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

作者：Cacic Vedran^*; Vrgoc Domagoj

来源：Studia Logica, 2013, 101(1): 31-44.

DOI：10.1007/s11225-011-9366-7

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

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%26apos;s why the usual counterexample showing the necessity of finite image property in Hennessy-Milner theorem (see [1]) doesn%26apos;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.

• 出版日期2013-2