by C. Russo In this paper we introduce the concept of MV-topology, a generalization of general topology to fuzzy subsets, and we prove a proper extension of Stone duality to, respectively, semisimple MV-algebras and a suitable category of MV-topologies.
by A. Di Nola, C. Russo In this paper we propose a new perspective on the theory of MV-algebras based on the connection between such algebras and idempotent semirings. Such a viewpoint yields, among other results, interesting representation theorems. We also present some results of more general interest, such as Read more…
by C. Russo Journal of Logic and Computation (2010), 20(4): 917-946.Advance access December 2008.doi:10.1093/logcom/exn088 The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined. Such operators – that turn Read more…
by S. Rampone, C. Russo Aim of this paper is to address the problem of learning Boolean functions from training data with missing values. We present an extension of the BRAIN algorithm, called U-BRAIN (Uncertainty-managing Batch Relevance-based Artificial INtelligence), conceived for learning DNF Boolean formulas from partial truth tables, possibly Read more…
by R. Cignoli, A. Di Nola A. Lettieri It is shown that the construction and the properties of the functor β from the category of MV-algebras to the category of bounded residuated lattices has a natural interpretation in the contest of Priestley dualities.
In this paper it is shown that the prime ideal space of an MV-algebra is the disjoint union of prime ideal spaces of suitable local MV-algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well.
Antonio Di Nola, Giacomo Lenzi, Luca Spada We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0, 1]. This result also implies the existence, Read more…
By A. Di Nola, I. Esposito, B. Gerla In this paper we present several results about local MV-algebras, extending existing results given for MV-chains. The role of local MV-algebras in sheaf representation and weak boolean product is stressed and the relationship of local MV-algebras with varieties of MV-algebras is analyzed.
By L.P. Belluce, A. Di Nola, B. Gerla We investigate the class of abelian l-groups with strong unit corresponding to perfect MV-algebras via the Gamma functor, showing that this is a universal subclass of the class of all abelian l-groups with strong unit and describing the formulas that axiomatize it. Read more…
by A. Di Nola, R. Grigolia and L. Spada It is proved that the n-generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the n-generated free MVn-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MVn-algebras Read more…