Abstract
We study the spatiotemporal logic that results by combining the propositional temporal logic (PTL) with a qualitative spatial constraint language, namely, the \(\mathcal{L}_1\) logic, and present a first semantic tableau method that given a \(\mathcal{L}_1\) formula φ systematically searches for a model for φ. Our approach builds on Wolper’s tableau method for PTL, while the ideas provided can be carried to other tableau methods for PTL as well. Further, we investigate the implication of the constraint properties of compactness and patchwork in spatiotemporal reasoning. We use these properties to strengthen results regarding the complexity of the satisfiability problem in \(\mathcal{L}_1\), by replacing the stricter global consistency property used in literature and generalizing to more qualitative spatial constraint languages. Finally, the obtained strengthened results allow us to prove the correctness of our tableau method for \(\mathcal{L}_1\).
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References
Allen, J.F.: Maintaining Knowledge about Temporal Intervals. Commun. ACM 26, 832–843 (1983)
Balbiani, P., Condotta, J.-F.: Computational complexity of propositional linear temporal logics based on qualitative spatial or temporal reasoning. In: Armando, A. (ed.) FroCos 2002. LNCS (LNAI), vol. 2309, pp. 162–176. Springer, Heidelberg (2002)
Demri, S., D’Souza, D.: An automata-theoretic approach to constraint LTL. Inf. Comput. 205, 380–415 (2007)
Frank, A.U.: Qualitative spatial reasoning with cardinal directions. In: ÖGAI (1991)
Gabelaia, D., Kontchakov, R., Kurucz, A., Wolter, F., Zakharyaschev, M.: On the computational complexity of spatio-temporal logics. In: FLAIRS (2003)
Gaintzarain, J., Hermo, M., Lucio, P., Navarro, M.: Systematic Semantic Tableaux for PLTL. Electr. Notes Theor. Comput. Sci. 206, 59–73 (2008)
Guesgen, H.W.: Spatial Reasoning Based on Allen’s Temporal Logic. Tech. rep., International Computer Science Institute (1989)
Huang, J.: Compactness and its implications for qualitative spatial and temporal reasoning. In: KR (2012)
Huth, M., Ryan, M.: Logic in Computer Science: Modelling and Reasoning About Systems (2004)
Ligozat, G.: Reasoning about cardinal directions. J. Vis. Lang. Comput. 9(1), 23–44 (1998)
Lutz, C., Milicic, M.: A Tableau Algorithm for DLs with Concrete Domains and GCIs. JAR 38, 227–259 (2007)
Munkres, J.: Topology. Prentice Hall, Incorporated (2000)
Preparata, F.P., Shamos, M.I.: Computational Geometry - An Introduction. Springer (1985)
Randell, D.A., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: KR (1992)
Renz, J.: Maximal tractable fragments of the region connection calculus: a complete analysis. In: IJCAI (1999)
Renz, J., Ligozat, G.: Weak composition for qualitative spatial and temporal reasoning. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 534–548. Springer, Heidelberg (2005)
Story, P.A., Worboys, M.F.: A design support environment for spatio-temporal database applications. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 413–430. Springer, Heidelberg (1995)
Wolper, P.: The tableau method for temporal logic: An overview. Logique et Analyse 28, 119–136 (1985)
Wolter, F., Zakharyaschev, M.: Spatio-temporal representation and reasoning based on RCC-8. In: KR (2000)
Wolter, F., Zakharyaschev, M.: Qualitative spatiotemporal representation and reasoning: a computational perspective. In: Exploring Artificial Intelligence in the New Millennium. Morgan Kaufmann Publishers Inc. (2003)
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Sioutis, M., Condotta, JF., Salhi, Y., Mazure, B. (2015). Generalized Qualitative Spatio-Temporal Reasoning: Complexity and Tableau Method. In: De Nivelle, H. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2015. Lecture Notes in Computer Science(), vol 9323. Springer, Cham. https://doi.org/10.1007/978-3-319-24312-2_5
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DOI: https://doi.org/10.1007/978-3-319-24312-2_5
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