A calculus for Belnap's logic in which each proof consists of two trees

Logique Et Analyse 220:643-656 (2012)
Stefan Wintein
Tilburg University
Reinhard Muskens
Tilburg University
In this paper we introduce a Gentzen calculus for (a functionally complete variant of) Belnap's logic in which establishing the provability of a sequent in general requires \emph{two} proof trees, one establishing that whenever all premises are true some conclusion is true and one that guarantees the falsity of at least one premise if all conclusions are false. The calculus can also be put to use in proving that one statement \emph{necessarily approximates} another, where necessary approximation is a natural dual of entailment. The calculus, and its tableau variant, not only capture the classical connectives, but also the `information' connectives of four-valued Belnap logics. This answers a question by Avron.
Keywords Belnap-Dunn logic  bilattice FOUR
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Analytic Tableaux for All of SIXTEEN_3.Reinhard Muskens & Stefan Wintein - 2015 - Journal of Philosophical Logic 44 (5):473-487.

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