On Some Systems for Two Versions of Many-valued Logics

Anahit Chubaryan

ISBN 10: 6202011041 / ISBN 13: 9786202011044

Verlag: LAP LAMBERT Academic Publishing, 2017

Beschreibung

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Bestandsnummer des Verkäufers 9786202011044

Bibliografische Details

• Titel: On Some Systems for Two Versions of Many-valued Logics
• Verlag: LAP LAMBERT Academic Publishing
• Erscheinungsjahr: 2017
• Sprache: Englisch
• ISBN-10: 6202011041
• ISBN-13: 9786202011044
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 220B x 150 H x 5 T Millimeter Breite: 220 mm, Höhe: 150 mm, Tiefe: 5 mm
• Gewicht: 137 Gramm

Über diesen Titel

Inhaltsangabe

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.