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Fuzzy Epistemic Logic is an important formalism for approximate reasoning. It extends the well known basic propositional logic BL, introduced by Hajek, 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 Godel 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 Hajek cite[chap. ~8]{HajekBook98}.
A mistake concerning the ultra textit{LI}-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an textit{LI}-ideal to be an ultra textit{LI}-ideal are given. Moreover, the notion of an textit{LI}
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stones representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completen
For any MV-algebra $A$ we equip the set $I(A)$ of intervals in $A$ with pointwise L ukasiewicz negation $ eg x={ eg alphamid alphain x}$, (truncated) Minkowski sum, $xoplus y={alphaoplus betamid alpha in x,,,betain y}$, pointwise L ukasiewicz conjunc
We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II$_{1}$ factor as Fraisse limits of suitable classes of structures. Moreover by means of Fraisse theory we provide new examples of AF algebras with strong homogeneity properties.
The only C*-algebras that admit elimination of quantifiers in continuous logic are $mathbb{C}, mathbb{C}^2$, $C($Cantor space$)$ and $M_2(mathbb{C})$. We also prove that the theory of C*-algebras does not have model companion and show that the theory