24 citations · 53 across the 7 of their papers we have counts for
8 papers
The spectrum problem for -groups and for MV-algebras: a categorical approach
Giuseppina Gerarda Barbieri, Antonio Di Nola, Giacomo Lenzi
As a main result, we characterize prime spectra of abelian lattice ordered groups. Further we introduce some categories based on spectral spaces, lattices and Priestley spaces, and…
Infinitary logic and basically disconnected compact Hausdorff spaces
Antonio Di Nola, Serafina Lapenta, Ioana Leustean
We extend Łukasiewicz logic obtaining the infinitary logic whose models are algebras , where is a basically disconnected compact Hausdorff space. Eq…
An analysis of the logic of Riesz Spaces with strong unit
Antonio Di Nola, Serafina Lapenta, Ioana Leustean
We study Łukasiewicz logic enriched with a scalar multiplication with scalars taken in . Its algebraic models, called {\em Riesz MV-algebras}, are, up to isomorphism, unit i…
Lukasiewicz logic and Riesz spaces
Antonio Di Nola, Ioana Leustean
We initiate a deep study of {\em Riesz MV-algebras} which are MV-algebras endowed with a scalar multiplication with scalars from . Extending Mundici's equivalence between MV…
The semiring-theoretic approach to MV-algebras: a survey
Antonio Di Nola, Ciro Russo
In this paper we review some of the main achievements of the semiring-theoretic approach to MV-algebras initiated and pursued mainly by the present authors and their collaborators.…
Stone Duality Type Theorems for MV-algebras with Internal State
Antonio Di Nola, Anatolij Dvurecenskij, Ada Lettieri
Recently in \cite{FM, FlMo}, the language of MV-algebras was extended by adding a unary operation, an internal operator, called also a state-operator. In \cite{DD1}, a stronger ver…
The Logic of CMV-Algebras
Antonio Di Nola, Brunella Gerla, Ciro Russo
In this paper, once recalled some properties of CMV-algebras, we introduce an expansion of the one-variable fragment of Lukasiewicz propositional logic whose algebraic semantics is…
Semiring and semimodule issues in MV-algebras
Antonio Di Nola, Ciro Russo
In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing t…