Abstract
Modal intuitionistic dependence logic (\(\mathcal MIDL \)) incorporates the notion of “dependence” between propositions into the usual modal logic and has connectives which correspond to intuitionistic connectives in a certain sense. It is the modal version of a variant of first-order dependence logic (Väänänen 2007) considered by Abramsky and Väänänen (2009) basing on Hodges’ team semantics (1997).
In this paper, we study the computational complexity of the model checking problem for \(\mathcal MIDL\) and its fragments built by restricting the operators allowed in the logics. In particular, we show that the model checking problem for \(\mathcal MIDL\) in general is PSPACE-complete and that for propositional intuitionistic dependence logic is coNP-complete.
This work was supported by DAAD grant 50740539 and by grant 138163 of the Academy of Finland. It was also partially supported by the EUROCORES LogICCC LINT programme and the NTH Focused Research School for IT Ecosystems.
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
Abramsky, S., Väänänen, J.: From IF to BI. Synthese 167(2), 207–230 (2009)
Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8(2), 244–263 (1986)
Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. J. ACM 28(1), 114–133 (1981)
Ciardelli, I., Roelofsen, F.: Inquisitive logic. Journal of Philosophical Logic 40(1), 55–94 (2011)
Ebbing, J., Lohmann, P.: Complexity of model checking for modal dependence logic, CoRR abs/1104.1034v1 (2011)
Enderton, H.: Finite partially-ordered quantifiers. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik (16), 393–397 (1970)
Hemaspaandra, E.: The complexity of poor man’s logic, CoRR cs.LO/9911014v2 (2005)
Henkin, L.: Some remarks on infinitely long formulas. In: Infinitistic Methods, Proceedings Symposium Foundations of Mathematics, pp. 167–183. Pergamon, Warsaw (1961)
Hodges, W.: Compositional semantics for a langauge of imperfect information. Logic Journal of the IGPL 5, 539–563 (1997)
Hodges, W.: Some Strange Quantifiers. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds.) Structures in Logic and Computer Science. LNCS, vol. 1261, pp. 51–65. Springer, Heidelberg (1997)
Hintikka, J., Sandu, G.: Informational independence as a semantical phenomenon. In: Fenstad, J.E., Frolov, I.T., Hilpinen, R. (eds.) Logic, Methodology and Philosophy of Science, vol. 8, pp. 571–589. Elsevier, Amsterdam (1989)
Hintikka, J., Sandu, G.: Game-theoretical semantics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language. Elsevier (1996)
Hemaspaandra, E., Schnoor, H., Schnoor, I.: Generalized modal satisfiability. J. Comput. Syst. Sci. 76(7), 561–578 (2010)
Lewis, H.: 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)
Maksimova, L.: On maximal intermediate logics with the disjunction property. Studia Logica 45(1), 69–75 (1986)
Parikh, R., Väänänen, J.: Finite information logic. Annals of Pure and Applied Logic 134(1), 83–93 (2005), Papers Presented at the 9th Workshop on Logic, Language, Information and Computation (WoLLIC 2002)
Servi, G.F.: Semantics for a class of intuitionistic modal calculi. In: Dalla Chiara, M.L. (ed.) Italian Studies in the Philosophy of Science, pp. 59–72. D. Reidel Publishing Company (1981)
Sevenster, M.: Model-theoretic and computational properties of modal dependence logic. Journal of Logic and Computation 19(6), 1157–1173 (2009)
Väänänen, J.: Dependence logic: A new approach to independence friendly logic. London Mathematical Society Student Texts, vol. 70. Cambridge University Press (2007)
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)
Walkoe, W.: Finite partially-ordered quantification. Journal of Symbolic Logic (35), 535–555 (1970)
Yang, F.: Expressing second-order sentences in intuitionistic dependence logic. In: Dependence and Independence in Logic Proceedings, pp. 118–132 (2010)
Yang, F.: Modal intuitionistic dependence logic (2012) (manuscript)
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
Ebbing, J., Lohmann, P., Yang, F. (2013). Model Checking for Modal Intuitionistic Dependence Logic. In: Bezhanishvili, G., Löbner, S., Marra, V., Richter, F. (eds) Logic, Language, and Computation. TbiLLC 2011. Lecture Notes in Computer Science, vol 7758. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36976-6_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-36976-6_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36975-9
Online ISBN: 978-3-642-36976-6
eBook Packages: Computer ScienceComputer Science (R0)