Hybrid Deduction–Refutation Systems
| Autor: | Valentin Goranko |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Filosofi
Logic Computer science hybrid deduction–refutation rules derivative hybrid rules soundness 0603 philosophy ethics and religion 01 natural sciences Calculus 0101 mathematics deductive refutability natural deduction meta-proof theory Mathematical Physics Mathematical logic Soundness Matematik refutation systems completeness Algebra and Number Theory Natural deduction lcsh:Mathematics 010102 general mathematics 06 humanities and the arts Propositional calculus lcsh:QA1-939 Differentiation rules Philosophy TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Completeness (logic) Data_GENERAL TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS 060302 philosophy Geometry and Topology Mathematics Analysis |
| Zdroj: | Axioms, Vol 8, Iss 4, p 118 (2019) Axioms; Volume 8; Issue 4; Pages: 118 |
| ISSN: | 2075-1680 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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