zbMATH — the first resource for mathematics

Logics containing K4. II. (English) Zbl 0574.03008
[For Part I see ibid. 39, 31-42 (1974; Zbl 0287.02010).]
Fine defines a class of modal logics containing K4, called sub-frame logics. These are all proved to be complete by the method of eliminating certain points from the canonical model of the system in question and showing that any finite sub-frame of the resulting model is a frame for the logic. Each sub-frame logic has the finite model property, and since the sub-frame logics turn out to be precisely those complete for a condition that is closed under sub-frames, it follows that every logic complete for a condition closed under sub-frames has the finite model property. Fine also proves that a sub-frame logic is compact iff its axioms express an elementary condition.
Reviewer: M.J.Cresswell

03B45 Modal logic (including the logic of norms)
Full Text: DOI
[1] An introduction to modal logic · Zbl 0804.03010
[2] Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 17 pp 371– · Zbl 0228.02011 · doi:10.1002/malq.19710170141
[3] Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 12 pp 341– · Zbl 0154.00407 · doi:10.1002/malq.19660120129
[4] The unprovability of consistency
[5] DOI: 10.1007/BF00293428 · Zbl 0465.03005 · doi:10.1007/BF00293428
[6] Logics containing K4 39 pp 31–
[7] Investigations in modal and tense logics with applications to problems in philosophy and linguistics · Zbl 0374.02013
[8] Algebraic logic 450 pp 163–
[9] Proceedings of the Third Scandinavian Logic Symposium pp 15–
[10] DOI: 10.1111/j.1755-2567.1974.tb00076.x · Zbl 0287.02011 · doi:10.1111/j.1755-2567.1974.tb00076.x
[11] DOI: 10.1111/j.1755-2567.1974.tb00081.x · Zbl 0307.02013 · doi:10.1111/j.1755-2567.1974.tb00081.x
[12] Indagationes Mathematicae 16 pp 572–
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.