A short introduction to formal fuzzy logic via t-norms
A VERY short introduction to formal fuzzy logic via t-norms.
A short introduction to formal fuzzy logic via t-norms
muMV-algebras: an approach to fixed points in Lukasiewicz logic
We study an expansion of MV-algebras, called $\mu$MV-algebras, in which minimum and maximum fixed points are definable. The first result is that $\mu$MV-algebras are term-wise equivalent to divisible MV$_\Delta$ algebras, i.e. a combination of two known MV-algebras expansion: divisible MV-algebras and MV$_\Delta$ algebras. Using methods from the two known extensions we derive a number of results about $\mu$MV-algebras; among others: subdirect representation, standard completeness, amalgamation property and a description of the free algebra.
muMV-algebras: an approach to fixed points in Lukasiewicz logic
Continuous approximations of MV-algebras with product and product residuation: a category-theoretic equivalence
A new class of $MV$-algebras with product, called L$\Pi_q$-algebras, has been introduced. In these algebras, the discontinuous product residuation $\to_\pi$ is replaced by a continuous approximation of it. These algebras seem to be a good compromise between the need ofexpressiveness 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 L$\Pi_q$-algebras and of $f$-quasifields are equivalent.
Continuous approximations of MV-algebras with product and product residuation
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 L$\Pi$-algebras. Even though the language of L$\Pi$-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 L$\Pi_q$-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 L$\Pi_q$-algebras whose lattice reduct is the unit interval [0,1] with the usual order.
Continuous approximations of MV-algebras with product and product residuation
μMV algebras an approach to fixed points in Lukasiewiczlogic
A presentation about adding fixed points operators in the language of MV-algebras given at the conference The Logic of Soft Computing in Malaga, $13^{th}−15^{th}$ September 2006.
μMV algebras an approach to fixed points in Lukasiewicz logic
