Pseudomonadic Algebras as Algebraic Models of Doxastic Modal Logic

Mathematical Logic Quarterly 48 (4):624-636 (2002)
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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: Characterization of subdirectly irreducible and simple pseudomonadic algebras, as well as Tokarz's proper filter algebras; Ordertopological representation of pseudomonadic algebras; Complete description of the lattice of subvarieties of the variety of pseudomonadic algebras

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Nick Bezhanishvili
University of Amsterdam

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References found in this work

An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
The lattice of modal logics: An algebraic investigation.W. J. Blok - 1980 - Journal of Symbolic Logic 45 (2):221-236.
Topology and duality in modal logic.Giovanni Sambin & Virginia Vaccaro - 1988 - Annals of Pure and Applied Logic 37 (3):249-296.

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