T-norm-based logics with an independent involutive negation

Authors:
Tommaso Flaminio;Enrico Marchioni
Affiliations:
Dipartimento di Matematica e Informatica, Università di Siena, Pian dei Mantellini 44, 53100 Siena, Italy;Departamento de Lógica, Universidad de Salamanca, Campus Unamuno - Edificio FES, 37007 Salamanca, Spain
Venue:
Fuzzy Sets and Systems
Year:
2006

Citing 2
Cited 7

On triangular norm-based propositional fuzzy logics

Fuzzy Sets and Systems - Special issue on fuzzy information processing
A first course in fuzzy logic

A first course in fuzzy logic

On the representation of fuzzy rules

International Journal of Approximate Reasoning
Graded Fuzzy Rules

IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
On Fuzzy Description Logics

Proceedings of the 2008 conference on Artificial Intelligence Research and Development: Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence
Algebras of Fuzzy Sets in Logics Based on Continuous Triangular Norms

ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Fuzzy logics with an additional involutive negation

Fuzzy Sets and Systems
First-order satisfiability in Gödel logics: An NP-complete fragment

Theoretical Computer Science
Proof theory for locally finite many-valued logics: Semi-projective logics

Theoretical Computer Science

Quantified Score

Hi-index	0.21

Visualization

Abstract

In this paper we investigate the addition of arbitrary independent involutive negations to t-norm-based logics. We deal with several extensions of MTL and establish general completeness results. Indeed, we will show that, given any t-norm-based logic satisfying some basic properties, its extension by means of an involutive negation preserves algebraic and (finite) strong standard completeness. We will deal with both propositional and predicate logics.