Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-07T05:08:54.356Z Has data issue: false hasContentIssue false
  • English
  • Français

Reasoning about Cardinal Directions between 3-Dimensional Extended Objects using Answer Set Programming

Published online by Cambridge University Press:  22 September 2020

Yusuf Izmirlioglu Open the ORCID record for Yusuf Izmirlioglu [Opens in a new window]  and
Esra Erdem Open the ORCID record for Esra Erdem [Opens in a new window]
Yusuf Izmirlioglu
Affiliation:
Sabanci University, Faculty of Engineering and Natural Sciences, 34956 Istanbul, Turkey yizmirlioglu@sabanciuniv.edu, esra.erdem@sabanciuniv.edu
Esra Erdem
Affiliation:
Sabanci University, Faculty of Engineering and Natural Sciences, 34956 Istanbul, Turkey yizmirlioglu@sabanciuniv.edu, esra.erdem@sabanciuniv.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We propose a novel formal framework (called 3D-NCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-NCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and NCDC-ASP to 3D. 3D-NCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-NCDC-ASP, and illustrate its usefulness with applications.

Keywords

Qualitative Spatial ReasoningAnswer Set ProgrammingCardinal Directional Calculus3D SpaceConsistency CheckingMarine ExplorationBuilding DesignDigital Forensics

Information

Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 6: 36th International Conference on Logic Programming Special Issue II , November 2020 , pp. 942 - 957
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

References

Allen, J. F. 1983. Maintaining knowledge about temporal intervals. Commun. ACM 26, 11, 832–843.Google Scholar
Balbiani, P., Condotta, J., and del Cerro, L. F. 2002. Tractability results in the block algebra. J. Log. Comput. 12, 5, 885–909.Google Scholar
Baryannis, G., Tachmazidis, I., Batsakis, S., Antoniou, G., Alviano, M., Sellis, T., and Tsai, P.-W. 2018. A trajectory calculus for qualitative spatial reasoning using answer set programming. Theory and Practice of Logic Programming 18, 3-4, 355–371.Google Scholar
Borrmann, A. and Beetz, J. 2010. Towards spatial reasoning on building information models. In Proceedings of the 8th European Conference on Product and Process Modeling (ECPPM). 61–67.Google Scholar
Brenton, C., Faber, W., and Batsakis, S. 2016. Answer set programming for qualitative spatio-temporal reasoning: Methods and experiments. In OASIcs-OpenAccess Series in Informatics. Vol. 52.Google Scholar
Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Maratea, M., Ricca, F., and Schaub, T. 2020. Asp-Core-2 input language format. Theory and Practice of Logic Programming 20, 2, 294–309.Google Scholar
Chen, J., Cohn, A. G., Liu, D., Wang, S., Ouyang, J., and Yu, Q. 2015. A survey of qualitative spatial representations. The Knowledge Engineering Review 30, 1, 106–136.Google Scholar
Chen, J., Liu, D., Jia, H., and Zhang, C. 2007. Cardinal direction relations in 3D space. In Proc. of International Conference on Knowledge Science, Engineering and Management. 623–629.Google Scholar
Cohn, A. G., Bennett, B., Gooday, J., and Gotts, N. M. 1997. Qualitative spatial representation and reasoning with the region connection calculus. GeoInformatica 1, 3, 275–316.Google Scholar
Costantini, S., Gasperis, G. D., and Olivieri, R. 2019. Digital forensics and investigations meet artificial intelligence. Ann. Math. Artif. Intell. 86, 1-3, 193–229.Google Scholar
Randell, David A., Z. C. and Cohn, A. G. 1992. A spatial logic based on regions and connection. In Proc. of KR.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. 337–340.Google Scholar
Dylla, F., Lee, J. H., Mossakowski, T., Schneider, T., Delden, A. V., Ven, J. V. D., and Wolter, D. 2017. A survey of qualitative spatial and temporal calculi: algebraic and computational properties. ACM Computing Surveys (CSUR) 50, 1, 7.Google Scholar
Gebser, M., Kaufmann, B., Kaminski, R., Ostrowski, M., Schaub, T., and Schneider, M. T. 2011. Potassco: The potsdam answer set solving collection. AI Commun. 24, 2, 107–124.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. of ICLP. MIT Press, 1070–1080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385.Google Scholar
Goyal, R. and Egenhofer, M. J. 1997. The direction-relation matrix: A representation for directions relations between extended spatial objects. The annual assembly and the summer retreat of University Consortium for Geographic Information Systems Science 3, 95–102.Google Scholar
Hou, R., Wu, T., and Yang, J. 2016. Reasoning with cardinal directions in 3D space based on block algebra. Proc. of ICEITI.Google Scholar
Izmirlioglu, Y. and Erdem, E. 2018. Qualitative reasoning about cardinal directions using answer set programming. In Proc. of AAAI.Google Scholar
Izmirlioglu, Y. and Erdem, E. 2020. Reasoning about Cardinal Directions between 3-Dimensional Extended Objects using Answer Set Programming (arXiv).Google Scholar
Li, C., Lu, J., Yin, C., and Ma, L. 2009. Qualitative spatial representation and reasoning in 3D space. In Proc. of ICICTA. 653–657.Google Scholar
Lifschitz, V. 2002. Answer set programming and plan generation. Artificial Intelligence 138, 39–54.Google Scholar
Liu, W., Zhang, X., Li, S., and Ying, M. 2010. Reasoning about cardinal directions between extended objects. Artificial Intelligence 174, 12-13, 951–983.Google Scholar
Marek, V. and Truszczyński, M. 1999. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: a 25-Year Perspective. Springer Verlag, 375–398.Google Scholar
Mota, T. and Sridharan, M. 2018. Incrementally grounding expressions for spatial relations between objects. In Proc. of IJCAI. 1928–1934.Google Scholar
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 241–273.CrossRefGoogle Scholar
Pais, J. and Pinto-Ferreira, C. 2000. Spatial representation and reasoning using the n-dimensional projective approach. In Tech. Report, AAAI Workshop on Spatial and Temporal Granularity. 79–82.Google Scholar
Skiadopoulos, S. and Koubarakis, M. 2004. Composing cardinal direction relations. Artificial Intelligence 152, 2, 143–171.Google Scholar
Skiadopoulos, S. and Koubarakis, M. 2005. On the consistency of cardinal direction constraints. Artificial Intelligence 163, 1, 91–135.Google Scholar
Walega, P. A., Schultz, C., and Bhatt, M. 2017. Non-monotonic spatial reasoning with answer set programming modulo theories. Theory and Practice of Logic Programming 17, 2, 205–225.Google Scholar
Zampogiannis, K., Yang, Y., Fermüller, C., and Aloimonos, Y. 2015. Learning the spatial semantics of manipulation actions through preposition grounding. In Proc. of ICRA. 1389–1396.CrossRefGoogle Scholar
Zereik, E., Bibuli, M., Miskovic, N., Ridao, P., and Pascoal, A. 2018. Challenges and future trends in marine robotics. Annual Reviews in Control.Google Scholar