The structure of lattices of subframe logics

Annals of Pure and Applied Logic 86 (1):47-100 (1997)
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Abstract

This paper investigates the structure of lattices of normal mono- and polymodal subframelogics, i.e., those modal logics whose frames are closed under a certain type of substructures. Nearly all basic modal logics belong to this class. The main lattice theoretic tool applied is the notion of a splitting of a complete lattice which turns out to be connected with the “geometry” and “topology” of frames, with Kripke completeness and with axiomatization problems. We investigate in detail subframe logics containing K4, those containing polymodal Altn and subframe logics which are tense logics

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References found in this work

An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Sweden: Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
An Ascending Chain of S4 Logics.Kit Fine - 1974 - Theoria 40 (2):110-116.
Varieties of Complex Algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
Canonical Formulas for K4. Part I: Basic Results.Michael Zakharyaschev - 1992 - Journal of Symbolic Logic 57 (4):1377-1402.
Logics Containing K4. Part I.Kit Fine - 1974 - Journal of Symbolic Logic 39 (1):31-42.

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