Bisimulations and bisimulation games between Verbrugge models

Mathematical Logic Quarterly 69 (2):231-243 (2023)
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Abstract

Interpretability logic is a modal formalization of relative interpretability between first‐order arithmetical theories. Verbrugge semantics is a generalization of Veltman semantics, the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. We study various notions of bisimulation between Verbrugge models and develop a new one, which we call w‐bisimulation. We show that the new notion, while keeping the basic property that bisimilarity implies modal equivalence, is weak enough to allow the converse to hold in the finitary case. To do this, we develop and use an appropriate notion of bisimulation games between Verbrugge models.

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References found in this work

The interpretability logic of peano arithmetic.Alessandro Berarducci - 1990 - Journal of Symbolic Logic 55 (3):1059-1089.
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.
Modal analysis of generalized Rosser sentences.Vítězslav Švejdar - 1983 - Journal of Symbolic Logic 48 (4):986-999.

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