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A Study in the Computational Complexity of Temporal Reasoning
Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
2002 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Reasoning about temporal and spatial information is a common task in computer science, especially in the field of artificial intelligence. The topic of this thesis is the study of such reasoning from a computational perspective. We study a number of different qualitative point based formalisms for temporal reasoning and provide a complete classification of computational tractability for different time models. We also develop more general methods which can be used for proving tractability and intractability of other relational algebras. Even though most of the thesis pertains to qualitative reasoning the methods employed here can also be used for quantitative reasoning. For instance, we introduce a tractable and useful extension to the quantitative point based formalism STP. This extension gives the algebra an expressibility which subsumes the largest tractable fragment of the augmented interval algebra and has a faster and simpler algorithm for deciding consistency.

The use of disjunctions in temporal formalisms is of great interest not only since disjunctions are a key element in different logics but also since the expressibility can be greatly enhanced in this way. If we allow arbitrary disjunctions, the problems under consideration typically become intractable and methods to identify tractable fragments of disjunctive formalisms are therefore useful. One such method is to use the independence property. We present an automatic method for deciding this property for many relational algebras. Furthermore, we show how this concept can not only be used for deciding tractability of sets of relations but also to demonstrate intractability of relations not having this property. Together with other methods for making total classifications of tractability this goes a long way towards easing the task of classifying and understanding relational algebras.

The tractable fragments of relational algebras are sometimes not expressive enough to model real-world problems and a backtracking solver is needed. For these cases we identify another property among relations which can be used to aid general backtracking based solvers to finnd solutions faster.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2002. , 21 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 779
Keyword [en]
temporal and spatial information, artificiell intelligens, algebra, tractable fragments, temporal formalisms, formalism STP
National Category
Computer Science
Identifiers
URN: urn:nbn:se:liu:diva-4984ISBN: 91-7373-440-3 (print)OAI: oai:DiVA.org:liu-4984DiVA: diva2:20874
Public defence
2002-12-10, Estraden, Hus E, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Supervisors
Note
Article I is a revised and extended version of the following three papers: 1. Mathias Broxvall and Peter Jonsson. Towards a Complete Classification of Tractability in Point Algebras for Nonlinear Time. In Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming (CP-99), pp. 129-143, Alexandria, VA, USA, Oct, 1999. 2. Mathias Broxvall and Peter Jonsson. Disjunctive Temporal Reasoning in Partially Ordered Time Structures. In Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI-2000), pp. 464-469, Austin, Texas, USA, Aug, 2000. 3. Mathias Broxvall. The Point Algebra for Branching Time Revisited. In Proceedings of the Joint German/Austrian Conference on Artificial Intelligence (KI-2001), pp. 106-121, Vienna, Austria, Sep, 2001. --- Article II is a revised and extended version of the following paper: Mathias Broxvall, Peter Jonsson and Jochen Renz: Refinements and Independence: A Simple Method for Identifying Tractable Disjunctive Constraints. In Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming (CP-2000), pp. 114-127, Singapore, Sep, 2000.Available from: 2003-01-18 Created: 2003-01-18 Last updated: 2012-01-25Bibliographically approved
List of papers
1. Point Algebras for Temporal Reasoning: Algorithms and Complexity
Open this publication in new window or tab >>Point Algebras for Temporal Reasoning: Algorithms and Complexity
2003 (English)In: Artificial Intelligence, ISSN 0004-3702, Vol. 149, no 2, 179-220 p.Article in journal (Refereed) Published
Abstract [en]

We investigate the computational complexity of temporal reasoning in different time models such as totally-ordered, partially-ordered and branching time. Our main result concerns the satisfiability problem for point algebras and point algebras extended with disjunctions—for these problems, we identify all tractable subclasses. We also provide a number of additional results; for instance, we present a new time model suitable for reasoning about systems with a bounded number of unsynchronized clocks, we investigate connections with spatial reasoning and we present improved algorithms for deciding satisfiability of the tractable point algebras.

Keyword
Temporal reasoning, Point algebras, Constraint satisfaction
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-13500 (URN)10.1016/S0004-3702(03)00075-4 (DOI)
Available from: 2003-01-18 Created: 2003-01-18 Last updated: 2017-02-23
2. Disjunctions, Independence, Refinements
Open this publication in new window or tab >>Disjunctions, Independence, Refinements
2002 (English)In: Artificial Intelligence, ISSN 0004-3702, Vol. 140, no 1-2, 153-173 p.Article in journal (Refereed) Published
Abstract [en]

An important question in constraint satisfaction is how to restrict the problem to ensure tractability (since the general problem is NP-hard). The use of disjunctions has proven to be a useful method for constructing tractable constraint classes from existing classes; the well-known ‘max-closed’ and ‘ORD-Horn’ constraints are examples of tractable classes that can be constructed this way. Three sufficient conditions (the guaranteed satisfaction property, 1-independence and 2-independence) that each ensure the tractability of constraints combined by disjunctions have been proposed in the literature. We show that these conditions are both necessary and sufficient for tractability in three different natural classes of disjunctive constraints. This suggests that deciding this kind of property is a very important task when dealing with disjunctive constraints. We provide a simple, automatic method for checking the 1-independence property—this method is applicable whenever the consistency of the constraints under consideration can be decided by path-consistency. Our method builds on a connection between independence and refinements (which is a way of reducing one constraint satisfaction problem to another.)

Keyword
Constraint satisfaction, Disjunctive constraints, Tractability
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-13501 (URN)10.1016/S0004-3702(02)00224-2 (DOI)
Available from: 2003-01-18 Created: 2003-01-18 Last updated: 2017-02-23
3. Constraint Satisfaction on In nite Domains: Composing Domains and Decomposing Constraints
Open this publication in new window or tab >>Constraint Satisfaction on In nite Domains: Composing Domains and Decomposing Constraints
2002 (English)In: Proceedings of the Eighth International Conference on Principles of Knowledge Representation and Reasoning (KR-2002), Toulouse, France, 2002, 509-520 p.Conference paper, Published paper (Refereed)
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-13502 (URN)
Available from: 2003-01-18 Created: 2003-01-18 Last updated: 2009-02-09
4. A Method for Metric Temporal Reasoning
Open this publication in new window or tab >>A Method for Metric Temporal Reasoning
2002 (English)In: Proceedings of the Eighteenth National Conference on Arti cial Intelligence (AAAI-02), Edmonton, Canada, 2002, 513-518 p.Conference paper, Published paper (Refereed)
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-13503 (URN)
Available from: 2003-01-18 Created: 2003-01-18

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