Continuous Approximations of MV-Algebra with Product and Product Residuation: A Categorical equivalence.
Author: Luca Spada
Abstract: In [MS03] a new class of MV-algebras with product, called LΠq-algebras, has been introduced. In these algebras, the discontinuous product residuation →π is replaced by a continuous approximation of it. These algebras seem to be a good compromise between the need of expressiveness and the need of continuity of connectives. Following a good tradition in many-valued logic, in this paper we introduce a class of commutative f-rings with strong unit and with a sort of weak divisibility property, called f-quasifields, and we show that the categories of LΠq-algebras and of f-quasifields are equivalent.
