The Consistent Labeling Problem in Temporal Reasoning

Temporal reasoning can be performed by maintaining a temporal relation network, a complete network in which the nodes are time intervals and each arc is the temporal relation between the two intervals which it connects. In this paper, we point out that the task of detecting inconsistency of the network and mapping the intervals onto a date line is a Consistent Labeling Problem (CLP). The problem is formalized and analyzed. The significance of identifying and analyzing the CLP in temporal reasoning is that CLPs have certain features which allow us to apply certain techniques to our problem. We also point out that the CLP exists when we reason with disjunctive temporal relations. Therefore, the intractability of the constraint propagation mechanism in temporal reasoning is inherent in the problem, not caused by the representation that we choose for time, as [Vilain & Kautz 86] claims.

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

[2]  Thomas Dean,et al.  Temporal imagery: an approach to reasoning about time for planning and problem solving , 1986 .

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

[4]  Edward P. K. Tsang.  Plan Generation in a Temporal Frame , 1986, ECAI.

[5]  Bernard Nudel,et al.  Consistent-Labeling Problems and Their Algorithms: Expected-Complexities and Theory-Based Heuristics , 1983, Artif. Intell..

[6]  Robert M. Haralick,et al.  Increasing Tree Search Efficiency for Constraint Satisfaction Problems , 1979, Artif. Intell..

[7]  Eugene C. Freuder.  A Sufficient Condition for Backtrack-Free Search , 1982, JACM.

[8]  Austin Tate,et al.  Generating Project Networks , 1977, IJCAI.

[9]  James F. Allen,et al.  Planning Using a Temporal World Model , 1983, IJCAI.

[10]  Steven A. Vere,et al.  Planning in Time: Windows and Durations for Activities and Goals , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  David P. Miller,et al.  Deadlines, Travel Time, and Robot Problem Solving , 1985, IJCAI.

[12]  Bertram C. Bruce.  A Model for Temporal References and Its Application in a Question Answering Program , 1972, Artif. Intell..

[13]  Kenneth M. Kahn,et al.  Mechanizing Temporal Knowledge , 1977, Artif. Intell..

[14]  Edward Tsang,et al.  TLP—a temporal planner , 1987 .

[15]  Stephen F. Smith,et al.  ISIS—a knowledge‐based system for factory scheduling , 1984 .

[16]  Eugene C. Freuder,et al.  The Complexity of Some Polynomial Network Consistency Algorithms for Constraint Satisfaction Problems , 1985, Artif. Intell..

[17]  Eugene C. Freuder.  Synthesizing constraint expressions , 1978, CACM.