On weakly cancellative fuzzy logics
From Mathfuzzlog
| Authors: |
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| Title: | On weakly cancellative fuzzy logics | |||
| Journal: | Journal of Logic and Computation | |||
| Volume | 16 | |||
| Number | 4 | |||
| Pages: | 423-450 | |||
| Year: | 2006 | |||
| Preprint | ||||
Abstract
Starting from a decomposition result of MTL-chains as ordinal sums, we focus our attention on a particular kind of indecomposable semihoops, namely weakly cancellative semihoops. Weak cancellation property is proved to be the difference between cancellation and pseudocomplementation, so it gives a new axiomatization of Product logic and 
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.
