Querying Temporal Constraint Networks: A Unifying Approach

We develop the scheme of indefinite constraint databases using first-order logic as our representation language. When this scheme is instantiated with temporal constraints, the resulting formalism is more expressive than standard temporal constraint networks. The extra representational power allows us to express temporal knowledge and queries that have been impossible to express before. To make our claim more persuasive, we survey previous works on querying temporal constraint networks and show that they can be viewed as an instance of the scheme of indefinite constraint databases.

[1]  Lenhart K. Schubert,et al.  Efficient Algorithms for Qualitative Reasoning about Time , 1995, Artif. Intell..

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

[3]  James F. Allen,et al.  Performance of temporal reasoning systems , 1993, SGAR.

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

[5]  Lenhart K. Schubert,et al.  On Point-Based Temporal Disjointness , 1994, Artif. Intell..

[6]  Gabriel M. Kuper,et al.  Constraint query languages (preliminary report) , 1990, PODS '90.

[7]  Eduardo D. Sontag,et al.  Real Addition and the Polynomial Hierarchy , 1985, Inf. Process. Lett..

[8]  Barbara Pernici,et al.  Later: Managing Temporal Information Efficiently , 1997, IEEE Expert.

[9]  Manolis Koubarakis,et al.  Complexity Results for First-Order Theories of Temporal Constraints , 1994, KR.

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

[11]  Albert R. Meyer,et al.  On time-space classes and their relation to the theory of real addition , 1978, STOC '78.

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

[13]  Richard Arthur,et al.  Tachyon: A constraint-based temporal reasoning model and its implementation , 1993, SGAR.

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

[15]  Martin Fürer,et al.  The Complexity of Presburger Arithmetic with Bounded Quantifier Alternation Depth , 1982, Theor. Comput. Sci..

[16]  Spiros Skiadopoulos,et al.  Querying Temporal Constraint Networks in PTIME , 1999, AAAI/IAAI.

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

[18]  Gösta Grahne,et al.  The Problem of Incomplete Information in Relational Databases , 1991, Lecture Notes in Computer Science.

[19]  Manolis Koubarakis,et al.  Database models for infinite and indefinite temporal information , 1994, Inf. Syst..

[20]  Manolis Koubarakis,et al.  Representation and querying in temporal databases: the power of temporal constraints , 1993, Proceedings of IEEE 9th International Conference on Data Engineering.

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

[22]  Lenhart K. Schubert,et al.  Temporal reasoning in Timegraph I–II , 1993, SGAR.

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

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

[25]  Raymond Reiter,et al.  Towards a Logical Reconstruction of Relational Database Theory , 1982, On Conceptual Modelling.

[26]  Tomasz Imielinski,et al.  Incomplete Information in Relational Databases , 1984, JACM.

[27]  Jeanne Ferrante,et al.  A Decision Procedure for the First Order Theory of Real Addition with Order , 1975, SIAM J. Comput..

[28]  Manolis Koubarakis,et al.  Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning , 2001, Theor. Comput. Sci..

[29]  Luca Console,et al.  Efficient Processing of Queries and Assertions about Qualitative and Quantitative Temporal Constraints , 1999 .

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

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

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

[33]  Matthias Jarke,et al.  Telos: representing knowledge about information systems , 1990, TOIS.

[34]  Peter B. Ladkin,et al.  Satisfying First-Order Constraints About Time Intervals , 1988, AAAI.

[35]  Luca Console,et al.  On the Computational Complexity of Querying Bounds on Differences Constraints , 1995, Artif. Intell..

[36]  Mark S. Boddy Temporal reasoning for planning and scheduling , 1993, SGAR.

[37]  Thomas Dean,et al.  Using temporal hierarchies to efficiently maintain large temporal databases , 1989, JACM.

[38]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[39]  Barbara Pernici,et al.  Qualitative and Quantitative Temporal Constraints and Relational Databases: Theory, Architecture, and Applications , 1999, IEEE Trans. Knowl. Data Eng..

[40]  M. Fischer,et al.  SUPER-EXPONENTIAL COMPLEXITY OF PRESBURGER ARITHMETIC , 1974 .

[41]  Spiros Skiadopoulos,et al.  Querying temporal and spatial constraint networks in PTIME , 2000, Artif. Intell..

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

[43]  Spiros Skiadopoulos,et al.  Tractable Query Answering in Indefinite Constraint Databases: Basic Results and Applications to Querying Spatiotemporal Information , 1999, Spatio-Temporal Database Management.

[44]  J. Ferrante,et al.  The computational complexity of logical theories , 1979 .

[45]  Moshe Y. Vardi Conference on Theoretical Aspects of Reasoning about Knowledge , 1990 .

[46]  Raymond Reiter,et al.  On Integrity Constraints , 1988, TARK.

[47]  Witold Lipski,et al.  On semantic issues connected with incomplete information databases , 1979, ACM Trans. Database Syst..

[48]  Donald W. Loveland,et al.  Presburger arithmetic with bounded quantifier alternation , 1978, STOC.

[49]  Alfonso Gerevini,et al.  Reasoning with Inequations in Temporal Constraint Networks , 1995, IJCAI 1995.

[50]  Larry J. Stockmeyer,et al.  The Polynomial-Time Hierarchy , 1976, Theor. Comput. Sci..

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

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

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

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

[55]  Gabriel M. Kuper,et al.  Constraint Query Languages , 1995, J. Comput. Syst. Sci..

[56]  James R. Geiser,et al.  An Efficient Decision Procedure for the Theory of Rational Order , 1977, Theor. Comput. Sci..

[57]  Manolis Koubarakis,et al.  The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases , 1997, Theor. Comput. Sci..

[58]  Hector J. Levesque,et al.  Foundations of a Functional Approach to Knowledge Representation , 1984, Artif. Intell..

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

[60]  Barbara Pernici,et al.  Extending Temporal Relational Databases to Deal with Imprecise and Qualitative Temporal Information , 1995, Temporal Databases.

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

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