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  1. N-valued maximal paraconsistent matrices.Adam Trybus - 2019 - Journal of Applied Non-Classical Logics 29 (2):171-183.
    ABSTRACTThe articles Maximality and Refutability Skura [. Maximality and refutability. Notre Dame Journal of Formal Logic, 45, 65–72] and Three-valued Maximal Paraconsistent Logics Skura and Tuziak [. Three-valued maximal paraconsistent logics. In Logika. Wydawnictwo Uniwersytetu Wrocławskiego] introduced a simple method of proving maximality of a given paraconsistent matrix. This method stemmed from the so-called refutation calculus, where the focus in on rejecting rather than accepting formulas. The article A Generalisation of a Refutation-related Method in Paraconsistent Logics Trybus [. A generalisation (...)
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  • A Generalisation of a Refutation-related Method in Paraconsistent Logics.Adam Trybus - forthcoming - Logic and Logical Philosophy.
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  • The RM paraconsistent refutation system.Tomasz Skura - 2009 - Logic and Logical Philosophy 18 (1):65-70.
    The aim of this paper is to study the refutation system consisting of the refutation axiom p ∧ ¬p → q and the refutation rules: reverse substitution and reverse modus ponens (B/A, if A → B ∈ RM). It is shown that the refutation system is characteristic for the logic of the 3-element RM algebra.
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  • A refutation theory.Tomasz Skura - 2009 - Logica Universalis 3 (2):293-302.
    A general theory of refutation systems is given. Some applications (concerning maximality and minimality in lattices of logics) are also discussed.
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  • Hybrid Deduction–Refutation Systems.Valentin Goranko - 2019 - Axioms 8 (4).
    Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for classical propositional logic, for which I (...)
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