Epistemic BL-Algebras

TL;DR

This paper introduces Epistemic BL-algebras, an algebraic framework for fuzzy epistemic logic that generalizes existing algebraic structures and connects to fuzzy possibilistic frames, advancing the formal understanding of approximate reasoning.

Contribution

It proposes Epistemic BL-algebras, generalizing Pseudomonadic and Bi-modal G"odel Algebras, and explores their connection to fuzzy possibilistic frames, addressing an open problem in fuzzy epistemic logic.

Findings

Defined Epistemic BL-algebras as a generalization of existing algebraic structures.

Established a connection between Epistemic BL-algebras and fuzzy possibilistic frames.

Provided a foundation for further algebraic and semantic analysis of fuzzy epistemic logic.

Abstract

Fuzzy Epistemic Logic is an important formalism for approximate reasoning. It extends the well known basic propositional logic BL, introduced by H\'ajek, by offering the ability to reason about possibility and necessity of fuzzy propositions. We consider an algebraic approach to study this logic, introducing Epistemic BL-algebras. These algebras turn to be a generalization of both, Pseudomonadic Algebras introduced by \cite{Bez2002} and serial, euclidean and transitive Bi-modal G\"odel Algebras proposed by \cite{CaiRod2015}. We present the connection between this class of algebras and fuzzy possibilistic frames, as a first step to solve an open problem proposed by H\'ajek \cite[chap. ~8]{HajekBook98}.