Propositional Logic as a Propositional Fuzzy Logic | Zendy

Benjamín Bedregal | Zendy; Anderson Cruz | Zendy

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Propositional Logic as a Propositional Fuzzy Logic

Author(s) -

Benjamín Bedregal,

Anderson Cruz

Publication year - 2005

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2005.05.023

Subject(s) - t norm fuzzy logics , propositional variable , well formed formula , zeroth order logic , monoidal t norm logic , mathematics , logical connective , negation , classical logic , propositional calculus , autoepistemic logic , intuitionistic logic , fuzzy logic , truth function , propositional formula , truth value , many valued logic , tautology (logic) , intermediate logic , discrete mathematics , fuzzy number , fuzzy set , computer science , artificial intelligence , description logic , programming language , multimodal logic

There are several ways to extend the classical logical connectives for fuzzy truth degrees, in such a way that their behavior for the values 0 and 1 work exactly as in the classical one. For each extension of logical connectives the formulas which are always true (the tautologies) changes. In this paper we will provide a fuzzy interpretation for the usual connectives (conjunction, disjunction, negation, implication and bi-implication) such that the set of tautologies is exactly the set of classical tautologies. Thus, when we see logics as set of formulas, then the propositional (classical) logic has a fuzzy model

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