On Some Systems for Two Versions of Many-valued Logics

Anahit Chubaryan

ISBN 10: 6202011041 / ISBN 13: 9786202011044

Editore: LAP LAMBERT Academic Publishing Aug 2017, 2017

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This item is printed on demand - it takes 3-4 days longer - Neuware -The current research refers to the problem of constructing several proof systems for two versions of many-valued propositional logic and investigating of their properties . The generalization of Kalmar's proof of deducibility for two-valued tautologies in the classical propositional logic gives us a possibility to suggest 1) a new method of proving the completeness of propositional proof system of three-valued logic of Lukasewicz that it is essentially simpler than other known proofs of completeness and can be easily modified into a proof of completeness for other versions of k-valued logics for k 3 and even for fuzzy logic as well, 2) a method of defining many traditional variants of proof systems for k-valued (k 3) logics, the completeness of which is easily proved directly, without the usual immersion into two-valued logic. Most of all the introduced proof systems are 'weak' ones with a 'simple strategist' of proof search and we have also investigated the quantitative properties, related to proof complexity characteristics in them. 80 pp. Englisch.

Codice articolo 9786202011044

Dati bibliografici

• Titolo: On Some Systems for Two Versions of Many-valued Logics
• Editore: LAP LAMBERT Academic Publishing Aug 2017
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 6202011041
• ISBN 13: 9786202011044
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 220 L x 150 A x 5 P (millimetri) 220 millimetri di larghezza per 150 millimetri di altezza per 5 millimetri di profondità
• Peso: 137 grammi

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Riassunto

The current research refers to the problem of constructing several proof systems for two versions of many-valued propositional logic and investigating of their properties . The generalization of Kalmar’s proof of deducibility for two-valued tautologies in the classical propositional logic gives us a possibility to suggest 1) a new method of proving the completeness of propositional proof system of three-valued logic of Lukasewicz that it is essentially simpler than other known proofs of completeness and can be easily modified into a proof of completeness for other versions of k-valued logics for k≥3 and even for fuzzy logic as well, 2) a method of defining many traditional variants of proof systems for k-valued (k≥3) logics, the completeness of which is easily proved directly, without the usual immersion into two-valued logic. Most of all the introduced proof systems are “weak” ones with a “simple strategist” of proof search and we have also investigated the quantitative properties, related to proof complexity characteristics in them.