The finite model property for logics with the tangle modality
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Published version
Author(s)
Goldblatt, R
Hodkinson, I
Type
Journal Article
Abstract
The tangle modality is a propositional connective that extends basic modal
logic to a language that is expressively equivalent over certain classes of finite frames to
the bisimulation-invariant fragments of both first-order and monadic second-order logic.
This paper axiomatises several logics with tangle, including some that have the universal
modality, and shows that they have the finite model property for Kripke frame semantics.
The logics are specified by a variety of conditions on their validating frames, including
local and global connectedness properties. Some of the results have been used to obtain
completeness theorems for interpretations of tangled modal logics in topological spaces.
logic to a language that is expressively equivalent over certain classes of finite frames to
the bisimulation-invariant fragments of both first-order and monadic second-order logic.
This paper axiomatises several logics with tangle, including some that have the universal
modality, and shows that they have the finite model property for Kripke frame semantics.
The logics are specified by a variety of conditions on their validating frames, including
local and global connectedness properties. Some of the results have been used to obtain
completeness theorems for interpretations of tangled modal logics in topological spaces.
Date Issued
2017-06-01
Date Acceptance
2017-02-23
Citation
Studia Logica, 2017, 106, pp.131-166
ISSN
1572-8730
Publisher
Springer Verlag (Germany)
Start Page
131
End Page
166
Journal / Book Title
Studia Logica
Volume
106
Copyright Statement
© The Author(s) 2017 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/L020750/1
Subjects
Science & Technology
Arts & Humanities
Physical Sciences
Mathematics
Logic
Philosophy
Science & Technology - Other Topics
Tangle modality
Finite model property
Kripke frame
Filtration
Connected
Universal modality
01 Mathematical Sciences
08 Information And Computing Sciences
22 Philosophy And Religious Studies
General Mathematics
Publication Status
Published