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Studia Logica

, Volume 101, Issue 1, pp 31–44 | Cite as

A Note on Bisimulation and Modal Equivalence in Provability Logic and Interpretability Logic

  • Vedran ČačićEmail author
  • Domagoj Vrgoč
Article

Abstract

Provability logic is a modal logic for studying properties of provability predicates, and Interpretability logic for studying interpretability between logical theories. Their natural models are GL-models and Veltman models, for which the accessibility relation is well-founded. That’s why the usual counterexample showing the necessity of finite image property in Hennessy-Milner theorem (see [1]) doesn’t exist for them. However, we show that the analogous condition must still hold, by constructing two GL-models with worlds in them that are modally equivalent but not bisimilar, and showing how these GL-models can be converted to Veltman models with the same properties. In the process we develop some useful constructions: games on Veltman models, chains, and general method of transformation from GL-models/frames to Veltman ones.

Keywords

Provability logic Interpretability logic GL-models Veltman models Bisimulation Modal equivalence 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ZagrebZagrebCroatia
  2. 2.School of InformaticsUniversity of EdinburghEdinburghScotland, UK
  3. 3.Faculty of AgricultureUniversity of ZagrebZagrebCroatia

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