PDL with negation of atomic programs

Journal of Applied Non-Classical Logics 15 (2):189-213 (2005)
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Propositional dynamic logic is one of the most successful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, as long-known, reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL with negation of atomic programs, only. We argue that this logic is still useful, e.g. in the context of description logics, and prove that satisfiability is decidable and EXPTIME-complete using an approach based on Büchi tree automata.



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References found in this work

Dynamic Logic.Lenore D. Zuck & David Harel - 1989 - Journal of Symbolic Logic 54 (4):1480.
Modal definability in enriched languages.Valentin Goranko - 1989 - Notre Dame Journal of Formal Logic 31 (1):81-105.
Inaccessible worlds.I. L. Humberstone - 1983 - Notre Dame Journal of Formal Logic 24 (3):346-352.

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