T-norm based logics with n-contraction

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Agata Ciabattoni
Francesc Esteva
Lluís Godo
Title: T-norm based logics with n-contraction
Journal: Neural Network World
Volume 12
Number 5
Pages: 441-452
Year: 2002


We consider two families of fuzzy propositional logics obtained by extending MTL and IMTL with the n-contraction axiom, for n>=2. These logics - called Cn-MTL and Cn-IMTL - range from Gödel and classical logic (when n=2) to MTL and IMTL (when n tends to infinity), respectively. We investigate the t-norm based semantics and the proof theory for Cn-MTL and Cn-IMTL. We show standard completeness and suitable analytic hipersequent calculi for them.