Pseudomonadic algebras as algebraic models of doxastic modal logic

Abstract

We generalize the notion of a monadic algebra to that of a pseudomonadic algebra. In the same way as monadic algebras serve as algebraic models of epistemic modal system S5, pseudomonadic algebras serve as algebraic models of doxastic modal system KD45. The main results of the paper are: (1) Characterization of subdirectly irreducible and simple pseudomonadic algebras, as well as Tokarz's proper filter algebras; (2) Order-topological representation of pseudomonadic algebras; (3) Complete description of the lattice of subvarieties of the variety of pseudomonadic algebras.