities to the full logic.
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Kaminski, M., Schneider, T., Smolka, G. (2011). Correctness and Worst-Case Optimality of Pratt-Style Decision Procedures for Modal and Hybrid Logics. In: Brünnler, K., Metcalfe, G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2011. Lecture Notes in Computer Science(), vol 6793. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22119-4_16
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DOI: https://doi.org/10.1007/978-3-642-22119-4_16
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