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Hybrid Deduction–Refutation Systems
Stockholm University, Faculty of Humanities, Department of Philosophy. University of Johannesburg, South Africa.ORCID iD: 0000-0002-0157-1644
2019 (English)In: Axioms, E-ISSN 2075-1680, Vol. 8, no 4, article id 118Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2019. Vol. 8, no 4, article id 118
Keywords [en]
deductive refutability, refutation systems, hybrid deduction–refutation rules, derivative hybrid rules, soundness, completeness, natural deduction, meta-proof theory
National Category
Mathematics Philosophy
Research subject
Mathematical Logic; Philosophy
Identifiers
URN: urn:nbn:se:su:diva-177315DOI: 10.3390/axioms8040118OAI: oai:DiVA.org:su-177315DiVA, id: diva2:1381489
Funder
Swedish Research Council, 2015-04388Available from: 2019-12-21 Created: 2019-12-21 Last updated: 2019-12-23

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