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Ciro Russo

Publications and source records attributed to Ciro Russo.

At least 19 recordsLinked to original sources
arXiv2026

Point-free MV-topologies

We propose a point-free approach to MV-topological spaces in the wake of previous works on both classical and fuzzy topology. In order to do that, we introduce suitable frame-type structures and a class of fuzzy topological spaces which includes and suitably extends the one of MV-topological spaces. Then we show an adjoint situation between such structures, and restrict such an adjointness to a duality between the corresponding classes of ``spatial frames'' and ``sober spaces''. We also use neighbourhood systems to characterize sobriety in this context.

math.LO↗
arXiv2025

Morita Equivalence for Quantales

We study Morita equivalence in the context of quantales with identity, in the wake of Katsov and Nam's analogous work on semirings. Among a number of other results, we prove a characterization of Morita equivalence and an Eilenberg-Watts-type Theorem for quantales.

math.CT↗
arXiv2025

The category of propositional deductive systems

We define the category $\QM$ of quantales and their modules and prove the existence of coproducts, and the existence of pushout and amalgamated coproducts under certain conditions. Then we define the non-full subcategory $\DS_0$ of propositional deductive systems, show that it is equivalent to the one of ``real'' propositional logics whose morphisms are interpretations (modulo a language translation, when needed), and prove that the coproduct in $\DS_0$ is precisely the deductive system called ``logical coproduct'' in \cite{ruslu}. Last, we discuss amalgamation in $\DS_0$.

math.LO↗
arXiv2025

An extension of Priestley duality to fuzzy topologies and positive MV-algebras

We extend Priestley Duality to suitable categories of fuzzy topological spaces and ordered algebraic structures that generalize bounded distributive lattices. The duality we prove extends not only classical Priestley Duality between Priestley Spaces and bounded distributive lattices, but also the duality between limit cut complete MV-algebras and Stone MV-topological spaces (proved by the second author in a previous paper) which, on its turn, is an extension of classical Stone Duality.

math.CT↗
arXiv2025

Fra\"iss\'e limit and Ramsey Theorem: the case of MV-algebras and a categorical generalization

In this paper we describe the Fra\"iss\'e limit of finite MV-algebras and then prove that finite MV-algebras verify the Ramsey property. Then we show that MV-algebras are just a special case of a more general situation. In fact, under minumum conditions for the application of the Kechris-Pestov-Todorcevic correspondence, Ramsey property holds for a certain category of finite structures if and only if it holds for a completion subcategory of it.

math.LO↗
arXiv2023

Gravity Network for end-to-end small lesion detection

This paper introduces a novel one-stage end-to-end detector specifically designed to detect small lesions in medical images. Precise localization of small lesions presents challenges due to their appearance and the diverse contextual backgrounds in which they are found. To address this, our approach introduces a new type of pixel-based anchor that dynamically moves towards the targeted lesion for detection. We refer to this new architecture as GravityNet, and the novel anchors as gravity points since they appear to be "attracted" by the lesions. We conducted experiments on two well-established medical problems involving small lesions to evaluate the performance of the proposed approach: microcalcifications detection in digital mammograms and microaneurysms detection in digital fundus images. Our method demonstrates promising results in effectively detecting small lesions in these medical imaging tasks.

cs.CV↗
arXiv2021

Coproduct and amalgamation of deductive systems by means of ordered algebras

We propose various methods for combining or amalgamating propositional languages and deductive systems. We make heavy use of quantales and quantale modules in the wake of previous works by the present and other authors. We also describe quite extensively the relationships among the algebraic and order-theoretic constructions and the corresponding ones based on a purely logical approach.

math.LO↗
arXiv2019

MV-Algebras as Sheaves of l-groups on Fuzzy Topological Spaces

We introduce the concept of fuzzy sheaf as a natural generalisation of a sheaf over a topological space in the context of fuzzy topologies. Then we prove a representation for a class of MV-algebras in which the representing object is an MV-sheaf of lattice-ordered Abelian groups, namely, a fuzzy sheaf in which the base (fuzzy) topological space is an MV-topological space and the stalks are Abelian $\ell$-groups.

math.LO↗
arXiv2017

Quantales and their modules: projective objects, ideals, and congruences

In this paper we characterize the projective modules over an arbitrary quantale, and then we apply such a characterization in order to define the K_0 group of a quantale. Then we study congruences of quantales and quantale modules by means of their ideals and of saturated elements w.r.t. a binary relation.

math.LO↗
arXiv2016

Compactness in MV-Topologies: Tychonoff Theorem and Stone-Cech Compactification

In this paper, we discuss some questions about compactness in MV-topological spaces. More precisely, we first present a Tychonoff theorem for such a class of fuzzy topological spaces and some consequence of this result, among which, for example, the existence of products in the category of Stone MV-spaces and, consequently, of coproducts in the one of limit cut complete MV-algebras. Then we show that our Tychonoff theorem is equivalent, in ZF, to the Axiom of Choice, classical Tychonoff theorem, and Lowen's analogous result for lattice-valued fuzzy topology. Last, we show an extension of the Stone-Cech compactification functor to the category of MV-topological spaces, and we discuss its relationship with previous works on compactification for fuzzy topological spaces.

math.LO↗
arXiv2015

An extension of Stone duality to fuzzy topologies and MV-algebras

In this paper we introduce the concept of MV-topology, a special class of fuzzy topological spaces, and prove a proper extension of Stone Duality to the categories of limit cut complete MV-algebras and Stone MV-spaces, namely, zero-dimensional compact Hausdorff MV-topological spaces. Then we describe the object class of limit cut complete MV-algebras, and show that any semisimple MV-algebra has a limit cut completion, namely, a minimum limit cut complete extension. Last, we compose our duality with other known ones, thus obtaining new categorical equivalences and dualities involving categories of MV-algebras.

math.LO↗
arXiv2015

The semiring-theoretic approach to MV-algebras: a survey

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. The survey focuses mainly on the connections between MV-algebras and other theories that such a semiringbased approach enabled, and on an application of such a framework to Digital Image Processing. We also give some suggestions for further developments by stating several open problems and possible research lines.

math.LO↗
arXiv2012

An order-theoretic analysis of interpretations among propositional deductive systems

In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have different underlying languages.

math.LO↗
arXiv2011

A fuzzified BRAIN algorithm for learning DNF from incomplete data

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 with uncertain values or missing bits. Such an algorithm is obtained from BRAIN by introducing fuzzy sets in order to manage uncertainty. In the case where no missing bits are present, the algorithm reduces to the original BRAIN.

cs.IT↗
arXiv2010

Semiring and semimodule issues in MV-algebras

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 the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. We present several results addressed toward a semiring theory for MV-algebras. In particular we show a representation of MV-algebras as a subsemiring of the endomorphism semiring of a semilattice, the construction of the Grothendieck group of a semiring and its functorial nature, and the effect of Mundici categorical equivalence between MV-algebras and lattice-ordered Abelian groups with a distinguished strong order unit upon the relationship between MV-semimodules and semimodules over idempotent semifields.

math.RA↗
arXiv2010

The Logic of CMV-Algebras

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 the variety of CMV-algebras.

math.LO↗
arXiv2010

Quantale Modules and their Operators, with Applications

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 out to be precisely the homomorphisms between free objects in those categories - find concrete applications in two different branches of image processing, namely fuzzy image compression and mathematical morphology.

math.LO↗