Abstract
Almost all existing methodologies for representing and reasoning about spatial knowledge are somehow based on classical mathematical logic or its various conservative extensions. This approach, however, may be suitable to searching and describing a formal proof of a previously specified statement, under the condition that we have complete and consistent knowledge, but not necessarily suitable to forming a new concept and discovering a new statement, in particular, in the case that our knowledge is incomplete and inconsistent. This paper proposes a new approach: representing and reasoning about spatial knowledge based on spatial relevant logic.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
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)
Caires, L., Cardelli, L.: A Spatial Logic for Concurrency (Part I). In: Kobayashi, N., Pierce, B.C. (eds.) TACS 2001. LNCS, vol. 2215, pp. 1–37. Springer, Heidelberg (2001)
Caires, L., Cardelli, L.: A Spatial Logic for Concurrency (Part II). In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 209–225. Springer, Heidelberg (2002)
Cardelli, L., Gardner, P., Ghelli, G.: A Spatial Logic for Querying Graphs. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 597–610. Springer, Heidelberg (2002)
Cheng, J.: Logical Tool of Knowledge Engineering: Using Entailment Logic rather than Mathematical Logic. In: Proc. ACM 19th Annual Computer Science Conference, pp. 228–238. ACM Press, New York (1991)
Cheng, J.: The Fundamental Role of Entailment in Knowledge Representation and Reasoning. Journal of Computing and Information 2(1), Special Issue: Proceedings of the 8th International Conference of Computing and Information. Waterloo, pp. 853–873 (1996)
Cheng, J.: EnCal: An Automated Forward Deduction System for General-Purpose Entailment Calculus. In: Terashima, N., Altman, E. (eds.) Advanced IT Tools, Proc. IFIP World Conference on IT Tools, IFIP 96 − 14th World Computer Congress, pp. 507–514. Chapman & Hall, London (1996)
Cheng, J.: Relevant Reasoning as the Logical Basis of Knowledge Engineering. In: Cantu, F.J., Soto, R., Liebowitz, J., Sucar, E. (eds.) Application of Advanced Information Technologies, - 4th World Congress on Expert Systems, vol. 1, pp. 449–457. Cognizant Communication Co. (1998)
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, pp. 136–159. IOS Press, Amsterdam (2000)
Cohn, A.G., Bennett, B., Gooday, J., Gotts, N.M.: RCC: A Calculus for Region based Qualitative Spatial Reasoning. GeoInformatica 1, 275–316 (1997)
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., Hazarika, S.M.: Qualitative Spatial Representation and Reasoning: An Overview. Fundamenta Informaticae 45, 1–29 (2001)
Diaz, M.R.: Topics in the Logic of Relevance. Philosophia Verlag, Munchen (1981)
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, New York (1998)
Godel, K.: Russell’s Mathematical Logic. In: Schilpp (ed.) The Philosophy of Bertrand Russell, Open Court Publishing Company, Chicago (1944)
Kneale, W., Kneale, M.: The Development of Logic. Oxford University Press, Oxford (1962)
Mares, E.D., Meyer, R.K.: Relevant Logics. In: Goble, L. (ed.) The Blackwell Guide to Philosophical Logic, Blackwell, Oxford, pp. 280–308 (2001)
Randell, D., Cui, Z., Cohn, A.: A Spatial Logic Based on Regions and Connection. In: Proc. 3rd International Conference on Knowledge Representation and Reasoning, pp. 165–176 (1992)
Read, S.: Relevant Logic: A Philosophical Examination of Inference. Basil Blackwell, Oxford (1988)
Russell, B.: The Principles of Mathematics. 2nd edition. Cambridge University Press, Cambridge (1903, 1938), Norton Paperback edition. Norton, New York London (1996)
Stock, O. (ed.): Spatial and Temporal Reasoning. Kluwer Academic, Dordrecht (1997)
Tarski, A.: Introduction to Logic and to the Methodology of the Deductive Sciences, 4th edn. Oxford University Press, Oxford (1994) (revised)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cheng, J., Goto, Y. (2004). Representing and Reasoning About Spatial Knowledge Based on Spatial Relevant Logic. In: Wang, S., et al. Conceptual Modeling for Advanced Application Domains. ER 2004. Lecture Notes in Computer Science, vol 3289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30466-1_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-30466-1_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23722-8
Online ISBN: 978-3-540-30466-1
eBook Packages: Springer Book Archive