Abstract
In this paper we investigate an extended version of modal dependence logic by allowing arbitrary Boolean connectives. Modal dependence logic was recently introduced by Jouko Väänänen by extending modal logic by a the dependence atom Dep(·). In this paper we study the computational complexity of the model checking problem. For a complete classification of arbitrary Boolean functions we are using a Lattice approach introduced by Emil Post. This classification is done for all fragments of the logical language allowing modalities \(\lozenge\) and □, the dependence atom, and logical symbols for arbitrary Boolean functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bauland, M., Mundhenk, M., Schneider, T., Schnoor, H., Schnoor, I., Vollmer, H.: The tractability of model checking for LTL: The good, the bad, and the ugly fragments. ACM Trans. Comput. Log. 12(2), 26 (2011)
Böhler, E., Creignou, N., Reith, S., Vollmer, H.: Playing with Boolean blocks, part I: Post’s lattice with applications to complexity theory. SIGACT News 34(4), 38–52 (2003)
Buss, S.R.: The boolean formula value problem is in alogtime. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing, pp. 123–131 (1987)
Ebbing, J., Lohmann, P.: Complexity of model checking for modal dependence logic. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 226–237. Springer, Heidelberg (2012)
Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. Journal of Computer and Systems Sciences 18(2), 194–211 (1979)
Hemaspaandra, E., Schnoor, H., Schnoor, I.: Generalized modal satisfiability. J. Comput. Syst. Sci. 76(7), 561–578 (2010)
Ladner, R.E.: The computational complexity of provability in systems of modal propositional logic. SIAM J. Comput. 6(3), 467–480 (1977)
Lewis, H.R.: Satisfiability problems for propositional calculi. Mathematical Systems Theory 13, 45–53 (1979)
Lohmann, P., Vollmer, H.: Complexity results for modal dependence logic. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 411–425. Springer, Heidelberg (2010)
Post, E.: The two-valued iterative systems of mathematical logic. Annals of Mathematical Studies 5, 1–122 (1941)
Sevenster, M.: Model-theoretic and computational properties of modal dependence logic. Journal of Logic and Computation 19(6), 1157–1173 (2009), http://logcom.oxfordjournals.org/cgi/content/abstract/exn102v1
Thomas, M.: On the applicability of Post’s lattice. Inf. Process. Lett. 112(10), 386–391 (2012)
Väänänen, J.: Modal dependence logic. In: Apt, K.R., van Rooij, R. (eds.) New Perspectives on Games and Interaction, Texts in Logic and Games, vol. 4, pp. 237–254. Amsterdam University Press (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Müller, JS., Vollmer, H. (2013). Model Checking for Modal Dependence Logic: An Approach through Post’s Lattice. In: Libkin, L., Kohlenbach, U., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2013. Lecture Notes in Computer Science, vol 8071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39992-3_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-39992-3_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39991-6
Online ISBN: 978-3-642-39992-3
eBook Packages: Computer ScienceComputer Science (R0)