Belnap–Dunn Modal Logic with Value Operators

Studia Logica 109 (4):759-789 (2020)
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The language of Belnap–Dunn modal logic \ expands the language of Belnap–Dunn four-valued logic with the modal operator \. We introduce the polarity semantics for \ and its two expansions \ and \ with value operators. The local finitary consequence relation \ in the language \ with respect to the class of all frames is axiomatized by a sequent system \ where \. We prove by using translations between sequents and formulas that these languages under the polarity semantics have the same expressive power on the level of frames with the language \ under the relational semantics for classical modal logic.



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Minghui Ma
Sun Yat-Sen University

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References found in this work

A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
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.

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