Epistemic BL-algebras: An algebraic characterization for the fuzzy logic of belief KD45

RICARDO O. RODRIGUEZ; PENÉLOPE CORDERO; MANUELA BUSANICHE

Niterói

Conferencia; Conference on Mathematical Logic; 2018

Sociedade Brasileira de Lógica y DLMPST/IUHPST.

Fuzzy Epistemic Logic is an important formalism for approximate reasoning. It extends the well known basic propositional logic BL, introduced by H´{a}jek, 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´{a}jek.