arXiv subjects

Brunella Gerla

Publications and source records attributed to Brunella Gerla.

5 recordsLinked to original sources

arXiv2024

Tropicalization through the lens of {\L}ukasiewicz logic, with a topos theoretic perspective

The main aim of this paper is to show the interconnections between {\L}ukasiewicz logic and algebraic geometry using algebraic, geometric and logical instruments. We continue our investigation into a new algebraic geometry based on idempotent semifields, in particular those related with MV-algebras, describing categorical equivalence between different structures related to tropical geometry and many valued logics. Further, we describe such connections in terms of topoi.

math.LO↗

arXiv2015

Querying with Łukasiewicz logic

In this paper we present, by way of case studies, a proof of concept, based on a prototype working on a automotive data set, aimed at showing the potential usefulness of using formulas of Łukasiewicz propositional logic to query databases in a fuzzy way. Our approach distinguishes itself for its stress on the purely linguistic, contraposed with numeric, formulations of queries. Our queries are expressed in the pure language of logic, and when we use (integer) numbers, these stand for shortenings of formulas on the syntactic level, and serve as linguistic hedges on the semantic one. Our case-study queries aim first at showing that each numeric-threshold fuzzy query is simulated by a Łukasiewicz formula. Then they focus on the expressing power of Łukasiewicz logic which easily allows for updating queries by clauses and for modifying them through a potentially infinite variety of linguistic hedges implemented with a uniform syntactic mechanism. Finally we shall hint how, already at propositional level, Łukasiewicz natural semantics enjoys a degree of reflection, allowing to write syntactically simple queries that semantically work as meta-queries weighing the contribution of simpler ones.

cs.LO↗

arXiv2012

Rational Lukasiewicz logic and DMV-algebras

In this paper we present some results on the variety of divisible MV-algebras. Any free divisible MV-algebra is an algebra of continuous piecewise linear functions with rational coefficients. Correspondingly, Rational {\L}ukasiewicz logic is defined.

math.LO↗

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

Representation of Perfect and Local MV-algebras

We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0,1]. Furthermore, we give a representation of local Abelian lattice-ordered groups with strong unit as quasi-constant functions on an ultraproduct of the reals. All the above theorems are proved to have a uniform version, depending only on the cardinality of the algebra to be embedded, as well as a definable construction in ZFC. The paper contains both known and new results and provides a complete overview of representation theorems for such classes.

math.LO↗