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  1. Reprint Of: A More General General Proof Theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.
    In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof system N2Int of the bi-intuitionistic (...)
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  • Deductive Inference as Indirect Verification.Takuro Onishi - 2015 - Journal of the Japan Association for Philosophy of Science 42 (2):81-95.
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  • Pragmatic and Dialogic Interpretations of Bi-Intuitionism. Part I.Gianluigi Bellin, Massimiliano Carrara, Daniele Chiffi & Alessandro Menti - 2014 - Logic and Logical Philosophy.
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  • A Modal Translation for Dual-Intuitionistic Logic.Yaroslav Shramko - 2016 - Review of Symbolic Logic 9 (2):251-265.
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  • Natural Deduction for Bi-Intuitionistic Logic.Luca Tranchini - 2017 - Journal of Applied Logic 25:S72-S96.
    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.
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