A Van Benthem Theorem for Modal Team Semantics

TL;DR

This paper extends van Benthem's theorem to modal dependence logic with team semantics, showing that modal team logic precisely captures FO-definable bisimulation invariant properties of Kripke structures and teams.

Contribution

It establishes an exact analogue of van Benthem's theorem within modal dependence logic and compares its expressive power to related variants.

Findings

Modal team logic captures FO-definable bisimulation invariant properties.

MTL extends MDL by classical negation, increasing expressive power.

The paper characterizes the expressive boundaries of MTL and related logics.

Abstract

The famous van Benthem theorem states that modal logic corresponds exactly to the fragment of first-order logic that is invariant under bisimulation. In this article we prove an exact analogue of this theorem in the framework of modal dependence logic MDL and team semantics. We show that modal team logic MTL, extending MDL by classical negation, captures exactly the FO-definable bisimulation invariant properties of Kripke structures and teams. We also compare the expressive power of MTL to most of the variants and extensions of MDL recently studied in the area.