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.

Rotations of Gödel algebras with modal operators

The present paper is devoted to study the effect of connected and disconnected rotations of G\"odel 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 G\"odel algebras endowed with modal operators.