2006
DOI: 10.1016/j.entcs.2005.05.023
|View full text |Cite
|
Sign up to set email alerts
|

Propositional Logic as a Propositional Fuzzy Logic

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… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2007
2007
2021
2021

Publication Types

Select...
3

Relationship

0
3

Authors

Journals

citations
Cited by 3 publications
(2 citation statements)
references
References 11 publications
0
2
0
Order By: Relevance
“…they have as 1-tautologies exactly the classical tautologies [3,4]. So, since INF(α) ≡ α for the propositional classic logic, the INF for the classic-like fuzzy semantics restricted to the conjunction, negation and implication connectives, clearly preserves tautologies and contradictions.…”
Section: -Tautologiesmentioning
confidence: 91%
“…they have as 1-tautologies exactly the classical tautologies [3,4]. So, since INF(α) ≡ α for the propositional classic logic, the INF for the classic-like fuzzy semantics restricted to the conjunction, negation and implication connectives, clearly preserves tautologies and contradictions.…”
Section: -Tautologiesmentioning
confidence: 91%
“…Others fuzzy (or many-valued) modal logics have already been defined (see for example [21][22][23][24][25][26][27]). In the approach proposed in [23,28], the propositional connectives are interpreted as t-norms, t-conorms, fuzzy implications, fuzzy negations are considered in such a way that the classical tautologies are preserved as in [20,29] and the modal connectives have a semantic similar to the proposed by Caicedo and Rodríguez [30]. In particular, the authors seek a characterisation of fuzzy connective which maintains the usual theorems of modal logic into fuzzy setting.…”
Section: Fuzzy Bdi Logicmentioning
confidence: 99%