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The Finite Model Property for Logics with the Tangle Modality

Studia Logica volume 106, pages 131–166 (2018)Cite this 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.

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Acknowledgements

The authors would like to thank the referees for their very helpful comments and suggestions. The second author was supported by UK EPSRC overseas travel grant EP-L020750-1.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand

    Robert Goldblatt

  2. Department of Computing, Imperial College, London, SW7 2AZ, UK

    Ian Hodkinson

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  1. Robert Goldblatt
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  2. Ian Hodkinson
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Correspondence to Ian Hodkinson.

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Presented by Yde Venema

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Goldblatt, R., Hodkinson, I. The Finite Model Property for Logics with the Tangle Modality. Stud Logica 106, 131–166 (2018). https://doi.org/10.1007/s11225-017-9732-1

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Keywords

  • Tangle modality
  • Finite model property
  • Kripke frame
  • Filtration
  • Connected
  • Universal modality