Natural deduction for bi-intuitionistic logic

Journal of Applied Logic 25:S72-S96 (2017)

Authors
Luca Tranchini
Universität Tübingen
Abstract
We present a multiple-assumption multiple-conclusion system for bi-intuitionistic logic. Derivations in the systems are graphs whose edges are labelled by formulas and whose nodes are labelled by rules. We show how to embed both the standard intuitionistic and dual-intuitionistic natural deduction systems into the proposed system. Soundness and completeness are established using translations with more traditional sequent calculi for bi-intuitionistic logic.
Keywords Multiple-conclusion  Refutation  Proofnet  Co-implication
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DOI 10.1016/j.jal.2017.12.001
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References found in this work BETA

Basic Proof Theory.Roy Dyckhoff - 2001 - Bulletin of Symbolic Logic 7 (2):280-280.
Constructive Negation, Implication, and Co-Implication.Heinrich Wansing - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):341-364.
Dual-Intuitionistic Logic.Igor Urbas - 1996 - Notre Dame Journal of Formal Logic 37 (3):440-451.
A More General General Proof Theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.
On Logics with Coimplication.Frank Wolter - 1998 - Journal of Philosophical Logic 27 (4):353-387.

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