Epistemic BL-Algebras

Manuela Busaniche; Penélope Cordero; Ricardo O. Rodríguez

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arXiv · 1804.10824

Epistemic BL-Algebras

Manuela Busaniche·Penélope Cordero·Ricardo O. Rodríguez

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Abstract

Fuzzy Epistemic Logic is an important formalism for approximate reasoning. It extends the well known basic propositional logic BL, introduced by Hájek, 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 Gödel 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 Hájek \cite[chap. ~8]{HajekBook98}.

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BibTeX RIS

Manuela Busaniche, Penélope Cordero, Ricardo O. Rodríguez. 2018-04-28. Epistemic BL-Algebras. https://arxiv.org/abs/1804.10824

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