Propositional Logic as a Propositional Fuzzy Logic

Authors:
Benjamín René Callejas Bedregal;Anderson Paiva Cruz
Affiliations:
Department of Informatics and Applied Mathematics, Laboratory of Logic a nd Computational Intelligence, Federal University of Rio Grande do Norte, CEP 59.072-970, Natal, Brazil;Department of Informatics and Applied Mathematics, Laboratory of Logic a nd Computational Intelligence, Federal University of Rio Grande do Norte, CEP 59.072-970, Natal, Brazil
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2006

Citing 4
Cited 1

On fuzzy implication operators

Fuzzy Sets and Systems
Operations fitting triangular-norm-based biresiduation

Fuzzy Sets and Systems - Special issue on triangular norms
Truth, Deduction, and Computation: Logic and Semantics for Computer Science

Truth, Deduction, and Computation: Logic and Semantics for Computer Science
Automorphisms, negations and implication operators

Fuzzy Sets and Systems - Implication operators

A normal form which preserves tautologies and contradictions in a class of fuzzy logics

Journal of Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.