Abstract
We propose CLP(QS), a declarative spatial reasoning framework capable of representing and reasoning about high-level, qualitative spatial knowledge about the world. We systematically formalize and implement the semantics of a range of qualitative spatial calculi using a system of non-linear polynomial equations in the context of a classical constraint logic programming framework. Whereas CLP(QS) is a general framework, we demonstrate its applicability for the domain of Computer Aided Architecture Design. With CLP(QS) serving as a prototype, we position declarative spatial reasoning as a general paradigm open to other formalizations, reinterpretations, and extensions. We argue that the accessibility of qualitative spatial representation and reasoning mechanisms via the medium of high-level, logic-based formalizations is crucial for their utility toward solving real-world problems.
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
Abelson, H., Sussman, G.J., Sussman, J.: Structure and Interpretation of Computer Programs. MIT Press, Cambridge (1985)
Aiello, M., Pratt-Hartmann, I., van Benthem, J. (eds.): Handbook of Spatial Logics. Springer, Heidelberg (2007)
Almendros-Jiménez, J.M.: Constraint logic programming over sets of spatial objects. In: Proceedings of the 2005 ACM SIGPLAN Workshop on Curry and Functional Logic Programming. ACM, New York (2005)
Balbiani, P., Condotta, J.-F., Ligozat, G.: On the consistency problem for the indu calculus. Journal of Applied Logic (2006)
Banerjee, B., Chandrasekaran, B.: A Constraint Satisfaction Framework for Executing Perceptions and Actions in Diagrammatic Reasoning. Journal of Artificial Intelligence Research (2010)
Bhatt, M.: Reasoning about space, actions and change: A paradigm for applications of spatial reasoning. In: Qualitative Spatial Representation and Reasoning: Trends and Future Directions. IGI Global, USA (2010)
Bhatt, M., Flanagan, G.: Spatio-temporal abduction for scenario and narrative completion. In: Bhatt, M., Guesgen, H., Hazarika, S. (eds.) Proceedings of the International Workshop on Spatio-Temporal Dynamics, Co-Located With the European Conference on Artificial Intelligence (ECAI 2010). ECAI Workshop Proceedings (August 2010)
Bhatt, M., Freksa, C.: Spatial computing for design: An artificial intelligence perspective. In: Visual and Spatial Reasoning for Design Creativity, SDC 2010 (2011)
Bhatt, M., Dylla, F., Hois, J.: Spatio-terminological inference for the design of ambient environments. In: Hornsby, K.S., Claramunt, C., Denis, M., Ligozat, G. (eds.) COSIT 2009. LNCS, vol. 5756, pp. 371–391. Springer, Heidelberg (2009)
Bhatt, M., Guesgen, H., Woelfl, S., Hazarika, S.: Qualitative Spatial and Temporal Reasoning: Emerging Applications, Trends and Directions. Journal of Spatial Cognition and Computation (2011)
Canny, J.: Some algebraic and geometric computations in pspace. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing. ACM, New York (1988)
Chazelle, B., Dobkin, D.: Optimal convex decompositions. In: Computational Geometry. North-Holland, Amsterdam (1985)
Chomicki, J., Revesz, P.Z.: Constraint-based interoperability of spatiotemporal databases*. GeoInformatica (September 01, 1999)
Cohn, A.G., Renz, J.: Qualitative spatial reasoning. In: Handbook of Knowledge Representation. Elsevier, Amsterdam (2007)
Collins, G.: Quantifier elimination for real closed fields by cylindrical algebraic decompostion. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, Springer, Heidelberg (1975)
Collins, G.E., Hong, H.: Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation (1991)
Colmerauer, A., Roussel, P.: The birth of prolog. In: History of Programming Languages—II. ACM, New York (1996)
Davenport, J.H., Heintz, J.: Real quantifier elimination is doubly exponential. Journal of Symbolic Computation (1988)
Dolzmann, A., Seidl, A., Sturm, T.: Redlog User Manual, 3.1 edn. (November 2006)
Duntsch, I., Wang, H., Mccloskey, S.: Relation algebras in qualitative spatial reasoning. Fundamenta Informaticae (1999)
Dylla, F., Wallgrün, J.: On generalizing orientation information in \(\mathcal{OPRA}_m\). In: Freksa, C., Kohlhase, M., Schill, K. (eds.) KI 2006. LNCS (LNAI), vol. 4314, pp. 274–288. Springer, Heidelberg (2007)
Egenhofer, M.J., Franzosa, R.D.: Point set topological relations. International Journal of Geographical Information Systems (1991)
Escrig, M.T., Toledo, F.: Qualitative spatial orientation with constraint handling rules. In: ECAI (1996)
Freksa, C.: Using orientation information for qualitative spatial reasoning. In: Frank, A.U., Formentini, U., Campari, I. (eds.) GIS 1992. LNCS, vol. 639. Springer, Heidelberg (1992)
Frommberger, L., Lee, J.H., Wallgrün, J.O., Dylla, F.: Composition in \(\mathcal{OPRA}_m\). Technical report, SFB/TR 8 Spatial Cognition (2007)
Hearn, A.C.: REDUCE User’s Manual, 3.8th edn., Santa Monica, CA, USA (February 2004)
Hoffmann, C.M.: Geometric and solid modeling: an introduction. Morgan Kaufmann Publishers Inc., San Francisco (1989)
Hong, H.: RISC-CLP (Real): logic programming with non-linear constraints over the reals. MIT Press, Cambridge (1993)
Jaffar, J., Maher, M.J.: Constraint logic programming: A survey. J. Log. Program. (1994)
Jaffar, J., Michaylov, S., Stuckey, P.J., Yap, R.H.C.: The clp( r ) language and system. ACM Trans. Program. Lang. Syst. (1992)
Kakas, A.C., Michael, A., Mourlas, C.: ACLP: Abductive constraint logic programming. J. Log. Program. (2000)
Kanellakis, P.C., Kuper, G.M., Revesz, P.Z.: Constraint query languages. In: Proceedings of the Ninth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. ACM, New York (1990) ISBN 0-89791-352-3
Kowalski, R.A.: The early years of logic programming. Commun. ACM (1988)
Kurup, U., Cassimatis, N.: Integrating constraint satisfaction and spatial reasoning. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence (2010)
Ladkin, P.B., Maddux, R.D.: On binary constraint networks. Technical report, Kestrel Institute (1988)
Lifschitz, V.: What is answer set programming? In: Proceedings of the 23rd National Conference on Artificial Intelligence, vol. 3. AAAI Press, Menlo Park (2008)
Lloyd, J.W.: Practical advtanages of declarative programming. In: Alpuente, M., Barbuti, R., Ramos, I. (eds.) GULP-PRODE, vol. (1) (1994)
Mishra, B.: Computational real algebraic geometry. In: Handbook of Discrete and Computational Geometry. CRC Press, Inc., Boca Raton (1997)
Moratz, R.: Representing relative direction as a binary relation of oriented points. In: Proceeding of the 2006 Conference on ECAI 2006: 17th European Conference on Artificial Intelligence, Riva del Garda, Italy, August 29–September 1, IOS Press, Amsterdam (2006)
Randell, D.A., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: Principles of Knowledge Representation and Reasoning, KR 1992. Morgan Kaufmann, San Francisco (1992)
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)
Renz, J., Nebel, B.: On the complexity of qualitative spatial reasoning: A maximal tractable fragment of the region connection calculus. In: IJCAI, vol. (1) (1997)
Schlieder, C.: Reasoning about ordering. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988. Springer, Heidelberg (1995)
Schrijvers, T., Frühwirth, T.W. (eds.): Constraint Handling Rules. LNCS, vol. 5388. Springer, Heidelberg (2008)
Scivos, A., Nebel, B.: The finest of its class: The natural point-based ternary calculus for qualitative spatial reasoning. In: Freksa, C., Knauff, M., Krieg-Brückner, B., Nebel, B., Barkowsky, T. (eds.) Spatial Cognition IV. LNCS (LNAI), vol. 3343, pp. 283–303. Springer, Heidelberg (2005)
Sturm, T.: Quantifier elimination for constraint logic programming. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2005. LNCS, vol. 3718, pp. 416–430. Springer, Heidelberg (2005)
Tarski, A.: A decision method for elementary algebra and geometry. Technical report, RAND Corporation, Santa Monica, CA (1951)
Tassoni, S., Foliaroni, P., Bhatt, M., De Felice, G.: Toward a Qualitative Model of 3D Visibility. In: 25th International Workshop on Qualitative Reasoning, IJCAI 2011 (2011) (position paper)
Uribe, T.E., Chaudhri, V., Hayes, P.J., Stickel, M.E.: Qualitative spatial reasoning for question-answering: Axiom reuse and algebraic methods. In: AAAI Spring Symposium on Mining Answers from Texts and Knowledge Bases (2002)
van Harmelen, F., Lifschitz, V., Porter, B. (eds.): Handbook of Knowledge Representation (Foundations of Artificial Intelligence). Elsevier Science, Amsterdam (2007)
Wielemaker, J., Schrijvers, T., Triska, M., Lager, T.: Swi-prolog. In: CoRR (2010)
Wolter, D., Lee, J.H.: Qualitative reasoning with directional relations. Artificial Intelligence (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bhatt, M., Lee, J.H., Schultz, C. (2011). CLP(QS): A Declarative Spatial Reasoning Framework. In: Egenhofer, M., Giudice, N., Moratz, R., Worboys, M. (eds) Spatial Information Theory. COSIT 2011. Lecture Notes in Computer Science, vol 6899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23196-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-23196-4_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23195-7
Online ISBN: 978-3-642-23196-4
eBook Packages: Computer ScienceComputer Science (R0)