On point-duration networks for temporal reasoning

We present here a point-duration network formalism which extends the point algebra model to include additional variables that represent durations between points of time. Thereafter the new qualitative model is enlarged for allowing unary metric constraints on points and durations, subsuming in this way several point-based approaches to temporal reasoning. We deal with some reasoning tasks within the new models and we show that the main problem, deciding consistency, is NP-complete. However, tractable special cases are identified and we show efficient algorithms for checking consistency, finding a solution and obtaining the minimal network.

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

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

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

[4]  Henry Kautz,et al.  A model of naive temporal reasoning , 1985 .

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

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

[7]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[8]  Robert C. Moore,et al.  Formal Theories of the Commonsense World , 1985 .

[9]  Edward P. K. Tsang,et al.  Foundations of constraint satisfaction , 1993, Computation in cognitive science.

[10]  Silvana Badaloni,et al.  Hybrid temporal reasoning for planning and scheduling , 1996, Proceedings Third International Workshop on Temporal Representation and Reasoning (TIME '96).

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

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

[13]  Rina Dechter,et al.  Tree Clustering for Constraint Networks , 1989, Artif. Intell..

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

[15]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

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

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

[18]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

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

[20]  Manolis Koubarakis,et al.  From Local to Global Consistency in Temporal Constraint Networks , 1995, Theor. Comput. Sci..

[21]  Eddie Schwalb,et al.  Temporal Constraints: A Survey , 1998, Constraints.

[22]  Peter van Beek,et al.  A Theoretical Evaluation of Selected Backtracking Algorithms , 1995, IJCAI.

[23]  Rina Dechter,et al.  From Local to Global Consistency , 1990, Artif. Intell..

[24]  Rina Dechter,et al.  Experimental Evaluation of Preprocessing Algorithms for Constraint Satisfaction Problems , 1994, Artif. Intell..

[25]  Drew McDermott,et al.  Temporal Data Base Management , 1987, Artif. Intell..

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

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

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

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

[30]  Peter B. Ladkin,et al.  On binary constraint problems , 1994, JACM.

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

[32]  Lina Khatib,et al.  Representation and Reasoning with Multi-Point Events , 2000, Constraints.

[33]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[34]  Peter van Beek,et al.  Exact and approximate reasoning about temporal relations 1 , 1990, Comput. Intell..

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