Terminating tableau calculi for modal logic K with global counting operators
نویسندگان
چکیده
This paper presents the first systematic treatment of tableau calculi for modal logic K with global counting operators. Using a recently introduced tableau synthesis framework we establish two terminating tableau calculi for the logic. Whereas the first calculus is a prefix tableau calculus, the second is a refinement that internalises the semantics of the logic without using nominals. We prove the finite model property for the logic and show that adding the unrestricted blocking mechanism does not break soundness and completeness of the calculi and ensures termination in both cases. We have successfully implemented the prefix tableau calculus in the MetTeL2 tableau prover generation platform.
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