Handling contingency in temporal constraint networks: from consistency to controllabilities

Temporal Constraint Networks (TCN) allow one to express minimal and maximal durations between time-points. Although being used in many research areas, this model disregards the contingent nature of some constraints, whose effective duration cannot be decided by the system but is provided by the external world. We propose an extension of TCN based on the definition of the Simple Temporal Problem under Uncertainty (STPU) in which the classical network consistency property must be redefined in terms of controllability: intuitively, we would like to say that a network is controllable iff it is consistent in any situation (i.e. any assignment of the whole set of contingent intervals) that may arise in the external world. Three levels of controllability must be distinguished, namely the Strong, the Weak and the Dynamic ones. This paper provides a full characterization of those properties and their usefulness in practice, and proposes algorithms for checking them. Complexity issues and tractable equivalence clas...

[1]  Brian Drabble,et al.  Associating AI Planner Entities with an Underlying Time Point Network , 1991, EWSP.

[2]  Thom W. Frühwirth,et al.  Contraint Logic Programming - An Informal Introduction , 1992, Logic Programming Summer School.

[3]  Peter Jonsson,et al.  Eight Maximal Tractable Subclasses of Allen's Algebra with Metric Time , 1997, J. Artif. Intell. Res..

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

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

[6]  Nicolas Beldiceanu,et al.  Constraint Logic Programming , 1997 .

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

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

[9]  Christian Bessiere,et al.  Global Consistency in Interval Algebra Networks: Tractable Subclasses , 1996, ECAI.

[10]  Barbara Pernici,et al.  LaTeR: A General Purpose Manager of Temporal Information , 1994, ISMIS.

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

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

[13]  Robert Schrag,et al.  Managing Disjunction for Practical Temporal Reasoning , 1992, KR.

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

[15]  Éric Rutten,et al.  Temporal Planner = Nonlinear Planner + Time Map Manager , 1993, AI Commun..

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

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

[18]  Jesfis Peral,et al.  Heuristics -- intelligent search strategies for computer problem solving , 1984 .

[19]  Pascal Van Hentenryck.  Constraint Solving for Combinatorial Search Problems: A Tutorial , 1995, CP.

[20]  Amedeo Cesta,et al.  Managing Dynamic Temporal Constraint Networks , 1994, AIPS.

[21]  Vipin Kumar,et al.  Algorithms for Constraint-Satisfaction Problems: A Survey , 1992, AI Mag..

[22]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[23]  Alan K. Mackworth.  The Logic of Constraint Satisfaction , 1991, Artif. Intell..

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

[25]  Peter van Beek,et al.  Temporal query processing with indefinite information , 1991, Artif. Intell. Medicine.

[26]  Thomas Schiex,et al.  Mixed Constraint Satisfaction: A Framework for Decision Problems under Incomplete Knowledge , 1996, AAAI/IAAI, Vol. 1.

[27]  Didier Dubois,et al.  The Use of Fuzzy Constraints in Job-Shop Scheduling. , 1994 .

[28]  Henry Kautz,et al.  Constraint propagation algorithms: A revised report , 1990 .

[29]  Muriel Jourdan,et al.  Using Temporal Constraints Networks to manage Temporal Scenario of Multimedia Documents , 1998 .

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

[31]  Malik Ghallab,et al.  Managing Efficiently Temporal Relations Through Indexed Spanning Trees , 1989, IJCAI.

[32]  Malik Ghallab,et al.  Situation Recognition: Representation and Algorithms , 1993, IJCAI.

[33]  Jürgen Dorn,et al.  Hybrid Temporal Reasoning , 1994, ECAI.

[34]  Nabil Layaida,et al.  Time representation and management in MADEUS: an authoring environment for multimedia documents , 1997, Electronic Imaging.

[35]  Judea Pearl,et al.  Heuristics : intelligent search strategies for computer problem solving , 1984 .

[36]  John W. L. Ogilvie,et al.  Heuristics: Intelligent Search Strategies for Com- Puter Problem , 2001 .

[37]  Moshe Ben-Horim,et al.  A linear programming approach , 1977 .

[38]  Malik Ghallab,et al.  Dealing with Uncertain Durations In Temporal Constraint Networks dedicated to Planning , 1996, ECAI.