A New Framework for Reasoning about Points, Intervals and Durations

We present a new framework for reasoning about points, intervals and durations--Point Interval Duration Network (PIDN). The PIDN adequately handles both qualitative and quantitaive temporal information. We show that Interval Algebra, Point Algebra, TCSP, PDN and APDN become special cases of PIDN. The underlying algebraic structure of PIDN is closed under composition and intersection. Determinig consistency of P I DN is NP-Ilard. However, we identify some tractable subclasses of PIDN. We show that path consistency is not sufficient to ensure global consistency of the tractable subclasses of PIDN. We identify a subclass for which enforcing 4-consistency suffices to ensure the global consistency, and prove that this subclass is maximal for qualitative constraints. Our approach is based on the geometric interpretation of the domains of temporal objects. Interestingly, the classical Helly's Theorem of 1923 is used to prove the complexity for the tractable subclass.

[1]  Peter van Beek,et al.  Reasoning About Qualitative Temporal Information , 1990, Artif. Intell..

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

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

[4]  Arun K. Pujari,et al.  Neighbourhood Logic and Interval Algebra , 1997 .

[5]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[6]  Federico Barber,et al.  A metric time-point and duration-based temporal model , 1993, SGAR.

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

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

[9]  Henry A. Kautz,et al.  Constraint Propagation Algorithms for Temporal Reasoning , 1986, AAAI.

[10]  Alfonso Gerevini,et al.  On Finding a Solution in Temporal Constraint Satisfaction Problems , 1997, IJCAI.

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

[12]  Bernhard Nebel,et al.  Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra , 1994, JACM.

[13]  Manolis Koubarakis,et al.  Dense Time and Temporal Constraints with != , 1992, KR.

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

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

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