A completeness proof for a logic with an alternative necessity operator

Studia Logica 58 (1):99-112 (1997)
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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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10.1023/a:1004944015811

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Citations of this work

Contingency and Knowing Whether.Jie Fan, Yanjing Wang & Hans van Ditmarsch - 2015 - Review of Symbolic Logic 8 (1):75-107.
The Modal Logic of Agreement and Noncontingency.Lloyd Humberstone - 2002 - Notre Dame Journal of Formal Logic 43 (2):95-127.
Modified Numerals and Split Disjunction: The First-Order Case.Maria Aloni & Peter van Ormondt - 2023 - Journal of Logic, Language and Information 32 (4):539-567.

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References found in this work

An Introduction to Modal Logic.George Edward Hughes & M. J. Cresswell - 1968 - London, England: Methuen. Edited by M. J. Cresswell.
An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
A completeness theorem in modal logic.Saul Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 31 (2):276-277.

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