Normal forms and free algebras for some extensions of MTL

Authors:
Stefano Aguzzoli;Brunella Gerla
Affiliations:
Dept. Computer Science, Università degli Studi di Milano, Via Comelico 39-41, 20135 Milano, Italy;DICOM, Università dell'Insubria, Via Mazzini 5, 21100 Varese, Italy
Venue:
Fuzzy Sets and Systems
Year:
2008

Citing 2
Cited 3

Spectral Duality for Finitely Generated Nilpotent Minimum Algebras, with Applications

Journal of Logic and Computation
Poset representation for gödel and nilpotent minimum logics

ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)

Fuzzy Sets and Systems
Stone-like representation theorems and three-valued filters in R0- algebras (nilpotent minimum algebras)

Fuzzy Sets and Systems
Lewis Dichotomies in Many-Valued Logics

Studia Logica

Quantified Score

Hi-index	0.20

Visualization

Abstract

We introduce a semantical definition of minterms and maxterms which generalizes the usual notion in Boolean logic to a class of many-valued logics. We apply this notion to get normal forms for logics G, NM, NMG. Then we obtain a combinatorial description of the n-generated free algebras in the varieties constituting the algebraic semantics of those logics. Specifically, we represent via combinatorial posets the embedding of the n-generated free algebra into the direct product of all n-generated chains in the variety.