Polarity Semantics for Negation as a Modal Operator

Studia Logica 108 (5):877-902 (2020)
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Abstract

The minimal weakening \ of Belnap-Dunn logic under the polarity semantics for negation as a modal operator is formulated as a sequent system which is characterized by the class of all birelational frames. Some extensions of \ with additional sequents as axioms are introduced. In particular, all three modal negation logics characterized by a frame with a single state are formalized as extensions of \. These logics have the finite model property and they are decidable.

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Minghui Ma
Sun Yat-Sen University

References found in this work

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Partiality and its dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.
A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein, Modern Uses of Multiple-Valued Logic. D. Reidel.
Correspondences between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.

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