On Weakly Cancellative Fuzzy Logics

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.

• Type: Journal
• Year: 2006
• Where: LOGCOM
• Authors: Franco Montagna, Carles Noguera, Rostislav Horcík
• Keywords: LOGCOM 2006, Ordinal Sums, Particular Kind, Weak Cancellation Property