Spatial and temporal reasoning: Beyond Allen's calculus

AI Communications

Volumn 17, Issue 4, 2004, Pages 223-233

  Ligozat, Gérard ^a   Mitra, Debasis ^b   Condotta, Jean François ^c  

^a CNRS   (France)

^b Florida Institute of Technology   (United States)

^c UNIVERSITÉ D'ARTOIS   (France)

Author keywords

Qualitative spatial and temporal reasoning; Relation algebra; Tractability; Weak representation

Indexed keywords

ALGORITHMS; COMPUTER PROGRAMMING LANGUAGES; DATABASE SYSTEMS; GEOGRAPHIC INFORMATION SYSTEMS; KNOWLEDGE ACQUISITION; LINEAR ALGEBRA; MATHEMATICAL MODELS; ROBOTICS;

QUALITATIVE SPATIAL AND TEMPORAL REASONING; RELATION ALGEBRA; TRACTABILITY; WEAK REPRESENTATION;

CONSTRAINT THEORY;

EID: 10644281122     PISSN: 09217126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. J.F. Allen, Maintaining knowledge about temporal intervals, Comm. of the ACM 26(11) (1983), 832-843.
2. F. Anger, D. Mitra and R. Rodriguez, Temporal constraint networks in nonlinear time, Technical report, ECAI Workshop on Temporal and Spatial Reasoning, 1998.
3. P. Balbiani and A. Osmani, A model for reasoning about topologic relations between cyclic intervals, in: Proc. of KK-2000, Breckenridge, CO, 2000.
4. P. Balbiani, J.-F. Condotta and G. Ligozat, Reasoning about generalized intervals: horn representation and tractability, in: Proceedings of the Seventh International Workshop on Temporal Representation and Reasoning (TIME-00), S. Goodwin and A. Trudel, eds, Cape Breton, NS, Canada, IEEE Computer Society, 2000, pp. 23-30.
5. P. Balbiani and J.-F. Condotta, Spatial reasoning about points in a multidimensional setting, Journal of Applied Intelligence, Kluwer, 2001.
6. P. Balbiani, J.-F. Condotta, L. Fariñas del Cerro and A. Osmani, A model for reasoning about generalized intervals, in: Proceedings of the Eighth International Conference on Artificial Intelligence: Methods, Systems, Applications (AIMSA'98), F. Giunchiglia, ed., LNAI 1480, 1998, pp. 50-61.
7. P. Balbiani, J.-F. Condotta and L. Fariñas del Cerro, A tractable subclass of the block algebra: constraint propagation and preconvex relations, in: Proceedings of the Ninth Portuguese Conference on Artificial Intelligence (EPIA'99), Évora, Portugal, 1999, pp. 75-89.
8. P. Balbiani, J.-F. Condotta and G. Ligozat, Reasoning about generalized intervals: Horn representability and tractability, in: Proceedings of the Seventh International Workshop on Temporal Representation an Reasoning (TIME'2000), Canada, 2000, pp. 23-30.
9. P. Balbiani, J.-F. Condotta and G. Ligozat, On the consistency problem for the INDU calculus, in: Proceedings of TIME-ICTL-2003, Cairns, Australia, 2003.
10. M. Broxvall, P. Jonsson and J. Renz, Refinements and independence: a simple method for identifying tractable disjunctive constraints, in: Proc. of the Sixth International Conference on the Principles and Applications of Constraint Programming (CP-2000), Singapore, 2000, pp. 114-127.
11. A.A. Bulatov, A.A. Krokhin and P. Jeavons, Constraint satisfaction problems and finite algebras, in: Proc. of the 27th International Conference on Automata, Languages and Programming (ICALP'OO), Number 1853 in LNCS, Springer, 2000, pp. 272-283.
12. T. Drakengren and P. Jonsson, Towards a complete classification of tractability in Allen's algebra, in: Proc. of IJCAI-97, Nagoya, Japan, 1997, pp. 1466-1475.
13. T. Drakengren and P. Jonsson, A complete classification of tractability in Allen's algebra relative to subsets of basic relations, Artificial Intelligence 106(2) (1998), 205-219.
14. I. Düntsch, Relation Algebras: Tutorial 2, Technical Report, COSIT'99 Tutorials, Stade, Germany, 1999.
15. N.M. Gotts, An axiomatic approach to topology for information systems, Technical Report TR-96-25, University of Leeds, School of Computer Studies, 1996.
16. A. Krokhin, P. Jeavons and P. Jonsson, Reasoning about Temporal Constraints: Classifying the Complexity in Allen's Algebra by using an Algebraic Technique, Technical Report PRG-RR-01-02, 2001, Oxford University Computing Laboratory, Programming Research Group, Oxford, UK, 2001.
17. A. Krokhin and P. Jeavons, Reasoning about temporal relations: The tractable subalgebras of Allen's interval algebra, Technical Report PRG-RR-01-12, Oxford University Computing Laboratory, Programming Research Group, Oxford, UK, 2001.
18. P. Ladkin, Time representation: A taxonomy of interval relations, in: Proceedings of the 5th National Conference on Artificial Intelligence, T. Kehler and S. Rosenschein, eds, Volume 1, Los Altos, CA, USA, Morgan Kaufmann, 1986, pp. 360-366.
19. P. Ladkin, The logic of time representation, PhD thesis, University of California, Berkeley, 1987.
20. P.B. Ladkin and Roger D. Maddux, On binary constraint problems, Journal of the ACM 41(3) (1994), 435-469.
21. G. Ligozat, Weak representations of interval algebras, in: Proc. of AAAI-90, 1990, pp. 715-720.
22. G. Ligozat, On generalized interval calculi, in: Proc. of AAAI-91, 1991, pp. 234-240.
23. G. Ligozat, When tables tell it all, in: Proc. of COSIT'01 (Conference on Spatial Information Theory), LNCS, Morro Bay, CA, Springer, 2001.
24. G. Ligozat, Corner relations in Allen's algebra, Constraints 3(2/3) (1998), 165-177.
25. G. Ligozat, Reasoning about cardinal directions, Journal of Visual Languages and Computing 1(9) (1998), 23-44.
26. G. Ligozat, Simple models for simple calculi, Lecture Notes in Computer Science, Vol. 1661, 1999.
27. G. Ligozat, On generalized interval calculi, in: Proceedings of the Ninth National Conference on Artificial Intelligence (AAAI'91), Menlo Park/Cambridge, American Association for Artificial Intelligence, AAAI Press/ The MIT Press, 1991, pp. 234-240.
28. D. Mitra, Qualitative reasoning with arbitrary angular directions, in: Proceedings of the AAAI-02 W20 Workshop on Spatial and Temporal Reasoning, Edmonton, Canada, 2002.
29. B. Nebel and H.-J. Bürckert, Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra, Journal of the ACM 42(1) (1995), 43-66.
30. A. Osmani, Introduction to reasoning about cyclic intervals, in: Multiple Approaches to Intelligent Systems, Proc. of IEA/AIE99, I. Imam, Y. Kodratoff, A. El-Dessouki and M. Ali, eds, Number 1611 in Springer LNCS, 1999, pp. 698-706.
31. A.K. Pujari, G. Vijaya Kumari and A. Sattar, INDU: An Interval and Duration Network, in: Australian Joint Conference on Artificial Intelligence, 1999, pp. 291-303.
32. A.K. Pujari and A. Sattar, A new framework for reasoning about points, intervals and durations, in: Proceedings of the 16th International Joint Conference on Artificial Intelligence (UCAI'99), D. Thomas, ed., Morgan Kaufmann, 1999, pp. 1259-1267.
33. D.A. Randell, Z. Cui and A.G. Cohn, A spatial logic based on regions and connection, in: Proceedings of the 3rd International Conference on Principles of Knowledge Representation and Reasoning (KR'92), B. Nebel and C. Rich, eds, Morgan Kaufmann, 1992, pp. 165-176.
34. J. Renz, A spatial odyssey of the interval algebra: 1. Directed intervals, in: IJCAI, 2001, pp. 51-56.
35. A. Tarski, On the calculus of relations, Journal of Symbolic Logic 6(3) (1941), 73-89.
36. P. van Beek, Reasoning about qualitative temporal information, in: Proceedings of the Eighth National Conference on Artificial Intelligence (AAAI'90), 1990, pp. 728-734.
37. P. van Beek, Reasoning about qualitative temporal information, Artificial Intelligence 58(1-3) (1992), 297-326.
38. G. Vijaya Kumari, INDU: Interval-Duration Network. A unified framework for reasoning with time intervals and their duration, PhD thesis, University of Hyderabad, India, 2002.
39. M. Vilain and H. Kautz, Constraint propagation algorithms for temporal reasoning, in: Proceedings of the Fifth National Conference on Artificial Intelligence (AAAI'86), T. Kehler and S. Rosenschein, eds, American Association for Artificial Intelligence, Morgan Kaufmann, 1986, pp. 377-382.