Authors: Franco Montagna and Luca Spada
Abstract: Recently, MV-algebras with product have been investigated from different points of view. In particular a variety resulting from the combination of MV-algebras and product algebras has been introduced. The elements of this variety are called LΠ-algebras. Even though the language of LΠ-algebras is strong enough to describe the main properties of product and of Lukasiewicz connectives on [0, 1], the discontinuity of product implication introduces some problems in the applications, because a small error in the data may cause a relevant error in the output. In this paper we try to overcome this difficulty, substituting the product implication by a continuous approximation of it. The resulting algebras, the LΠq-algebras, are investigated in the present paper. In this paper we give a complete axiomatization of the quasivariety obtained in this way, and we show that such quasivariety is generated by the class of all LΠq-algebras whose lattice reduct is the unit.
[…] with a sort of weak divisibility property, called $f$-quasifields, and show that the categories of L$Pi_q$-algebras and of $f$-quasifields are […]