Abstract
We study dynamic modal operators that can change the model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to swap, delete or add pairs of related elements of the domain, while traversing an edge of the accessibility relation. We study these languages together with the sabotage modal logic, which can arbitrarily delete edges of the model. We define a suitable notion of bisimulation for the basic modal logic extended with each of the new dynamic operators and investigate their expressive power, showing that they are all uncomparable. We also show that the complexity of their model checking problems is PSpace-complete.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Areces, C., Figueira, D., Figueira, S., Mera, S.: The expressive power of memory logics. Review of Symbolic Logic 4(2), 290–318 (2011)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001)
Blackburn, P., Seligman, J.: Hybrid languages. Journal of Logic, Language and Information 4, 251–272 (1995)
Blackburn, P., Wolter, F., van Benthem, J. (eds.): Handbook of Modal Logics. Elsevier (2006)
Gerbrandy, J.: Bisimulations on Planet Kripke. Ph.D. thesis, University of Amsterdam. ILLC Dissertation series DS-1999-01 (1999)
Löding, C., Rohde, P.: Model Checking and Satisfiability for Sabotage Modal Logic. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 302–313. Springer, Heidelberg (2003)
Löding, C., Rohde, P.: Solving the Sabotage Game Is PSPACE-Hard. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 531–540. Springer, Heidelberg (2003)
Papadimitriou, C.: Computational Complexity. Addison-Wesley (1994)
Plaza, J.: Logics of public communications. Synthese 158(2), 165–179 (2007)
Rohde, P.: On games and logics over dynamically changing structures. Ph.D. thesis, RWTH Aachen (2006)
van Benthem, J.: Logics for information update. In: TARK 2001: Proceedings of the 8th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 51–67. Morgan Kaufmann Publishers Inc. (2001)
van Benthem, J.: An Essay on Sabotage and Obstruction. In: Hutter, D., Stephan, W. (eds.) Mechanizing Mathematical Reasoning. LNCS (LNAI), vol. 2605, pp. 268–276. Springer, Heidelberg (2005)
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Kluwer (2007)
Vardi, M.Y.: The complexity of relational query languages (extended abstract). In: Lewis, H.R., Simons, B.B., Burkhard, W.A., Landweber, L.H. (eds.) STOC, pp. 137–146. ACM (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Areces, C., Fervari, R., Hoffmann, G. (2012). Moving Arrows and Four Model Checking Results. In: Ong, L., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2012. Lecture Notes in Computer Science, vol 7456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32621-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-32621-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32620-2
Online ISBN: 978-3-642-32621-9
eBook Packages: Computer ScienceComputer Science (R0)