Speaker
Description
The basic semantics for the interpretability logics are Veltman models.
R. Verbrugge defined a new relational semantics for interpretability logics, which today is called Verbrugge semantics in her honor.
It has turned out that this semantics has various good properties.
Bisimulations are the basic equivalence relations between Veltman models.
M. Vuković and T. Perkov used them to prove the van Benthem's characterization theorem with respect to Veltman semantics.
Van Benthem's characterization theorems belong to the field of correspondence theory which systematically investigates the relationship between modal and classical logic.
They show that modal languages correspond to the bisimulation invariant fragment of first–order languages.
M. Vuković defined bisimulations for Verbrugge semantics. However, in [2] we proved that with such a definition of bisimulation for Verbrugge semantics, the analogues of some of the results for the Veltman semantics do not hold in case of Verbrugge semantics.
Therefore, in [2] we gave a new version of bisimulations, which we called weak bisimulations.
In this talk, we will make an overview of the results that can be obtained using weak bisimulations.
Among these results, we will especially highlight van Benthem's theorem with respect to Verbrugge semantics, which we proved in [1].
Finally, we will give an overview of the main steps required to prove the van Benthem - Rosen theorem with respect to Verbrugge semantics,
which is a version of the van Benthem theorem for finite models.
References:
[1] S. Horvat, T. Perkov, Correspondence theorem for interpretability logic with respect to Verbrugge semantics, preprint, 2024.
[2] S. Horvat, T. Perkov, M. Vuković, Bisimulations and bisimulation games for Verbrugge semantics, Mathematical Logic Quarterly 69(2023), 231-243
