Studia Logica 39 (2-3):101 - 124 (1980)
Abstract |
We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras.
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DOI | 10.1007/BF00370315 |
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References found in this work BETA
Some Embedding Theorems for Modal Logic.David Makinson - 1971 - Notre Dame Journal of Formal Logic 12 (2):252-254.
Citations of this work BETA
Amalgamation and Interpolation in Normal Modal Logics.Larisa Maksimova - 1991 - Studia Logica 50 (3-4):457 - 471.
The Structure of Lattices of Subframe Logics.Frank Wolter - 1997 - Annals of Pure and Applied Logic 86 (1):47-100.
A Second Pretabular Classical Relevance Logic.Asadollah Fallahi - 2018 - Studia Logica 106 (1):191-214.
Algebraic Semantics for Quasi-Classical Modal Logics.W. J. Blok & P. Köhler - 1983 - Journal of Symbolic Logic 48 (4):941-964.
On Superintuitionistic Logics as Fragments of Proof Logic Extensions.A. V. Kuznetsov & A. Yu Muravitsky - 1986 - Studia Logica 45 (1):77 - 99.
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