Abstract
Propositional interval temporal logics are quite expressive temporal logics that allow one to naturally express statements that refer to time intervals. Unfortunately, most such logics turned out to be (highly) undecidable. To get decidability, severe syntactic and/or semantic restrictions have been imposed to interval-based temporal logics that make it possible to reduce them to point-based ones. The problem of identifying expressive enough, yet decidable, new interval logics or fragments of existing ones which are genuinely interval-based is still largely unexplored. In this paper, we make one step in this direction by devising an original tableau-based decision procedure for the future fragment of Propositional Neighborhood Interval Temporal Logic, interpreted over natural numbers.
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
Bresolin, D., Montanari, A.: A tableau-based decision procedure for Right Propositional Neighborhood Logic, Research Report 02, Dipartimento di Matematica e Informatica, Università di Udine, Italy (2005)
Goranko, V., Montanari, A., Sciavicco, G.: Propositional interval neighborhood temporal logics. Journal of Universal Computer Science 9(9), 1137–1167 (2003)
Goranko, V., Montanari, A., Sciavicco, G.: A general tableau method for propositional interval temporal logics. In: Cialdea Mayer, M., Pirri, F. (eds.) TABLEAUX 2003. LNCS(LNAI), vol. 2796, pp. 102–116. Springer, Heidelberg (2003)
Goranko, V., Montanari, A., Sciavicco, G.: A road map of interval temporal logics and duration calculi. Journal of Applied Non-Classical Logics 14(1-2), 9–54 (2004)
Goranko, V., Montanari, A., Sciavicco, G., Sala, P.: A general tableau method for propositional interval temporal logics: theory and implementation. Journal of Applied Logic (2005) (to appear)
Halpern, J., Shoham, Y.: A propositional modal logic of time intervals. Journal of the ACM 38(4), 935–962 (1991)
Montanari, A., Sciavicco, G., Vitacolonna, N.: Decidability of interval temporal logics over split-frames via granularity. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS(LNAI), vol. 2424, pp. 259–270. Springer, Heidelberg (2002)
Montanari, A.: Propositional interval temporal logics: some promising paths. In: Proc. of the 12th International Symposium on Temporal Representation and Reasoning (TIME), pp. 201–203. IEEE Computer Society Press, Los Alamitos (2005)
Moszkowski, B.: Reasoning about digital circuits, Ph.D. thesis, Dept. of Computer Science, Stanford University, Tech. Rep. STAN-CS-83-970, Stanford, CA (1983)
Venema, Y.: A modal logic for chopping intervals. Journal of Logic and Computation 1(4), 453–476 (1991)
Wolper, P.: The tableau method for temporal logic: An overview. Logique et Analyse 28, 119–136 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bresolin, D., Montanari, A. (2005). A Tableau-Based Decision Procedure for Right Propositional Neighborhood Logic. In: Beckert, B. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2005. Lecture Notes in Computer Science(), vol 3702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11554554_7
Download citation
DOI: https://doi.org/10.1007/11554554_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28931-9
Online ISBN: 978-3-540-31822-4
eBook Packages: Computer ScienceComputer Science (R0)