A Van Benthem Theorem for Modal Team Semantics

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.

[1]  Pietro Galliani,et al.  Inclusion and exclusion dependencies in team semantics - On some logics of imperfect information , 2011, Ann. Pure Appl. Log..

[2]  Pietro Galliani,et al.  On Dependence Logic , 2013, Johan van Benthem on Logic and Information Dynamics.

[3]  Julian-Steffen Müller,et al.  Modal Independence Logic , 2014, Advances in Modal Logic.

[4]  Jonni Virtema,et al.  Axiomatizing Propositional Dependence Logics , 2015, CSL.

[5]  W. Hanf.  MODEL-THEORETIC METHODS IN THE STUDY OF ELEMENTARY LOGIC , 2014 .

[6]  Erich Grädel,et al.  Dependence and Independence , 2012, Stud Logica.

[7]  Johannes Ebbing,et al.  Extended Modal Dependence Logic , 2013, WoLLIC.

[8]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[9]  Julian-Steffen Müller.  Satisfiability and model checking in team based logics , 2014 .

[10]  Jouko Väänänen,et al.  From IF to BI , 2009, Synthese.

[11]  Johannes Ebbing,et al.  Complexity of Model Checking for Modal Dependence Logic , 2011, SOFSEM.

[12]  Lauri Hella,et al.  The Expressive Power of Modal Dependence Logic , 2014, Advances in Modal Logic.

[13]  J.F.A.K. van Benthem,et al.  Modal logic and classical logic , 1983 .

[14]  Leonid Libkin,et al.  Elements of Finite Model Theory , 2004, Texts in Theoretical Computer Science.

[15]  Antti Kuusisto.  A Double Team Semantics for Generalized Quantifiers , 2015, J. Log. Lang. Inf..

[16]  Fan Yang,et al.  On Extensions and Variants of Dependence Logic : A study of intuitionistic connectives in the team semantics setting , 2014 .

[17]  J. Väänänen,et al.  Modal Dependence Logic , 2008 .

[18]  Advances in Modal Logic 10, invited and contributed papers from the tenth conference on "Advances in Modal Logic," held in Groningen, The Netherlands, August 5-8, 2014 , 2014, Advances in Modal Logic.

[19]  Merlijn Sevenster,et al.  Model-theoretic and Computational Properties of Modal Dependence Logic , 2009, J. Log. Comput..

[20]  Frank Wolter,et al.  Handbook of Modal Logic , 2007, Studies in logic and practical reasoning.

[21]  Heribert Vollmer,et al.  Complexity Results for Modal Dependence Logic , 2013, Stud Logica.

[22]  J.F.A.K. van Benthem,et al.  Modal Correspondence Theory , 1977 .

[23]  Lauri Hella,et al.  Inclusion Logic and Fixed Point Logic , 2013, CSL.

[24]  Heribert Vollmer,et al.  Complexity Results for Modal Dependence Logic , 2010, Studia Logica.

[25]  Jouko Väänänen,et al.  Modal Dependence Logic , 2008 .