Hybrid Deduction–Refutation Systems
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 d...
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2019-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/8/4/118 |
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doaj-c9ff38dcb1f64c3b8058fd39d841cea62020-11-24T21:51:16ZengMDPI AGAxioms2075-16802019-10-018411810.3390/axioms8040118axioms8040118Hybrid Deduction–Refutation SystemsValentin Goranko0Department of Philosophy, Stockholm University, SE-10691 Stockholm, SwedenHybrid 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.https://www.mdpi.com/2075-1680/8/4/118deductive refutabilityrefutation systemshybrid deduction–refutation rulesderivative hybrid rulessoundnesscompletenessnatural deductionmeta-proof theory |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Valentin Goranko |
| spellingShingle |
Valentin Goranko Hybrid Deduction–Refutation Systems Axioms deductive refutability refutation systems hybrid deduction–refutation rules derivative hybrid rules soundness completeness natural deduction meta-proof theory |
| author_facet |
Valentin Goranko |
| author_sort |
Valentin Goranko |
| title |
Hybrid Deduction–Refutation Systems |
| title_short |
Hybrid Deduction–Refutation Systems |
| title_full |
Hybrid Deduction–Refutation Systems |
| title_fullStr |
Hybrid Deduction–Refutation Systems |
| title_full_unstemmed |
Hybrid Deduction–Refutation Systems |
| title_sort |
hybrid deduction–refutation systems |
| publisher |
MDPI AG |
| series |
Axioms |
| issn |
2075-1680 |
| publishDate |
2019-10-01 |
| description |
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. |
| topic |
deductive refutability refutation systems hybrid deduction–refutation rules derivative hybrid rules soundness completeness natural deduction meta-proof theory |
| url |
https://www.mdpi.com/2075-1680/8/4/118 |
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AT valentingoranko hybriddeductionrefutationsystems |
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1725879571443613696 |