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  1. Paraconsistency in classical logic.Gabriele Pulcini & Achille C. Varzi - 2018 - Synthese 195 (12):5485-5496.
    Classical propositional logic can be characterized, indirectly, by means of a complementary formal system whose theorems are exactly those formulas that are not classical tautologies, i.e., contradictions and truth-functional contingencies. Since a formula is contingent if and only if its negation is also contingent, the system in question is paraconsistent. Hence classical propositional logic itself admits of a paraconsistent characterization, albeit “in the negative”. More generally, any decidable logic with a syntactically incomplete proof theory allows for a paraconsistent characterization of (...)
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  • Complementary Proof Nets for Classical Logic.Gabriele Pulcini & Achille C. Varzi - 2023 - Logica Universalis 17 (4):411-432.
    A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, $$\textsf{CPN}$$ CPN, that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in $$\textsf{CPN}$$ CPN enjoys strong normalization along with (...)
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  • Towards a Non-classical Meta-theory for Substructural Approaches to Paradox.Lucas Rosenblatt - 2021 - Journal of Philosophical Logic 50 (5):1007-1055.
    In the literature on self-referential paradoxes one of the hardest and most challenging problems is that of revenge. This problem can take many shapes, but, typically, it besets non-classical accounts of some semantic notion, such as truth, that depend on a set of classically defined meta-theoretic concepts, like validity, consistency, and so on. A particularly troubling form of revenge that has received a lot of attention lately involves the concept of validity. The difficulty lies in that the non-classical logician cannot (...)
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  • A meta-logic of inference rules: Syntax.Alex Citkin - 2015 - Logic and Logical Philosophy 24 (3).
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