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A Completeness Proof for a Logic with an Alternative Necessity Operator

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Abstract

We show the completeness of a Hilbert-style system LK defined by M. Valiev involving the knowledge operator K dedicated to the reasoning with incomplete information. The completeness proof uses a variant of Makinson's canonical model construction. Furthermore we prove that the theoremhood problem for LK is co-NP-complete, using techniques similar to those used to prove that the satisfiability problem for propositional S5 is NP-complete.

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  1. Laboratoire Leibniz - C.N.R.S, 46, Avenue Félix Viallet, 38031, Grenoble, France

    Stéphane Demri

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  1. Stéphane Demri
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Demri, S. A Completeness Proof for a Logic with an Alternative Necessity Operator. Studia Logica 58, 99–112 (1997). https://doi.org/10.1023/A:1004944015811

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