Algebraic Semantics for BL-Possilistic Logic

RICARDO O. RODRIGUEZ; PENÉLOPE CORDERO; MANUELA BUSANICHE

Puebla

Simposio; SLALM2017; 2017

Benemérita Universidad Autónoma de Puebla

In cite{CCDR2016}, the authors introduce the variety of monadic BL-algebras as BL-algebras endowedwith two monadic operators $orall$ and $exists$. Furthermore, they study the basic properties of this variety andthey show that this class is the equivalent algebraic semantics of the monadic fragment ofH´ajek´s basic predicate logic. In addition, they start a systematic study of the main subvarietiesof monadic BL-algebras, some of which constitute the algebraic semantics of well-known monadic logics: monadic G"odel logic and monadic L ukasiewicz logic. Finally, theygive a complete characterization of totally ordered monadic BL-algebras.This monadic BL-algebras was used by H´ajek in order to proof completeness for the fuzzy modal logic $S5(mathcal{C})$ (see cite{Hajek2010}).In current work, we take the paper mentioned above, as our starting point. Then, we consider a bigger variety of algebras that we have called {it Epistemic BL-algebras}. This new family of algebras can be considered as a generalization of the pseudomonadic algebras introduced by Bezhanisvili in cite{Bez2002}.At the end of our paper, we are going to proof that this class of algebras characterizes the fuzzy modal logic $KD45(mathcal{C})$. This characterization solves an open problem proposed by H´ajek in Chapter 8 of cite{HajekBook98}.