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The structure of lattices of subframe logics

Authors
Journal
Annals of Pure and Applied Logic
0168-0072
Publisher
Elsevier
Publication Date
Volume
86
Issue
1
Identifiers
DOI: 10.1016/s0168-0072(96)00049-8
Keywords
  • Modal Logic
  • Subframe Logic
  • Tense Logic
  • Lattice
  • Splitting
  • Kripke Completeness
  • Decidability
  • 03B45
  • 03B25
  • 06B20
Disciplines
  • Logic
  • Mathematics

Abstract

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 Alt n and subframe logics which are tense logics.

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