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Journal of Logic and Computation Advance Access originally published online on July 26, 2006
Journal of Logic and Computation 2006 16(4):423-450; doi:10.1093/logcom/exl002
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

On Weakly Cancellative Fuzzy Logics

Franco Montagna

Department of Mathematics and Computer Science, University of Siena.

Carles Noguera

Artificial Intelligence Research Institute (IIIA), Spanish Council for Scientific Research (CSIC). E-mail: cnoguera{at}iiia.csic.es

Rostislav Horcík

Institute of Computer Science, Academy of Sciences of the Czech Republic. E-mail: horcik{at}cs.cas.cz

E-mail: montagna{at}unisi.it

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 {Pi}MTL. 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.

Keywords: Algebraic logic; fuzzy logics; left-continuous t-norms; MTL-algebras; residuated lattices; weak cancellation


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