Abstract
A tableau calculus constituting a decision procedure for hybrid logic with the converse modalities, the global ones and a restricted use of the binder has been defined in a previous paper. This work shows how to extend such a calculus to multi-modal logic equipped with two features largely used in description logics, i.e. transitivity and relation inclusion assertions. An implementation of the proof procedure is also briefly presented, along with the results of some preliminary experiments.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Areces, C., Blackburn, P., Marx, M.: A road-map on complexity for hybrid logics. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 307–321. Springer, Heidelberg (1999)
Areces, C., Heguiabehere, J.: hGen: A random CNF formula generator for hybrid languages. In: Methods for Modalities 3 (M4M-3), Nancy, France (2003)
Areces, C., ten Cate, B.: Hybrid logics. In: Handbook of Modal Logics, pp. 821–868. Elsevier (2007)
Blackburn, P., Seligman, J.: Hybrid languages. Journal of Logic, Language and Information 4, 251–272 (1995)
Bolander, T., Blackburn, P.: Terminating tableau calculi for hybrid logics extending K. Electronic Notes in Theoretical Computer Science 231, 21–39 (2009)
Cerrito, S., Cialdea Mayer, M.: An efficient approach to nominal equalities in hybrid logic tableaux. Journal of Applied Non-classical Logics 20(1-2), 39–61 (2010)
Cerrito, S., Cialdea Mayer, M.: Nominal substitution at work with the global and converse modalities. In: Advances in Modal Logic, vol. 8, pp. 57–74. College Publications (2010)
Cerrito, S., Cialdea Mayer, M.: A tableaux based decision procedure for a broad class of hybrid formulae with binders. In: Brünnler, K., Metcalfe, G. (eds.) TABLEAUX 2011. LNCS, vol. 6793, pp. 104–118. Springer, Heidelberg (2011)
Cerrito, S., Cialdea Mayer, M.: A tableau based decision procedure for a fragment of hybrid logic with binders. Journal of Automated Reasoning (2012) (published online, to appear on paper)
Cialdea Mayer, M.: Tableaux for multi-modal hybrid logic with binders, transitive relations and relation hierarchies. Technical Report RT-DIA-199-2012, Dipartimento di Informatica e Automazione, Università di Roma Tre (2012)
Cialdea Mayer, M., Cerrito, S.: Herod and Pilate: two tableau provers for basic hybrid logic. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 255–262. Springer, Heidelberg (2010)
Grädel, E.: On the restraining power of guards. Journal of Symbolic Logic 64, 1719–1742 (1998)
Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. Journal of Logic and Computation 9(3), 385–410 (1999)
Horrocks, I., Sattler, U.: A tableau decision procedure for \(\mathcal{SHOIQ}\). Journal of Automated Reasoning 39(3), 249–276 (2007)
Kaminski, M., Schneider, S., Smolka, G.: Terminating tableaux for graded hybrid logic with global modalities and role hierarchies. Logical Methods in Computer Science 7(1) (2011)
Kaminski, M., Smolka, G.: Terminating tableau systems for hybrid logic with difference and converse. Journal of Logic, Language and Information 18(4), 437–464 (2009)
Mundhenk, M., Schneider, T.: Undecidability of multi-modal hybrid logics. Electronic Notes in Theoretical Computer Science 174(6), 29–43 (2007)
Mundhenk, M., Schneider, T., Schwentick, T., Weber, V.: Complexity of hybrid logics over transitive frames. Journal of Applied Logic 8(4), 422–440 (2010)
Szwast, W., Tendera, L.: On the decision problem for the guarded fragment with transitivity. In: Proc. of the 16th Symposium on Logic in Computer Science (LICS), pp. 147–156 (2001)
ten Cate, B., Franceschet, M.: On the complexity of hybrid logics with binders. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 339–354. Springer, Heidelberg (2005)
Weidenbach, C., Dimova, D., Fietzke, A., Kumar, R., Suda, M., Wischnewski, P.: SPASS version 3.5. In: Schmidt, R.A. (ed.) CADE 2009. LNCS, vol. 5663, pp. 140–145. Springer, Heidelberg (2009)
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
Cialdea Mayer, M. (2013). A Proof Procedure for Hybrid Logic with Binders, Transitivity and Relation Hierarchies. In: Bonacina, M.P. (eds) Automated Deduction – CADE-24. CADE 2013. Lecture Notes in Computer Science(), vol 7898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38574-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-38574-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38573-5
Online ISBN: 978-3-642-38574-2
eBook Packages: Computer ScienceComputer Science (R0)