Studia Logica 101 (1):31-44 (2013)

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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DOI 10.1007/s11225-011-9366-7
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References found in this work BETA

An Overview of Interpretability Logic.Albert Visser - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 307-359.
An Overview of Interpretability Logic.Albert Visser - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 1. CSLI Publications. pp. 307-359.

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