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The Lattice of Modal Logics: An Algebraic Investigation

W. J. Blok

Journal of Symbolic Logic 49 (4):1419-1420 (1984)

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Varieties of monadic Heyting algebras. Part I.Guram Bezhanishvili - 1998 - Studia Logica 61 (3):367-402.details This paper deals with the varieties of monadic Heyting algebras, algebraic models of intuitionistic modal logic MIPC. We investigate semisimple, locally finite, finitely approximated and splitting varieties of monadic Heyting algebras as well as varieties with the disjunction and the existence properties. The investigation of monadic Heyting algebras clarifies the correspondence between intuitionistic modal logics over MIPC and superintuitionistic predicate logics and provides us with the solutions of several problems raised by Ono [35]. Download Export citation Bookmark 20 citations
Minimal p-morphic images, axiomatizations and coverings in the modal logic K.Fabio Bellissima & Saverio Cittadini - 1999 - Studia Logica 62 (3):371-398.details We define the concepts of minimal p-morphic image and basic p-morphism for transitive Kripke frames. These concepts are used to determine effectively the least number of variables necessary to axiomatize a tabular extension of K4, and to describe the covers and co-covers of such a logic in the lattice of the extensions of K4. Download Export citation Bookmark 1 citation
Varieties of monadic Heyting algebras. Part III.Guram Bezhanishvili - 2000 - Studia Logica 64 (2):215-256.details This paper is the concluding part of [1] and [2], and it investigates the inner structure of the lattice (MHA) of all varieties of monadic Heyting algebras. For every n , we introduce and investigate varieties of depth n and cluster n, and present two partitions of (MHA), into varieties of depth n, and into varieties of cluster n. We pay a special attention to the lower part of (MHA) and investigate finite and critical varieties of monadic Heyting algebras in (...) Download Export citation Bookmark 5 citations
Some descending chains of incomplete modal logics.Ming Xu - 1991 - Journal of Philosophical Logic 20 (3):265 - 283.details Download Export citation Bookmark 1 citation
A splitting logic in NExt(KTB).Yutaka Miyazaki - 2007 - Studia Logica 85 (3):381 - 394.details It is shown that the normal modal logic of two reflexive points jointed with a symmetric binary relation splits the lattice of normal extensions of the logic KTB. By this fact, it is easily seen that there exists the third largest logic in the class of all normal extensions of KTB. Download Export citation Bookmark 1 citation
Modal incompleteness revisited.Tadeusz Litak - 2004 - Studia Logica 76 (3):329 - 342.details In this paper, we are going to analyze the phenomenon of modal incompleteness from an algebraic point of view. The usual method of showing that a given logic L is incomplete is to show that for some L and some cannot be separated from by a suitably wide class of complete algebras — usually Kripke algebras. We are going to show that classical examples of incomplete logics, e.g., Fine logic, are not complete with respect to any class of complete BAOs. (...) Download Export citation Bookmark 3 citations

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