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A Van Benthem Theorem for Modal Team Semantics

Authors Juha Kontinen, Julian-Steffen Müller, Henning Schnoor, Heribert Vollmer

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Juha Kontinen
Julian-Steffen Müller
Henning Schnoor
Heribert Vollmer

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Juha Kontinen, Julian-Steffen Müller, Henning Schnoor, and Heribert Vollmer. A Van Benthem Theorem for Modal Team Semantics. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 277-291, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.CSL.2015.277

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.

Subject Classification

Keywords
  • modal logic
  • dependence logic
  • team semantics
  • expressivity
  • bisimulation
  • independence
  • inclusion
  • generalized dependence atom

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