Abstract
The systematic modelling of dynamic spatial systems [9] is a key requirement in a wide range of application areas such as comonsense cognitive robotics, computer-aided architecture design, dynamic geographic information systems. We present ASPMT(QS), a novel approach and fully-implemented prototype for non-monotonic spatial reasoning —a crucial requirement within dynamic spatial systems– based on Answer Set Programming Modulo Theories (ASPMT). ASPMT(QS) consists of a (qualitative) spatial representation module (QS) and a method for turning tight ASPMT instances into Sat Modulo Theories (SMT) instances in order to compute stable models by means of SMT solvers. We formalise and implement concepts of default spatial reasoning and spatial frame axioms using choice formulas. Spatial reasoning is performed by encoding spatial relations as systems of polynomial constraints, and solving via SMT with the theory of real nonlinear arithmetic. We empirically evaluate ASPMT(QS) in comparison with other prominent contemporary spatial reasoning systems. Our results show that ASPMT(QS) is the only existing system that is capable of reasoning about indirect spatial effects (i.e. addressing the ramification problem), and integrating geometric and qualitative spatial information within a non-monotonic spatial reasoning context.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Allen, J.F.: Maintaining knowledge about temporal intervals. Commun. ACM 26(11), 832–843 (1983)
Bartholomew, M., Lee, J.: Stable models of formulas with intensional functions. In: KR (2012)
Bartholomew, M., Lee, J.: Functional stable model semantics and answer set programming modulo theories. In: Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, pp. 718–724. AAAI Press (2013)
Bartholomew, M., Lee, J.: System aspmt2smt: computing ASPMT theories by SMT solvers. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS, vol. 8761, pp. 529–542. Springer, Heidelberg (2014)
Bhatt, M.: (Some) Default and non-monotonic aspects of qualitative spatial reasoning. In: AAAI 2008 Technical reports, Workshop on Spatial and Temporal Reasoning, pp. 1–6 (2008)
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 (2012)
Bhatt, M., Guesgen, H., Wölfl, S., Hazarika, S.: Qualitative spatial and temporal reasoning: emerging applications, trends, and directions. Spat. Cogn. Comput. 11(1), 1–14 (2011)
Bhatt, M., Lee, J.H., Schultz, C.: CLP(QS): a declarative spatial reasoning framework. In: Egenhofer, M., Giudice, N., Moratz, R., Worboys, M. (eds.) COSIT 2011. LNCS, vol. 6899, pp. 210–230. Springer, Heidelberg (2011)
Bhatt, M., Loke, S.: Modelling dynamic spatial systems in the situation calculus. Spat. Cogn. Comput. 8(1), 86–130 (2008)
Bhatt, M., Wallgrün, J.O.: Geospatial narratives and their spatio-temporal dynamics: commonsense reasoning for high-level analyses in geographic information systems. ISPRS Int. J. Geo-Inf. 3(1), 166–205 (2014)
Bouhineau, D.: Solving geometrical constraint systems using CLP based on linear constraint solver. In: Pfalzgraf, J., Calmet, J., Campbell, J. (eds.) AISMC 1996. LNCS, vol. 1138. Springer, Heidelberg (1996)
Bouhineau, D., Trilling, L., Cohen, J.: An application of CLP: checking the correctness of theorems in geometry. Constraints 4(4), 383–405 (1999)
Ferraris, P.: Answer sets for propositional theories. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 119–131. Springer, Heidelberg (2005)
Ferraris, P., Lee, J., Lifschitz, V.: Stable models and circumscription. Artif. Intell. 175(1), 236–263 (2011)
Frank, A.U.: Qualitative spatial reasoning with cardinal directions. In: Kaindl, H. (ed.) 7. Österreichische Artificial-Intelligence-Tagung/Seventh Austrian Conference on Artificial Intelligence. Informatik-Fachberichte, vol. 287, pp. 157–167. Springer, Heidelberg (1991)
Freksa, C.: Using orientation information for qualitative spatial reasoning. In: Frank, A.U., Formentini, U., Campari, I. (eds.) GIS 1992. LNCS, vol. 639, pp. 162–178. Springer, Heidelberg (1992)
Gantner, Z., Westphal, M., Wölfl, S.: GQR-A fast reasoner for binary qualitative constraint calculi. In: Proceedings of AAAI, vol. 8 (2008)
Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T.: Clingo= ASP+ control: Preliminary report. arXiv preprint arXiv:1405.3694 (2014)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. ICLP/SLP, vol. 88, pp. 1070–1080 (1988)
Guesgen, H.W.: Spatial reasoning based on Allen’s temporal logic. Technical report TR-89-049, International Computer Science Institute Berkeley (1989)
Lee, J.H.: The complexity of reasoning with relative directions. In: 21st European Conference on Artificial Intelligence (ECAI 2014) (2014)
Moratz, R.: Representing relative direction as a binary relation of oriented points. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) ECAI. Frontiers in Artificial Intelligence and Applications, vol. 141, pp. 407–411. IOS Press (2006)
Pesant, G., Boyer, M.: QUAD-CLP(R): adding the power of quadratic constraints. In: Borning, A. (ed.) PPCP 1994. LNCS, vol. 874, pp. 95–108. Springer, Heidelberg (1994)
Pesant, G., Boyer, M.: Reasoning about solids using constraint logic programming. J. Autom. Reasoning 22(3), 241–262 (1999)
Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: KR, vol. 92, pp. 165–176 (1992)
Schultz, C., Bhatt, M.: Towards a declarative spatial reasoning system. In: 20th European Conference on Artificial Intelligence (ECAI 2012) (2012)
Schultz, C., Bhatt, M.: Declarative spatial reasoning with boolean combinations of axis-aligned rectangular polytopes. In: ECAI 2014–21st European Conference on Artificial Intelligence, pp. 795–800 (2014)
Varzi, A.C.: Parts, wholes, and part-whole relations: the prospects of mereotopology. Data Knowl. Eng. 20(3), 259–286 (1996)
Wölfl, S., Westphal, M.: On combinations of binary qualitative constraint calculi. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence. IJCAI 2009, Pasadena, California, USA, 11–17 July 2009, pp. 967–973 (2009)
Acknowledgments
This research is partially supported by: (a) the Polish National Science Centre grant 2011/02/A/HS1/0039; and (b). the DesignSpace Research Group www.design-space.org.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Wałęga, P.A., Bhatt, M., Schultz, C. (2015). ASPMT(QS): Non-Monotonic Spatial Reasoning with Answer Set Programming Modulo Theories. In: Calimeri, F., Ianni, G., Truszczynski, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2015. Lecture Notes in Computer Science(), vol 9345. Springer, Cham. https://doi.org/10.1007/978-3-319-23264-5_41
Download citation
DOI: https://doi.org/10.1007/978-3-319-23264-5_41
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23263-8
Online ISBN: 978-3-319-23264-5
eBook Packages: Computer ScienceComputer Science (R0)