Studia Logica 105 (6):1193-1219 (2017)

Heinrich Wansing
Ruhr-Universität Bochum
In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic determined by the algebraic structure of multilattices. Similar completeness and embedding results are also shown for another logic called bi-intuitionistic connexive multilattice logic, obtained by replacing the connectives of intuitionistic implication and co-implication with their connexive variants.
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DOI 10.1007/s11225-017-9752-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.
Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.

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