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Non-monotonic spatial reasoning with answer set programming modulo theories* †

Published online by Cambridge University Press:  30 August 2016

PRZEMYSŁAW ANDRZEJ WAŁĘGA ,
CARL SCHULTZ  and
MEHUL BHATT
PRZEMYSŁAW ANDRZEJ WAŁĘGA
Affiliation:
Spatial Reasoning (www.spatial-reasoning.com) The DesignSpace Group, Germany (www.design-space.org) University of Warsaw, Warsaw, Poland University of Münster, Münster, Germany University of Bremen, Bremen, Germany (e-mail: p.a.walega@gmail.com, schultzc@uni-muenster.de, bhatt@uni-bremen.de)
CARL SCHULTZ
Affiliation:
Spatial Reasoning (www.spatial-reasoning.com) The DesignSpace Group, Germany (www.design-space.org) University of Warsaw, Warsaw, Poland University of Münster, Münster, Germany University of Bremen, Bremen, Germany (e-mail: p.a.walega@gmail.com, schultzc@uni-muenster.de, bhatt@uni-bremen.de)
MEHUL BHATT
Affiliation:
Spatial Reasoning (www.spatial-reasoning.com) The DesignSpace Group, Germany (www.design-space.org) University of Warsaw, Warsaw, Poland University of Münster, Münster, Germany University of Bremen, Bremen, Germany (e-mail: p.a.walega@gmail.com, schultzc@uni-muenster.de, bhatt@uni-bremen.de)
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Abstract

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The systematic modelling of dynamic spatial systems is a key requirement in a wide range of application areas such as commonsense cognitive robotics, computer-aided architecture design, and dynamic geographic information systems. We present Answer Set Programming Modulo Theories (ASPMT)(QS), a novel approach and fully implemented prototype for non-monotonic spatial reasoning — a crucial requirement within dynamic spatial systems — based on ASPMT. ASPMT(QS) consists of a (qualitative) spatial representation module (QS) and a method for turning tight ASPMT instances into Satisfiability 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. Spatial reasoning is performed by encoding spatial relations as systems of polynomial constraints, and solving via SMT with the theory of real non-linear arithmetic. We empirically evaluate ASPMT(QS) in comparison with other contemporary spatial reasoning systems both within and outside the context of logic programming. ASPMT(QS) is currently the only existing system that is capable of reasoning about indirect spatial effects (i.e., addressing the ramification problem), and integrating geometric and QS information within a non-monotonic spatial reasoning context.

Keywords

non-monotonic spatial reasoninganswer set programming modulo theoriesdeclarative spatial reasoningdynamic spatial systemsreasoning about spaceactionsand change

Information

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 17 , Issue 2 , March 2017 , pp. 205 - 225
Copyright
Copyright © Cambridge University Press 2016 

Footnotes

*

This is an extended version of a paper presented at the Logic Programming and Nonmonotonic Reasoning Conference (LPNMR 2015), invited as a rapid communication in TPLP. The authors acknowledge the assistance of the conference program chairs Giovambattista Ianni and Miroslaw Truszczynski.

†

This paper comes with an online appendix containing Appendices A-H. The online appendix is available via the supplementary materials link from the TPLP web-site.

References

Aiello, M., Pratt-Hartmann, I. E. and Benthem, J. F. V. 2007. In Handbook of Spatial Logics. Springer-Verlag, New York, Inc., Secaucus, NJ, USA.Google Scholar
Allen, J. F. 1983. Maintaining knowledge about temporal intervals. Communications of the ACM 26 (11), 832–843.Google Scholar
Arnon, D. S., Collins, G. E. and McCallum, S. 1984. Cylindrical algebraic decomposition I: The basic algorithm. SIAM Journal on Computing 13 (4), 865–877.Google Scholar
Bartholomew, M. and Lee, J. 2012. Stable models of formulas with intensional functions. In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR), 2–12.Google Scholar
Bartholomew, M. and Lee, J. 2013. Functional stable model semantics and answer set programming modulo theories. In Proc. of the Twenty-Third International Joint Conference on Artificial Intelligence. AAAI Press, 718–724.Google Scholar
Bartholomew, M. and Lee, J. 2014. System aspmt2smt: Computing ASPMT theories by SMT solvers. In Logics in Artificial Intelligence. Springer, 529–542.Google Scholar
Bhatt, M. 2008. (Some) default and non-monotonic aspects of qualitative spatial reasoning. In AAAI-08 Technical Reports, Workshop on Spatial and Temporal Reasoning. AAAI Press, 1–6.Google Scholar
Bhatt, M. 2010. Commonsense inference in dynamic spatial systems: Epistemological requirements. In Proc. of the Twenty-Third International Florida Artificial Intelligence Research Society Conference, May 19–21, 2010. AAAI Press, Daytona Beach, Florida.Google Scholar
Bhatt, M. 2012. 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.Google Scholar
Bhatt, M., Guesgen, H., Wölfl, S. and Hazarika, S. 2011. Qualitative spatial and temporal reasoning: Emerging applications, trends, and directions. Spatial Cognition & Computation 11 (1), 1–14.Google Scholar
Bhatt, M., Lee, J. H. and Schultz, C. 2011. CLP(QS): A declarative spatial reasoning framework. In COSIT 2011 - Spatial Information Theory. Springer-Verlag, Berlin, Heidelberg, 210–230.Google Scholar
Bhatt, M. and Loke, S. 2008. Modelling dynamic spatial systems in the situation calculus. Spatial Cognition and Computation 8 (1), 86–130.CrossRefGoogle Scholar
Bhatt, M., Schultz, C. and Freksa, C. 2013. The ‘space’ in spatial assistance systems: Conception, formalisation and computation. In Representing Space in Cognition: Interrelations of Behavior, Language, and Formal Models. Series: Explorations in Language and Space, Tenbrink, T., Wiener, J. and Claramunt, C., Eds. 978-0-19-967991-1, Oxford University Press, 171–214.Google Scholar
Bhatt, M., Schultz, C. P. L. and Thosar, M. 2014. Computing narratives of cognitive user experience for building design analysis: KR for industry scale computer-aided architecture design. In KR 2014, Baral, C., Giacomo, G. D. and Eiter, T., Eds. AAAI Press, 508–517.Google Scholar
Bhatt, M., Suchan, J. and Schultz, C. 2013. Cognitive interpretation of everyday activities – toward perceptual narrative based visuo-spatial scene interpretation. In Computational Models of Narrative (CMN) 2013., A Satellite Workshop of CogSci 2013: The 35th Meeting of the Cognitive Science Society., Finlayson, M., Fisseni, B., Loewe, B. and Meister, J. C., Eds. OpenAccess Series in Informatics (OASIcs), Dagstuhl, Germany.Google Scholar
Bhatt, M. and Wallgrün, J. O. 2014. Geospatial narratives and their spatio-temporal dynamics: Commonsense reasoning for high-level analyses in geographic information systems. ISPRS Int. J. Geo-Information 3 (1), 166–205.Google Scholar
Bouhineau, D. 1996. Solving geometrical constraint systems using CLP based on linear constraint solver. In Artificial Intelligence and Symbolic Mathematical Computation. Springer, 274–288.Google Scholar
Bouhineau, D., Trilling, L. and Cohen, J. 1999. An application of CLP: Checking the correctness of theorems in geometry. Constraints 4 (4), 383–405.CrossRefGoogle Scholar
Cabalar, P. and Santos, P. E. 2011. Formalising the fisherman's folly puzzle. Artificial Intelligence 175 (1), 346–377.Google Scholar
Cohn, A. G. and Gotts, N. M. 1996. The ‘egg-yolk’representation of regions with indeterminate boundaries. Geographic Objects with Indeterminate Boundaries 2, 171–187.Google Scholar
Collins, G. E. 1975. Quantifier elimination for real closed fields by cylindrical algebraic decompostion. In Automata Theory and Formal Languages 2nd GI Conference Kaiserslautern, May 20–23, 1975. Springer, 134–183.Google Scholar
Collins, G. E. and Hong, H. 1991. Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation 12 (3), 299–328.Google Scholar
Davis, E. 2008. Pouring liquids: A study in commonsense physical reasoning. Artif. Intell. 172 (12–13), 1540–1578.Google Scholar
Davis, E. 2011. How does a box work? A study in the qualitative dynamics of solid objects. Artificial Intelligence 175 (1), 299–345.Google Scholar
De Moura, L. and Bjørner, N. 2008. Z3: An efficient smt solver. In Tools and Algorithms for the Construction and Analysis of Systems. Springer, 337–340.Google Scholar
Eppe, M. and Bhatt, M. 2013. Narrative based postdictive reasoning for cognitive robotics. In COMMONSENSE 2013: 11th International Symposium on Logical Formalizations of Commonsense Reasoning. AAAI Press.Google Scholar
Ferraris, P. 2005. Answer sets for propositional theories. In Logic Programming and Nonmonotonic Reasoning. Springer, 119–131.Google Scholar
Ferraris, P., Lee, J. and Lifschitz, V. 2011. Stable models and circumscription. Artificial Intelligence 175 (1), 236–263.Google Scholar
Frank, A. U. 1991. Qualitative spatial reasoning with cardinal directions. In 7. Österreichische Artificial-Intelligence-Tagung/Seventh Austrian Conference on Artificial Intelligence. Springer, 157–167.Google Scholar
Gantner, Z., Westphal, M. and Wölfl, S. 2008. GQR-A fast reasoner for binary qualitative constraint calculi. In Proc. of AAAI, AAAI Press, vol. 8.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2014. Clingo= ASP+ control: Preliminary report. arXiv preprint arXiv:1405.3694v1. Available at http://arxiv.org/abs/1405.3694v1.Google Scholar
Gelfond, M. 2008. Answer sets. In Handbook of Knowledge Representation, Vol. 1. Elsevier, 285.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. of ICLP/SLP, vol. 88. MIT Press, 1070–1080.Google Scholar
Guesgen, H. W. 1989. Spatial reasoning based on Allen's temporal logic. Technical Report TR-89-049. International Computer Science Institute Berkeley.Google Scholar
Kapur, D. and Mundy, J. L., Eds. 1988. Geometric Reasoning. MIT Press, Cambridge, MA, USA.Google Scholar
Lee, J. H. 2014. The complexity of reasoning with relative directions. In Proc. of 21st European Conference on Artificial Intelligence (ECAI 2014), IOS Press.Google Scholar
Ligozat, G. 2011. Qualitative Spatial and Temporal Reasoning. Wiley-ISTE.Google Scholar
McCarthy, J. and Hayes, P. J. 1969. Some philosophical problems from the standpoint of artificial intelligence. In Machine Intelligence 4, Meltzer, B. and Michie, D., Eds. Edinburgh University Press, 463–502.Google Scholar
Moratz, R. 2006. Representing relative direction as a binary relation of oriented points. In ECAI, Brewka, G., Coradeschi, S., Perini, A., and Traverso, P., Eds. Frontiers in Artificial Intelligence and Applications, vol. 141. IOS Press, 407–411.Google Scholar
Pesant, G. and Boyer, M. 1994. QUAD-CLP (R): Adding the power of quadratic constraints. In Principles and Practice of Constraint Programming. Springer, 95–108.Google Scholar
Pesant, G. and Boyer, M. 1999. Reasoning about solids using constraint logic programming. Journal of Automated Reasoning 22 (3), 241–262.Google Scholar
Randell, D. A., Cui, Z. and Cohn, A. G. 1992. A spatial logic based on regions and connection. KR 92, 165–176.Google Scholar
Reiter, R. 2001. Knowledge in Action: Logical Foundations for Describing and Implementing Dynamical Systems. MIT Press.Google Scholar
Sandewall, E. 1994. Features and Fluents (Vol. 1): The Representation of Knowledge about Dynamical Systems. Oxford University Press, Inc., New York, NY, USA.Google Scholar
Schultz, C. and Bhatt, M. 2012. Towards a declarative spatial reasoning system. In Proc. of 20th European Conference on Artificial Intelligence (ECAI 2012), IOS Press.Google Scholar
Schultz, C. and Bhatt, M. 2014. Declarative spatial reasoning with boolean combinations of axis-aligned rectangular polytopes. In Proc. ECAI 2014 - 21st European Conference on Artificial Intelligence, 795–800.Google Scholar
Schultz, C. and Bhatt, M. 2015a. Encoding relative orientation and mereotopology relations with geometric constraints in CLP(QS). In Proc. 1st Workshop on Logics for Qualitative Modelling and Reasoning (LQMR'15). Lodz, Poland.CrossRefGoogle Scholar
Schultz, C. and Bhatt, M. 2015b. Spatial symmetry driven pruning strategies for efficient declarative spatial reasoning. In Proc. of COSIT 2015 - Spatial Information Theory. Springer, 331–353.Google Scholar
Scivos, A. and Nebel, B. 2004. The finest of its class: The natural, point-based ternary calculus LR for qualitative spatial reasoning. In Proc. of Spatial Cognition IV. Reasoning, Action, Interaction: International Conference Spatial Cognition, Freksa, C. et al., Ed. (2005), Lecture Notes in Computer Science, vol. 3343, Springer, Berlin Heidelberg, 283–303.Google Scholar
Shanahan, M. 1995. Default reasoning about spatial occupancy. Artificial Intelligence 74 (1), 147–163.Google Scholar
Spranger, M., Suchan, J. and Bhatt, M. 2016. Robust natural language processing - combining reasoning, cognitive semantics and construction grammar for spatial language. In Proc. of IJCAI 2016: International Joint Conference on Artificial Intelligence., New York, United States. AAAI Press, 2908–2914.Google Scholar
Spranger, M., Suchan, J., Bhatt, M. and Eppe, M. 2014. Grounding dynamic spatial relations for embodied (robot) interaction. In Proc. of PRICAI 2014: Pacific Rim Int. Conf. on Artificial Intelligence, Pham, D. N. and Park, S., Eds. Lecture Notes in Computer Science, vol. 8862. Springer, 958–971.Google Scholar
Suchan, J. and Bhatt, M. 2016a. Semantic question-answering with video and eye-tracking data – AI foundations for human visual perception driven cognitive film studies. In Proc. of IJCAI 2016: International Joint Conference on Artificial Intelligence. AAAI Press, New York, United States.Google Scholar
Suchan, J. and Bhatt, M. 2016b. The geometry of a scene: On deep semantics for visual perception driven cognitive film studies. In Proc. of WACV 2016: IEEE Winter Conference on Applications of Computer Vision (WACV 2016). IEEE, Lake Placid, NY, USA.Google Scholar
Suchan, J., Bhatt, M. and Santos, P. E. 2014. Perceptual narratives of space and motion for semantic interpretation of visual data. In Proc. of Computer Vision - ECCV 2014 Workshops, September 6–7 and 12, 2014, Part II, Zurich, Switzerland, Springer, 339–354.Google Scholar
Varzi, A. C. 1996. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data & Knowledge Engineering 20 (3), 259–286.Google Scholar
Wałęga, P. A., Bhatt, M. and Schultz, C. P. L. 2015. ASPMT(QS): Non-monotonic spatial reasoning with answer set programming modulo theories. In Proc. of Logic Programming and Nonmonotonic Reasoning - 13th International Conference, LPNMR 2015, September 27–30, 2015. Lecture Notes in Computer Science, vol. 9345. Springer, Lexington, KY, USA, 488–501.Google Scholar
Wölfl, S. and Westphal, M. 2009. On combinations of binary qualitative constraint calculi. In IJCAI 2009, AAAI Press, 967–973.Google Scholar
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