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Semisimplicity, EDPC and Discriminator Varieties of Bounded Weak-commutative Residuated Lattices with an S4-like Modal Operator

Hiroki Takamura

Studia Logica 100 (6):1137-1148 (2012)

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Semisimple Varieties of Modal Algebras.Tomasz Kowalski & Marcus Kracht - 2006 - Studia Logica 83 (1-3):351-363.details In this paper we show that a variety of modal algebras of finite type is semisimple iff it is discriminator iff it is both weakly transitive and cyclic. This fact has been claimed already in [4] (based on joint work by the two authors) but the proof was fatally flawed. Download Export citation Bookmark 8 citations
The variety of modal FLew-algebras is generated by its finite simple members.Hiroki Takamura - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 469-479.details Download Export citation Bookmark 1 citation
Semisimplicity, EDPC and discriminator varieties of residuated lattices.Tomasz Kowalski - 2004 - Studia Logica 77 (2):255 - 265.details We prove that all semisimple varieties of FL ew-algebras are discriminator varieties. A characterisation of discriminator and EDPC varieties of FL ew-algebras follows. It matches exactly a natural classification of logics over FL ew proposed by H. Ono. Download Export citation Bookmark 12 citations
The Variety Of Residuated Lattices Is Generated By Its Finite Simple Members.Tomasz Kowalski & Hiroakira Ono - 2000 - Reports on Mathematical Logic:59-77.details We show that the variety of residuated lattices is generated by its finite simple members, improving upon a finite model property result of Okada and Terui. The reasoning is a blend of proof-theoretic and algebraic arguments. Download Export citation Bookmark 5 citations

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