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The Finite Model Property for Logics with the Tangle Modality


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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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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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).

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