Algebraic study of possibilistic BL-logic

RICARDO O. RODRIGUEZ; PENÉLOPE CORDERO; MANUELA BUSANICHE

Vancouver

Workshop; WiL2019; 2019

Simon Fraiser University

In [2], we dene the class of Pseudomonadic BL-algebras (PBL-algebras for short) asan algebraic approach to possibilistic BL-logic. In this work, we show that, given a possibilisticBL-frame, its associated complex algebra is a special case of PBL-algebra, namelyc-PBL-algebra. In this sense, the complex c-PBL-algebras algebras allow to establish aconnection between relational and algebraic semantics and, taking into account that notionslike completeness and denability can be studied through these algebras, we focusto characterize the subdirectly irreducible members in this class. For this purpose, overa complex c-PBL-algebra, we begin by identifying the pseudomonadic lters for each ofthe most important subvarieties of BL. And subsequently, since the congruences are incorrespondence with these lters, we show necessary and sucient conditions to obtainsubdirectly irreducible complex c-PBL-algebras.