Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Constraint propagation algorithms for temporal reasoning: a revised report
Readings in qualitative reasoning about physical systems
Artificial Intelligence - Special issue on knowledge representation
A metric time-point and duration-based temporal model
ACM SIGART Bulletin
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
Combining qualitative and quantitative constraints in temporal reasoning
Artificial Intelligence
A unifying approach to temporal constraint reasoning
Artificial Intelligence
Temporal reasoning with qualitative and quantitative information about points and durations
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Temporal Constraints: A Survey
Constraints
’’Corner‘‘ Relations in Allen‘s algebra
Constraints
Qualitative temporal reasoning with points and durations
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
On finding a solution in temporal constraint satisfaction problems
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
INDU: An Interval and Duration Network
AI '99 Proceedings of the 12th Australian Joint Conference on Artificial Intelligence: Advanced Topics in Artificial Intelligence
Complexity classification in qualitative temporal constraint reasoning
Artificial Intelligence
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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.