The power of Belnap: sequent systems for \(SIXTEEN_{3 }\)
The trilattice \(SIXTEEN_3\) is a natural generalization of Belnap and Dunn's four-valued logic, called useful four-valued logic (see [\textit{N. D. Belnap}, ``A useful four-valued logic'', in: J. M. Dunn et al. (eds.), Mod. uses of multiple-valued logic, 5th int. symp., Bloomington 1975, 5--37 (1977; Zbl 0424.03012)], [\textit{J. M. Dunn}, ``Intuitive semantics for first-degree entailment and `coupled trees'{}'', Philosophical Studies 29, 149--168 (1976)]), based on the bilattice \(FOUR_2\) (see [\textit{M. Ginsberg}, ``Multivalued logics: a uniform appoach to reasoning in AI'', Computer Intelligence 4, 256--316 (1988)], [\textit{O. Arieli} and \textit{A. Avron}, ``Reasoning with logical bilattices'', J. Logic Lang. Inf. 5, No.~1, 25--63 (1996; Zbl 0851.03017)]). The author presents sound and complete cut-free sequent calculi for truth entailment and falsity entailment in \(SIXTEEN_3\).
scientific article; zbMATH DE number 5796519
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