Notre Dame Journal of Formal Logic 58 (2):287-299 (2017)

Abstract
There are two known general results on the finite model property of commutators [L0,L1]. If L is finitely axiomatizable by modal formulas having universal Horn first-order correspondents, then both [L,K] and [L,S5] are determined by classes of frames that admit filtration, and so they have the fmp. On the negative side, if both L0 and L1 are determined by transitive frames and have frames of arbitrarily large depth, then [L0,L1] does not have the fmp. In this paper we show that commutators with a “weakly connected” component often lack the fmp. Our results imply that the above positive result does not generalize to universally axiomatizable component logics, and even commutators without “transitive” components such as [K3,K] can lack the fmp. We also generalize the above negative result to cases where one of the component logics has frames of depth one only, such as [S4.3,S5] and the decidable product logic S4.3×S5. We also show cases when already half of commutativity is enough to force infinite frames.
Keywords finite model property   linear orders  multimodal logic
Categories (categorize this paper)
DOI 10.1215/00294527-3870247
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,436
Through your library

References found in this work BETA

An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Sweden: Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
[Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.
Products of Modal Logics, Part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.
Properties of Independently Axiomatizable Bimodal Logics.Marcus Kracht & Frank Wolter - 1991 - Journal of Symbolic Logic 56 (4):1469-1485.
That All Normal Extensions of S4.3 Have the Finite Model Property.R. A. Bull - 1966 - Mathematical Logic Quarterly 12 (1):341-344.

View all 12 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Splittings and the Finite Model Property.Marcus Kracht - 1993 - Journal of Symbolic Logic 58 (1):139-157.
The Finite Model Property in Tense Logic.Frank Wolter - 1995 - Journal of Symbolic Logic 60 (3):757-774.
Some Normal Extensions of K4.3.Ming Xu - 2013 - Studia Logica 101 (3):583-599.
Prefinitely Axiomatizable Modal and Intermediate Logics.Marcus Kracht - 1993 - Mathematical Logic Quarterly 39 (1):301-322.

Analytics

Added to PP index
2017-03-09

Total views
10 ( #903,513 of 2,520,359 )

Recent downloads (6 months)
1 ( #406,012 of 2,520,359 )

How can I increase my downloads?

Downloads

My notes