arXiv subjects

Ricardo O. Rodriguez

Publications and source records attributed to Ricardo O. Rodriguez.

5 recordsLinked to original sources

arXiv2026

Twist-structures isomorphic to modal Nelson lattices

In this paper, we introduce a new variety of Heyting algebras with two unary modal operators that are not interdefinable but satisfy the weakest condition necessary to define modal operators on Nelson lattices. To achieve this, we utilize the representation of Nelson lattices as twist structures over Heyting algebras and establish a categorical equivalence. Finally, we develop a topological duality for this new variety and apply it to derive a topological duality for modal Nelson lattices.

math.LO↗

arXiv2026

An Abstract Worlds Semantic Framework for Belief Change Operators

This article proposes a set-theoretic framework for belief change, called Abstract Worlds Semantics, in which no logical syntax is assumed. Inspired by Grove's (1988) results, our approach treats worlds as primitive elements, over which world contraction and world revision operators are defined. This semantic framework enables a unified analysis of belief change models. Within this framework, we unify classical and non-prioritized belief change constructions by defining versatile operators. When classical propositional logic is considered, our framework provides a homogeneous account of AGM, KM, and Multiple Change models. In summary, AWS systematizes belief change frameworks and operators, simplifying and generalizing belief change theory over belief sets.

cs.AI↗

arXiv2026

Axiomatizing logics of finite Gödel-Kripke models

We investigate completeness for modal Gödel logics with respect to finite Gödel-Kripke models, along with related aspects. It is well known that the logics studied in [4, 11] fail to be complete with respect to finite Gödel-Kripke models. We show that the natural candidate axiomatic extensions do not restore completeness, thereby resolving a 15 year open problem posed in the aforementioned works. We then provide new axiomatizations that are complete for finite models and characterize intermediate witnessing conditions that hold for the basic logics.

math.LO↗

arXiv2024

Rotations of Gödel algebras with modal operators

The present paper is devoted to study the effect of connected and disconnected rotations of Gödel algebras with operators grounded on directly indecomposable structures. The structures resulting from this construction we will present are nilpotent minimum (with or without negation fixpoint, depending on whether the rotation is connected or disconnected) with special modal operators defined on a directly indecomposable algebra. In this paper we will present a (quasi-)equational definition of these latter structures. Our main results show that directly indecomposable nilpotent minimum algebras (with or without negation fixpoint) with modal operators are fully characterized as connected and disconnected rotations of directly indecomposable Gödel algebras endowed with modal operators.

math.GM↗

arXiv2021

Algebras and relational frames for Gödel modal logic and some of its extensions

Gödel modal logics can be seen as extenions of intutionistic modal logics with the prelinearity axiom. In this paper we focus on the algebraic and relational semantics for Gödel modal logics that leverages on the duality between finite Gödel algebras and finite forests, i.e. finite posets whose principal downsets are totally ordered. We consider different subvarieties of the basic variety of Gödel algebras with two modal operators (GAOs for short) and their corresponding classes of forest frames, either with one or two accessibility relations. These relational structures can be considered as prelinear versions of the usual relational semantics of intuitionistic modal logic. More precisely we consider two main extensions of finite Gödel algebras with operators: the one obtained by adding Dunn axioms, typically studied in the fragment of positive classical (and intuitionistic) logic, and the one determined by adding Fischer Servi axioms. We present Jónsson-Tarski like representation theorems for the different types of finite GAOs considered in the paper.

math.LO↗