From binary temporal relations to non-binary ones and back

Abstract In this paper a new approach towards temporal reasoning is presented that scales up from the temporal relations commonly used in Allen's qualitative interval calculus and in quantitative temporal constraint satisfaction problems to include interval relations with distances, temporal rules and other non-binary relations into the reasoning scheme. For this purpose, we generalize well-known methods for constraint propagation, determination of consistency and computation of the minimal network from simpler schemes that only allow for binary relations. Thereby, we find that levels of granularity play a major role for applying these techniques in our more expressive framework. Indeed, the technical preliminaries we provide are especially apt to investigate the switching between different granularities of representation, hence illucitating and exploiting the tradeoff between expressiveness and efficiency of temporal reasoning schemes on the one side and between expressiveness and understandability on the other side.

[1]  Steffen Staab,et al.  "Tall", "Good", "High" - Compared to What? , 1997, IJCAI.

[2]  Christer Bäckström,et al.  A Linear-Programming Approach to Temporal Reasoning , 1996, AAAI/IAAI, Vol. 2.

[3]  Lina Khatib,et al.  Path Consistency in a Network of Non-Convex Intervals , 1993, IJCAI.

[4]  Steffen Staab,et al.  On Non-Binary Temporal Relations , 1998, ECAI.

[5]  Peter F. Patel-Schneider,et al.  Usability Issues in Knowledge Representation Systems , 1998, AAAI/IAAI.

[6]  Mitsunori Matsushita,et al.  A visualization method of time expressions using starting/ending point plane , 1998, Proceedings. Fifth International Workshop on Temporal Representation and Reasoning (Cat. No.98EX157).

[7]  Fausto Giunchiglia,et al.  A Theory of Abstraction , 1992, Artif. Intell..

[8]  Shlomo Zilberstein,et al.  Composing Real-Time Systems , 1991, IJCAI.

[9]  Manolis Koubarakis,et al.  Backtracking algorithms for disjunctions of temporal constraints , 1998, Artif. Intell..

[10]  Thomas Dean,et al.  Using temporal hierarchies to efficiently maintain large temporal databases , 1989, JACM.

[11]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[12]  Christian Bessiere,et al.  Arc Consistency for General Constraint Networks: Preliminary Results , 1997, IJCAI.

[13]  Michael Stonebraker,et al.  Implementing calendars and temporal rules in next generation databases , 1994, Proceedings of 1994 IEEE 10th International Conference on Data Engineering.

[14]  Eliseo Clementini,et al.  Qualitative Representation of Positional Information , 1997, Artif. Intell..

[15]  Henry A. Kautz,et al.  Constraint propagation algorithms for temporal reasoning: a revised report , 1989 .

[16]  Alexander Nakhimovsky,et al.  Aspect, Aspectual Class, and the Temporal Structure of Narrative , 1988, Comput. Linguistics.

[17]  Boi Faltings,et al.  Local Consistency for Ternary Numeric Constraints , 1997, IJCAI.

[18]  Itay Meiri,et al.  Combining Qualitative and Quantitative Constraints in Temporal Reasoning , 1991, Artif. Intell..

[19]  Rina Dechter,et al.  Temporal Constraint Networks , 1989, Artif. Intell..

[20]  Christer Bäckström,et al.  A Unifying Approach to Temporal Constraint Reasoning , 1998, Artif. Intell..

[21]  Christian Freksa,et al.  Temporal Reasoning Based on Semi-Intervals , 1992, Artif. Intell..

[22]  Manolis Koubarakis,et al.  Tractable Disjunctions of Linear Constraints , 1996, CP.

[23]  Abdul Sattar,et al.  A New Framework for Reasoning about Points, Intervals and Durations , 1999, IJCAI.

[24]  Roque Marín,et al.  Qualitative Temporal Reasoning with Points and Durations , 1997, IJCAI.

[25]  Rina Dechter,et al.  Processing Disjunctions in Temporal Constraint Networks , 1997, Artif. Intell..

[26]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[27]  Henry A. Kautz,et al.  Integrating Metric and Qualitative Temporal Reasoning , 1991, AAAI.

[28]  Christer Bäckström,et al.  Computational Complexity of Relating Time Points with Intervals , 1999, Artif. Intell..

[29]  Martin Romacker,et al.  How knowledge drives understandingmatching medical ontologies with the needs of medical language processing , 1999, Artif. Intell. Medicine.

[30]  Yuval Shahar,et al.  Model-based visualization of temporal abstractions , 1998, Proceedings. Fifth International Workshop on Temporal Representation and Reasoning (Cat. No.98EX157).

[31]  Steffen Staab,et al.  Scalable Temporal Reasoning , 1999, IJCAI.

[32]  Lenhart K. Schubert,et al.  On Point-Based Temporal Disjointness , 1994, Artif. Intell..

[33]  Abdul Sattar,et al.  Temporal Reasoning with Qualitative and Quantitative Information about Points and Durations , 1998, AAAI/IAAI.

[34]  Sushil Jajodia,et al.  Satisfiability of Quantitative Temporal Constraints with Multiple Granularities , 1997, CP.

[35]  Abdul Sattar,et al.  INDU: An Interval and Duration Network , 1999, Australian Joint Conference on Artificial Intelligence.

[36]  Mark S. Fox,et al.  Representation of Activity Knowledge for Project Management , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[37]  Boi Faltings,et al.  Solving Non-binary Convez CSPs in Continous Domains , 1996, CP.