Hybrid Deduction–Refutation Systems
Department of Philosophy, Stockholm University, SE-10691 Stockholm, Sweden
Visiting professorship at Department of Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
Axioms 2019, 8(4), 118; https://doi.org/10.3390/axioms8040118
Received: 27 August 2019 / Revised: 8 October 2019 / Accepted: 10 October 2019 / Published: 21 October 2019
(This article belongs to the Special Issue Deductive Systems in Traditional and Modern Logic)
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 show soundness and completeness for both deductions and refutations. View Full-Text
Keywords: deductive refutability; refutation systems; hybrid deduction–refutation rules; derivative hybrid rules; soundness; completeness; natural deduction; meta-proof theory
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Goranko, V. Hybrid Deduction–Refutation Systems. Axioms 2019, 8, 118.
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Goranko V. Hybrid Deduction–Refutation Systems. Axioms. 2019; 8(4):118.Chicago/Turabian Style
Goranko, Valentin. 2019. "Hybrid Deduction–Refutation Systems." Axioms 8, no. 4: 118.
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