Studia Logica 107 (2):283-312 (2019)

Abstract
A deterministic weakening \ of the Belnap–Dunn four-valued logic \ is introduced to formalize the acceptance and rejection of a proposition at a state in a linearly ordered informational frame with persistent valuations. The logic \ is formalized as a sequent calculus. The completeness and decidability of \ with respect to relational semantics are shown in terms of normal forms. From an algebraic perspective, the class of all algebras for \ is described, and found to be a subvariety of Berman’s variety \. Every linearly ordered frame is logically equivalent to its dual algebra. It is proved that \ is the logic of a nine-element distributive lattice with a negation. Moreover, \ is embedded into \ by Glivenko’s double-negation translation.
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DOI 10.1007/s11225-018-9792-x
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References found in this work BETA

A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.
Partiality and its Dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.

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Citations of this work BETA

A Paraconsistent Conditional Logic.Minghui Ma & Chun-Ting Wong - 2020 - Journal of Philosophical Logic 49 (5):883-903.

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