Abstract
To represent and reason about moving objects in three-dimensional space qualitatively, we need a right fundamental logic system to provide us with a criterion of logical validity for reasoning as well as a formal representation language. In order to reason about new spatio-temporal knowledge with incomplete or sometime even inconsistent knowledge, the fundamental logic must be able to underlie relevant and truth-preserving reasoning in the sense of conditional, ampliative reasoning, paracomplete and paraconsistent reasoning, and spatio-temporal reasoning. This paper proposes a new family of three-dimensional spatio-temporal relevant logics as a hopeful candidate for the fundamental logic, and shows that the logics can satisfy all the requirements for the fundamental logic we need.
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
Anderson, A.R., Belnap Jr., N.D.: Entailment: The Logic of Relevance and Necessity, vol. I. Princeton University Press, Princeton (1975)
Anderson, A.R., Belnap Jr., N.D., Dunn, J.M.: Entailment: The Logic of Relevance and Necessity, vol. II. Princeton University Press, Princeton (1992)
Bennett, B., Cohn, A.G., Wolter, F., Zakharyaschev, M.: Multi-Dimensional Modal Logic as a Framework for Spatio-Temporal Reasoning. Applied Intelligence 17(3), 239–251 (2002)
Burgess, J.P.: Basic Tense Logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 7, pp. 1–42. Kluwer Academic, Dordrecht (2002)
Cheng, J.: A Strong Relevant Logic Model of Epistemic Processes in Scientific Discovery. In: Kawaguchi, E., Kangassalo, H., Jaakkola, H., Hamid, I.A. (eds.) Information Modelling and Knowledge Bases XI. Frontiers in Artificial Intelligence and Applications, vol. 61, pp. 136–159. IOS Press, Amsterdam (2000)
Cheng, J.: Automated Knowledge Acquisition by Relevant Reasoning Based on Strong Relevant Logic. In: Palade, V., Howlett, R.J., Jain, L.C. (eds.) KES 2003. LNCS, vol. 2773, pp. 68–80. Springer, Heidelberg (2003)
Cheng, J.: Temporal Relevant Logic as the Logical Basis of Anticipatory Reasoning-Reacting Systems. In: Dubois, D.M. (ed.) Computing Anticipatory Systems: CASYS 2003. AIP Conference Proceedings, vol. 718, pp. 362–375. American Institute of Physics (2004)
Cheng, J.: Spatio-temporal Relevant Logic as the Logical Basis for Spatio-temporal Information Systems. In: Proc. 17th Annual International Conference on Tools with Artificial Intelligence, pp. 270–274. IEEE Computer Society Press, Los Alamitos (2005)
Cheng, J.: Strong Relevant Logic as the Universal Basis of Various Applied Logics for Knowledge Representation and Reasoning. In: Kiyoki, Y., Henno, J., Jaakkola, H., Kangassalo, H. (eds.) Information Modelling and Knowledge Bases XVII. Frontiers in Artificial Intelligence and Applications, vol. 136, pp. 310–320. IOS Press, Amsterdam (2006)
Cheng, J., Goto, Y., Kitajima, N.: Anticipatory Reasoning about Mobile Objects in Anticipatory Reasoning-Reacting Systems. In: Dubois, D.M. (ed.) Computing Anticipatory Systems: CASYS 2007. AIP Conference Proceedings, American Institute of Physics (to appear, 2008)
Cohn, A.G., Bennett, B., Gooday, J., Gotts, N.M.: Representing and Reasoning with Qualitative Spatial Relations About Regions. In: Stock, O. (ed.) Spatial and Temporal Reasoning, pp. 97–134. Kluwer Academic, Dordrecht (1997)
Cohn, A.G., Bennett, B., Gooday, J., Gotts, N.M.: Qualitative Spatial Representation and Reasoning with the Region Connection Calculus. GeoInformatica 1(3), 275–316 (1997)
Cohn, A.G., Gotts, N.M., Cui, Z., Randell, D.A., Bennett, B., Gooday, J.M.: Exploiting Temporal Continuity in Qualitative Spatial Calculi. In: Egenhofer, M.J., Golledge, R.G. (eds.) Spatial and Temporal Reasoning in Geographic Information Systems, pp. 5–24. Oxford University Press, Oxford (1998)
Cohn, A.G., Hazarika, S.M.: Qualitative Spatial Representation and Reasoning: An Overview. Fundamenta Informaticae 46(1-2), 1–29 (2001)
Dunn, J.M., Restall, G.: Relevance Logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 6, pp. 1–128. Kluwer Academic, Dordrecht (2002)
Egenhofer, M.J., Golledge, R.G. (eds.): Spatial and Temporal Reasoning in Geographic Information Systems. Oxford University Press, Oxford (1998)
Erwig, M., Schneider, M.: Spatio-Temporal Predicates. IEEE Transactions on Knowledge and Data Engineering 14(4), 881–901 (2002)
Mares, E.D.: Relevant Logic: A Philosophical Interpretation. Cambridge University Press, Cambridge (2004)
Merz, S., Wirsing, M., Zappe, J.: A Spatio-Temporal Logic for the Specification and Refinement of Mobile Systems. In: Pezzé, M. (ed.) FASE 2003. LNCS, vol. 2621, pp. 87–101. Springer, Heidelberg (2003)
Renz, J.: Qualitative Spatial Reasoning with Topological Information. LNCS(LNAI), vol. 2293. Springer, Heidelberg (2002)
Stock, O. (ed.): Spatial and Temporal Reasoning. Kluwer Academic, Dordrecht (1997)
Venema, Y.: Temporal Logic. In: Goble, L. (ed.) The Blackwell Guide to Philosophical Logic, pp. 203–223. Blackwell, Oxford (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cheng, J. (2008). Qualitative Spatio-temporal Reasoning about Moving Objects in Three-Dimensional Space. In: Kang, L., Cai, Z., Yan, X., Liu, Y. (eds) Advances in Computation and Intelligence. ISICA 2008. Lecture Notes in Computer Science, vol 5370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92137-0_70
Download citation
DOI: https://doi.org/10.1007/978-3-540-92137-0_70
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92136-3
Online ISBN: 978-3-540-92137-0
eBook Packages: Computer ScienceComputer Science (R0)