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.
Montagna, F., Noguera, C., Horcik, R. (2006). On weakly cancellative fuzzy logics. JOURNAL OF LOGIC AND COMPUTATION, 16(4), 423-450 [10.1093/logcom/exl002].
On weakly cancellative fuzzy logics
MONTAGNA F.;NOGUERA C.;
2006-01-01
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 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.
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https://hdl.handle.net/11365/7165
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