Abstract
Hybrid logic is a valuable tool for specifying relational structures, at the same time that allows defining accessibility relations between states, it provides a way to nominate and make mention to what happens at each specific state. However, due to the many sources nowadays available, we may need to deal with contradictory information. This is the reason why we came with the idea of Quasi-hybrid logic, which is a paraconsistent version of hybrid logic capable of dealing with inconsistencies in the information, written as hybrid formulas.
In [5] we have already developed a semantics for this paraconsistent logic. In this paper we go a step forward, namely we study its proof-theoretical aspects. We present a complete tableau system for Quasi-hybrid logic, by combining both tableaux for Quasi-classical and Hybrid logics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Blackburn, P.: Representation, reasoning, and relational structures: a hybrid logic manifesto. Log. J. IGPL 8(3), 339–365 (2000)
Boolos, G.S., Burgess, J.P., Jeffrey, R.C.: Computability and Logic, 5th edn. Cambridge University Press, Cambridge (2007)
Braüner, T.: Hybrid Logic and Its Proof-Theory. Springer, Heidelberg (2010)
Costa, D., Martins, M.: Inconsistencies in health care knowledge. In: 2014 IEEE 16th International Conference on e-Health Networking, Applications and Services (Healthcom), pp. 37–42, October 2014
Costa, D., Martins, M.: Paraconsistency in hybrid logic. Accepted in the Journal of Logic and Computation (2016). http://sweet.ua.pt/martins/documentos/preprint_2014/phl14.pdf
Grant, J., Hunter, A.: Measuring inconsistency in knowledge bases. J. Intell. Inf. Syst. 27(2), 159–184 (2006)
Grant, J., Hunter, A.: Analysing inconsistent first-order knowledge bases. Artif. Intell. 172(8–9), 1064–1093 (2008)
Hunter, A.: A semantic tableau version of first-order quasi-classical logic. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 544–555. Springer, Heidelberg (2001)
Odintsov, S.P., Wansing, H.: Modal logics with Belnapian truth values. J. Appl. Non-Class. Logics 20(3), 279–304 (2010)
Rivieccio, U., Jung, A., Jansana, R.: Four-valued modal logic: Kripke semantics and duality. J. Logic Comput. (2015). http://logcom.oxfordjournals.org/citmgr?gca=logcom%3Bexv038v1. doi:10.1093/logcom/exv038
Acknowledgements
We are very grateful to J. Marcos for productive discussions, in several related topics, that were very important for achieving the reported results. We would also like to mention that the careful work of the anonymous reviewers have improved the quality of the present paper.
This work was supported in part by the Portuguese Foundation for Science and Technology (FCT) through CIDMA within project UID/MAT/04106/2013 and the project EU FP7 Marie Curie PIRSES-GA-2012-318986 GeTFun: Generalizing Truth-Functionality. Diana Costa also thanks the support of FCT via the Ph.D. scholarship PD/BD/105730/2014, and the Calouste Gulbenkian Foundation through the Research Stimulus Program 2015 (Programa de EstÃmulo à Investigação 2015).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Costa, D., Martins, M.A. (2016). A Tableau System for Quasi-Hybrid Logic. In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_30
Download citation
DOI: https://doi.org/10.1007/978-3-319-40229-1_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40228-4
Online ISBN: 978-3-319-40229-1
eBook Packages: Computer ScienceComputer Science (R0)