On Weakly Cancellative Fuzzy Logics

Authors:
Franco Montagna;Carles Noguera;Rostislav Horčík
Affiliations:
Department of Mathematics and Computer Science, University of Siena.;Artificial Intelligence Research Institute (IIIA), Spanish Council for Scientific Research (CSIC). E-mail: cnoguera@iiia.csic.es;Institute of Computer Science, Academy of Sciences of the Czech Republic. E-mail: horcik@cs.cas.cz
Venue:
Journal of Logic and Computation
Year:
2006

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Abstract

Starting from a decomposition result of monoidal t-norm-based logic (MTL)-chains as ordinal sums, we focus our attention on a particular kind of indecomposable semihoops, namely weakly cancellative semihoops. The weak cancellation property is proved to be the difference between cancellation and pseudocomplementation, so it gives a new axiomatization of product logic and ΠMTL. By adding this property, some new fuzzy logics (propositional and first-order) are defined and studied obtaining some results about their (finite) strong standard completeness and other logical and algebraic properties.