Diaz-Varela et al. have introduced the variety of monadic BL-algebras as BL-algebras endowed with two monadic operators $\forall$ and $\exists$. Furthermore, they study the basic properties of this variety and they show that this class is the equivalent algebraic semantics of the monadic fragment of Hajek's basic predicate logic. In addition, they start a systematic study of the main subvarieties of monadic BL-algebras, some of which constitute the algebraic semantics of well-known monadic logics: monadic Godel logic and monadic Lukasiewicz logic. Finally, they give a complete characterization of totally ordered monadic BL-algebras. These monadic BL-algebras were used by Hajek in order to prove completeness for the fuzzy modal logic S5(C). In this presentation, we take the paper mentioned above, as our starting point. Then, we consider a bigger variety of algebras that we have called Epistemic BL-algebras. This new family of algebras can be considered as a generalization of the pseudomonadic algebras introduced by Bezhanisvili in 2002. At the end of my presentation, we are going to prove that this class of algebras characterizes the fuzzy modal logic KD45(C). This characterization solves an open problem proposed by Hajek in Chapter 8 of his book.
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