Skip to main content
SpringerLink
Log in

ASPMT(QS): Non-Monotonic Spatial Reasoning with Answer Set Programming Modulo Theories

  • Conference paper
  • First Online:
Logic Programming and Nonmonotonic Reasoning (LPNMR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9345))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Allen, J.F.: Maintaining knowledge about temporal intervals. Commun. ACM 26(11), 832–843 (1983)

    Article  MATH  Google Scholar 

  2. Bartholomew, M., Lee, J.: Stable models of formulas with intensional functions. In: KR (2012)

    Google Scholar 

  3. 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)

    Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. 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)

    Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. Bhatt, M., Loke, S.: Modelling dynamic spatial systems in the situation calculus. Spat. Cogn. Comput. 8(1), 86–130 (2008)

    Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. 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)

    Chapter  Google Scholar 

  12. Bouhineau, D., Trilling, L., Cohen, J.: An application of CLP: checking the correctness of theorems in geometry. Constraints 4(4), 383–405 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  14. Ferraris, P., Lee, J., Lifschitz, V.: Stable models and circumscription. Artif. Intell. 175(1), 236–263 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  15. 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)

    Google Scholar 

  16. 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)

    Chapter  Google Scholar 

  17. Gantner, Z., Westphal, M., Wölfl, S.: GQR-A fast reasoner for binary qualitative constraint calculi. In: Proceedings of AAAI, vol. 8 (2008)

    Google Scholar 

  18. Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T.: Clingo= ASP+ control: Preliminary report. arXiv preprint arXiv:1405.3694 (2014)

  19. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. ICLP/SLP, vol. 88, pp. 1070–1080 (1988)

    Google Scholar 

  20. Guesgen, H.W.: Spatial reasoning based on Allen’s temporal logic. Technical report TR-89-049, International Computer Science Institute Berkeley (1989)

    Google Scholar 

  21. Lee, J.H.: The complexity of reasoning with relative directions. In: 21st European Conference on Artificial Intelligence (ECAI 2014) (2014)

    Google Scholar 

  22. 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)

    Google Scholar 

  23. 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)

    Chapter  Google Scholar 

  24. Pesant, G., Boyer, M.: Reasoning about solids using constraint logic programming. J. Autom. Reasoning 22(3), 241–262 (1999)

    Article  MATH  Google Scholar 

  25. Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: KR, vol. 92, pp. 165–176 (1992)

    Google Scholar 

  26. Schultz, C., Bhatt, M.: Towards a declarative spatial reasoning system. In: 20th European Conference on Artificial Intelligence (ECAI 2012) (2012)

    Google Scholar 

  27. 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)

    Google Scholar 

  28. Varzi, A.C.: Parts, wholes, and part-whole relations: the prospects of mereotopology. Data Knowl. Eng. 20(3), 259–286 (1996)

    Article  MATH  Google Scholar 

  29. 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)

    Google Scholar 

Download references

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

  1. Institute of Philosophy, University of Warsaw, Warsaw, Poland

    Przemysław Andrzej Wałęga

  2. Department of Computer Science, University of Bremen, Bremen, Germany

    Mehul Bhatt & Carl Schultz

Authors
  1. Przemysław Andrzej Wałęga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehul Bhatt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Carl Schultz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Przemysław Andrzej Wałęga .

Editor information

Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Francesco Calimeri

  2. University of Calabria, Rende, Italy

    Giovambattista Ianni

  3. University of Kentucky Dept. Computer Science, Lexington, Kentucky, USA

    Miroslaw Truszczynski

Rights and permissions

Reprints 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)

Publish with us

Policies and ethics

Search

Navigation