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Hybrid Deduction–Refutation Systems
Stockholms universitet, Humanistiska fakulteten, Filosofiska institutionen. University of Johannesburg, South Africa.ORCID-id: 0000-0002-0157-1644
2019 (engelsk)Inngår i: Axioms, E-ISSN 2075-1680, Vol. 8, nr 4, artikkel-id 118Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2019. Vol. 8, nr 4, artikkel-id 118
Emneord [en]
deductive refutability, refutation systems, hybrid deduction–refutation rules, derivative hybrid rules, soundness, completeness, natural deduction, meta-proof theory
HSV kategori
Forskningsprogram
matematisk logik; filosofi
Identifikatorer
URN: urn:nbn:se:su:diva-177315DOI: 10.3390/axioms8040118ISI: 000505589700018OAI: oai:DiVA.org:su-177315DiVA, id: diva2:1381489
Forskningsfinansiär
Swedish Research Council, 2015-04388Tilgjengelig fra: 2019-12-21 Laget: 2019-12-21 Sist oppdatert: 2020-02-05bibliografisk kontrollert

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