This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Reasoning System of Ternary Projective Relations
February 2010 (vol. 22 no. 2)
pp. 161-178
ASCII Text
x 
 
Eliseo Clementini, Spiros Skiadopoulos, Roland Billen, Francesco Tarquini, "A Reasoning System of Ternary Projective Relations," IEEE Transactions on Knowledge and Data Engineering, vol. 22, no. 2, pp. 161-178, February, 2010.
 
 
BibTex
x
 
@article{ 10.1109/TKDE.2009.79,
author = {Eliseo Clementini and Spiros Skiadopoulos and Roland Billen and Francesco Tarquini},
title = {A Reasoning System of Ternary Projective Relations},
journal ={IEEE Transactions on Knowledge and Data Engineering},
volume = {22},
number = {2},
issn = {1041-4347},
year = {2010},
pages = {161-178},
doi = {http://doi.ieeecomputersociety.org/10.1109/TKDE.2009.79},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Knowledge and Data Engineering
TI - A Reasoning System of Ternary Projective Relations
IS - 2
SN - 1041-4347
SP161
EP178
EPD - 161-178
A1 - Eliseo Clementini,
A1 - Spiros Skiadopoulos,
A1 - Roland Billen,
A1 - Francesco Tarquini,
PY - 2010
KW - Qualitative spatial reasoning
KW - spatial relations
KW - projective relations
KW - ternary relations
KW - reasoning system
KW - composition tables
KW - geometric configurations.
VL - 22
JA - IEEE Transactions on Knowledge and Data Engineering
ER -
 
Eliseo Clementini, University of L'Aquila, L'Aquila
Spiros Skiadopoulos, University of Peloponnese, Tripolis
Roland Billen, University of Liege, Liege
Francesco Tarquini, University of L'Aquila, L'Aquila
This paper introduces a reasoning system based on a previously developed model for ternary projective relations between spatial objects. The model applies to spatial objects of the kind point and region is based on basic projective invariants and takes into account the size and shape of the three objects that are involved in a relation. The reasoning system proposes a set of permutation and composition rules, which allow the inference of unknown relations from given ones.

[1] A. Cohn and S. Hazarika, “Qualitative Spatial Representation and Reasoning: An Overview,” Fundamenta Informaticae, vol. 16, nos. 1/2, pp. 1-29, 2001.
[2] M. Egenhofer and J. Herring, “Categorizing Binary Topological Relationships between Regions, Lines, and Points in Geographic Databases,” technical report, Dept. of Surveying Eng., Univ. of Maine, 1991.
[3] M. Egenhofer, “Deriving the Composition of Binary Topological Relations,” J. Visual Languages and Computing, vol. 5, no. 1, pp. 133-149, 1994.
[4] E. Clementini and P. Di Felice, “Spatial Operators,” SIGMOD Record, vol. 29, no. 3, pp. 31-38, 2000.
[5] D. Waller, J. Loomis, R. Golledge, and A. Beall, “Place Learning in Humans: The Role of Distance and Direction Information,” Spatial Cognition and Computation, vol. 2, pp. 333-354, 2000.
[6] E. Clementini, P. Di Felice, and D. Hernández, “Qualitative Representation of Positional Information,” Artificial Intelligence, vol. 95, pp. 317-356, 1997.
[7] E. Clementini and P. Di Felice, “A Global Framework for Qualitative Shape Description,” GeoInformatica, vol. 1, no. 1, pp. 1-17, 1997.
[8] R. Billen and E. Clementini, “Semantics of Collinearity Among Regions,” Proc. OTM Workshops '05—First Int'l Workshop Semantic-Based Geographical Information Systems (SeBGIS '05), R. Meersman, ed., pp. 1066-1076, 2005.
[9] E. Clementini and R. Billen, “Modeling and Computing Ternary Projective Relations between Regions,” IEEE Trans. Knowledge and Data Eng., vol. 18, no. 6, pp. 799-814, June 2006.
[10] R. Billen and E. Clementini, “A Model for Ternary Projective Relations between Regions,” Proc. Int'l Conf. Extending Database Technology (EDBT '04), E. Bertino, ed., pp. 310-328, 2004.
[11] R. Billen and E. Clementini, “Introducing a Reasoning System Based on Ternary Projective Relations,” Proc. Int'l Symp. Spatial Data Handling (SDH '04), P. Fisher, ed., pp. 381-394, 2004.
[12] C. Freksa, “Using Orientation Information for Qualitative Spatial Reasoning,” Proc. Int'l Conf. Theories and Models of Spatio-Temporal Reasoning in Geographic Space, pp. 162-178, 1992.
[13] A. Scivos and B. Nebel, “Double-Crossing: Decidability and Computational Complexity of a Qualitative Calculus for Navigation,” Proc. Int'l Conf. Spatial Information Theory: Foundations of Geographic Information Science (COSIT '01), pp. 431-446, 2001.
[14] A. Isli, “Combining Cardinal Direction Relations and Other Orientation Relations in QSR,” Proc. Eighth Int'l Symp. Artificial Intelligence and Math. (AI&M '04), 2004.
[15] G. Retz-Schmidt, “Various Views on Spatial Prepositions,” AI Magazine, vol. 9, no. 2, pp. 95-105, 1988.
[16] D. Hernández, Qualitative Representation of Spatial Knowledge. Springer-Verlag, 1994.
[17] K.-P. Gapp, “From Vision to Language: A Cognitive Approach to the Computation of Spatial Relations in 3d Space,” Proc. European Conf. Cognitive Science in Industry, pp. 339-357, 1994.
[18] I. Bloch, O. Colliot, and R.M. Cesar,Jr., “On the Ternary Spatial Relation ‘Between’,” IEEE Trans. Systems, Man, and Cybernetics, vol. 36, no. 2, pp. 312-327, Apr. 2006.
[19] M. Worboys, M. Duckham, and L. Kulik, “Commonsense Notions of Proximity and Direction in Environmental Space,” Spatial Cognition and Computation, vol. 4, no. 4, pp. 285-312, 2004.
[20] D. Hernández, “Maintaining Qualitative Spatial Knowledge,” Proc. Int'l Conf. Spatial Information Theory: A Theoretical Basis for GIS (COSIT '93), A. Frank and I. Campari, eds., pp.36-53, 1993.
[21] K.-P. Gapp, “Angle, Distance, Shape, and Their Relationship to Projective Relations,” Proc. 17th Conf. Cognitive Science Soc., pp.112-117, 1995.
[22] C. Schlieder, “Reasoning about Ordering,” Proc. Int'l Conf. Spatial Information Theory: A Theoretical Basis for GIS (COSIT '95), A. Frank and W. Kuhn, eds., pp. 341-349, 1995.
[23] C. Kray and A. Blocher, “Modeling the Basic Meanings of Path Relations,” Proc. Int'l Joint Conf. Artificial Intelligence (IJCAI '99), pp. 384-389, 1999.
[24] R. Moratz and K. Fischer, “Cognitively Adequate Modelling of Spatial Reference in Human-Robot Interaction,” Proc. IEEE Int'l Conf. Tools with Artificial Intelligence (ICTAI '00), pp. 222-228, 2000.
[25] A. Frank, “Qualitative Spatial Reasoning about Distances and Directions in Geographic Space,” J. Visual Languages and Computing, vol. 3, pp. 343-371, 1992.
[26] L. Kulik and A. Klippel, “Reasoning about Cardinal Directions Using Grids as Qualitative Geographic Coordinates,” Proc. Int'l Conf. Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science (COSIT '99), C. Freksa and D. Mark, eds., pp. 205-220, 1999.
[27] R. Goyal and M. Egenhofer, “The Direction-Relation Matrix: A Representation for Directions Relations between Extended Spatial Objects,” Proc. Univ. Consortium for Geographic Information Systems Science (UCGIS) Ann. Assembly and Summer Retreat, June 1997.
[28] C. Vorwerg, G. Socher, T. Fuhr, G. Sagerer, and G. Rickheit, “Projective Relations for 3d Space: Computational Model, Application, and Psychological Evaluation,” Proc. Nat'l Conf. Artificial Intelligence (AAAI '97), pp. 159-164, 1997.
[29] H. Schmidtke, “The House Is North of the River: Relative Localization of Extended Objects,” Proc. Int'l Conf. Spatial Information Theory: Foundations of Geographic Information Science (COSIT '01), D. Montello, ed., pp. 415-430, 2001.
[30] L. Kulik, C. Eschenbach, C. Habel, and H. Schmidtke, “A Graded Approach to Directions between Extended Objects,” Proc. Int'l Conf. Geographic Information Science (GIScience '02), M. Egenhofer and D. Mark, eds., pp. 119-131, 2002.
[31] S. Skiadopoulos, N. Sarkas, T. Sellis, and M. Koubarakis, “A Family of Directional Relation Models for Extended Objects,” IEEE Trans. Knowledge and Data Eng., vol. 19, no. 8, pp. 1116-1130, Aug. 2007.
[32] V. Dugat, P. Gambarotto, and Y. Larvor, “Qualitative Theory of Shape and Orientation,” Proc. Int'l Joint Conf. Artificial Intelligence (IJCAI '99), pp. 45-53, 1999.
[33] S. Skiadopoulos and M. Koubarakis, “Composing Cardinal Direction Relations,” Artificial Intelligence, vol. 152, no. 2, pp.143-171, 2004.
[34] S. Skiadopoulos and M. Koubarakis, “On the Consistency of Cardinal Directions Constraints,” Artificial Intelligence, vol. 163, no. 1, pp. 91-135, 2005.
[35] R. Moratz and M. Ragni, “Qualitative Spatial Reasoning about Relative Point Position,” J. Visual Languages and Computing, vol. 19, pp. 75-98, 2008.
[36] C. Gallistel, “Language and Spatial Frames of Reference in Mind and Brain,” Trends in Cognitive Sciences, vol. 6, pp. 321-322, 2002.
[37] F. Tarquini, G. De Felice, P. Fogliaroni, and E. Clementini, “A Qualitative Model for Visibility Relations,” Proc. Ann. German Conf. Artificial Intelligence (KI '07), J. Hertzberg, M. Beetz, and R. Englert, eds., pp. 510-513, 2007.
[38] E. Clementini, “Projective Relations on the Sphere,” Proc. Second Int'l Workshop Semantic and Conceptual Issues in GIS (SeCoGIS '08), I.-Y. Song, ed., pp. 313-322, 2008.
[39] B. Bennett, A. Isli, and A. Cohn, “When Does a Composition Table Provide a Complete and Tractable Proof Procedure for a Relational Constraint Language?” Proc. Int'l Joint Conf. Artificial Intelligence (IJCAI '97) Workshop Spatial and Temporal Reasoning, 1997.
[40] G. Ligozat, “When Tables Tell It All: Qualitative Spatial and Temporal Reasoning Based on Linear Ordering,” Proc. Int'l Conf. Spatial Information Theory: Foundations of Geographic Information Science (COSIT '01), D. Montello, ed., pp. 60-75, 2001.
[41] A. Isli and A. Cohn, “An Algebra for Cyclic Ordering of 2D Orientations,” Proc. Nat'l Conf. Artificial Intelligence (AAAI '98), pp. 643-649, July 1998.
[42] I. Düntsch, H. Wang, and S. McCloskey, “Relation Algebras in Qualitative Spatial Reasoning,” Fundamenta Informaticae, vol. 39, pp. 229-248, 1999.
[43] I. Düntsch, H. Wang, and S. McCloskey, “A Relation-Algebraic Approach to the Region Connection Calculus,” Theoretical Computer Science, vol. 255, pp. 63-83, 2001.
[44] J. Renz and G. Ligozat, “Weak Composition for Qualitative Spatial and Temporal Reasoning,” Proc. Int'l Conf. Principles and Practice of Constraint Programming (CP '05), 2005.

Index Terms:
Qualitative spatial reasoning, spatial relations, projective relations, ternary relations, reasoning system, composition tables, geometric configurations.
Citation:
Eliseo Clementini, Spiros Skiadopoulos, Roland Billen, Francesco Tarquini, "A Reasoning System of Ternary Projective Relations," IEEE Transactions on Knowledge and Data Engineering, vol. 22, no. 2, pp. 161-178, Feb. 2010, doi:10.1109/TKDE.2009.79
Usage of this product signifies your acceptance of the Terms of Use.