arXiv subjects

Sergio Celani

Publications and source records attributed to Sergio Celani.

3 recordsLinked to original sources

arXiv2026

A Modal Expansion of Kleene Algebras via Twist Structures

Kleene triples, introduced by Jalali, provide a representation of arbitrary Kleene algebras in terms of twist-products. We introduce modal Kleene algebras and modal Kleene triples, and establish a categorical equivalence between the corresponding categories, extending Jalali's duality to the modal setting. We study the centered case and show that Kleene algebras with implication can be naturally described within this framework by viewing implication as a family of modal operators. Finally, we develop a topological duality for modal Kleene triples.

math.LO↗

arXiv2025

Conditional algebras

Drawing on the classic paper by Chellas "Basic conditional logic" (1975), we propose a general algebraic framework for studying a binary operation of conditional that models universal features of the "if..., then..." connective as strictly related to the unary modal necessity operator. To this end, we introduce a variety of conditional algebras, and we develop its duality and canonical extensions theory.

math.LO↗

arXiv2023

Bounded distributive lattices with strict implication and weak difference

In this paper we introduce the class of weak Heyting Brouwer algebras (WHB-algebras, for short). We extend the well known duality between distributive lattices and Priestley spaces, in order to exhibit a relational Priestley-like duality for WHB-algebras. Finally, as an application of the duality, we build the tense extension of a WHB-algebra and we employ it as a tool for proving structural properties of the variety such as the finite model property, the amalgamation property, the congruence extension property and the Maehara interpolation property.

math.LO↗