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Backtracking Algorithms for Disjunctions of Temporal Constraints
 Artificial Intelligence
, 1998
"... We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. W ..."
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We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. We have implemented four progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints. We have partially ordered those algorithms according to the number of visited search nodes and the number of performed consistency checks. Finally, we have carried out a series of experimental results on the location of the hard region. The results show that hard problems occur at a critical value of the ratio of disjunctions to variables. This value is between 6 and 7. Introduction Reasoning with temporal constraints has been a hot research topic for the last fifteen years. The importance of this problem has been demonstrated in many areas of artifici...
Handling contingency in temporal constraint networks: from consistency to controllabilities
 Journal of Experimental and Theoretical Artificial Intelligence
, 1999
"... This paper has been accepted for publication by the Journal of Experimental and Theoretical Arti cial Intelligence (JETAI) published byTaylor & Francis Ltd. Anyway, it should be pointed out that this version slightly di ers from the nal published one. Copyright 1999 T&F Ltd. Personal use of ..."
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Cited by 74 (4 self)
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This paper has been accepted for publication by the Journal of Experimental and Theoretical Arti cial Intelligence (JETAI) published byTaylor & Francis Ltd. Anyway, it should be pointed out that this version slightly di ers from the nal published one. Copyright 1999 T&F Ltd. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from Taylor & Francis Ltd
CTP: A New ConstraintBased Formalism for Conditional, Temporal Planning
, 2003
"... Temporal constraints pose a challenge for conditional planning, because it is necessary for a conditional planner to determine whether a candidate plan will satisfy the specified temporal constraints. This can be diflCicult, because temporal assignments that satisfy the constraints associated with o ..."
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Cited by 36 (8 self)
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Temporal constraints pose a challenge for conditional planning, because it is necessary for a conditional planner to determine whether a candidate plan will satisfy the specified temporal constraints. This can be diflCicult, because temporal assignments that satisfy the constraints associated with one conditional branch may fail to satisfy the constraints along a different branch. In this paper we adch'ess this challenge by developing the Conditional Temporal Problem (CTP) formalism, an extension of standard temporal constraintsatisfaction processing models used in nonconditional temporal planning. Specifically, we augment temporal CSP frameworks by (1) adding observation nodes, and (2) attaching labels to all nodes to indicate the situation(s) in which each will be executed. Our extended framework allows for the construction of conditional plans that are guaranteed to satisfy complex temporal constraints. Importantly, this can be achieved even while allowing for decisions about the precise timing of actions to be postponed until execution time, thereby adding flexibility and making it possible to dynamically adapt the plan in response to the observations made during execution. We also show that, even for plans without explicit quantitative temporal constraints, our approach fixes a problem in the earlier approaches to conditional planning, which resulted in their being incomplete.
Constraint Satisfaction
 In In the MIT Encyclopedia of the Cognitive Sciences (MITECS
, 1991
"... to A, true to B, false to C and false to D, is a satisfying truth value assignment. The structure of a constraintnetwork is depicted by a constraint graph whose nodes represents the variables and anytwo nodes are connected if the corresponding variables participate in the same constraint. In the k ..."
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Cited by 19 (5 self)
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to A, true to B, false to C and false to D, is a satisfying truth value assignment. The structure of a constraintnetwork is depicted by a constraint graph whose nodes represents the variables and anytwo nodes are connected if the corresponding variables participate in the same constraint. In the k colorability formulation, the graph to be colored is the constraint graph. In our SAT example the constraint graph has A connected to D and A; B and C are connected to each other. Constraintnetworks haveproven successful in modeling mundane cognitive tasks such as vision, language comprehension, default reasoning, and abduction, as well as in applications suchasscheduling, design, diagnosis, and temporal and spatial reasoning. In general, constraint satisfaction tasks are computationally intractable #NPhard# #see COMPUTATIONAL COMPLEXITY #. Techniques for pr
Reasoning on Interval and Pointbased Disjunctive Metric Constraints in Temporal Contexts
 Journal of Artificial Intelligence Research
, 2000
"... We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled temporal algebra defineslabeled disjunctive metric pointbased co ..."
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Cited by 17 (1 self)
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We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled temporal algebra defineslabeled disjunctive metric pointbased constraints, where each disjunct in each input disjunctive constraint is univocally associated to a label. Reasoning algorithms manage labeled constraints, associated label lists, and sets of mutually inconsistent disjuncts. These algorithms guarantee consistency and obtain a minimal network. Additionally, constraints can be organized in a hierarchy of alternative temporal contexts. Therefore, we can reason on contextdependent disjunctive metric constraints on intervals and points. Moreover, the model is able to represent nonbinary constraints, such that logical dependencies on disjuncts in constraints can be handled. The computational cost of reasoning algorithms is exponential in ac...
Path Consistency for Triangulated Constraint Graphs
 In Proc. of the 16 �¡ IJCAI
, 1999
"... bliekQilog.fr Among the local consistency techniques used in the resolution of constraint satisfaction problems (CSPs), path consistency (PC) has received a great deal of attention. A constraint graph G is PC if for any valuation of a pair of variables that satisfy the constraint in G between them, ..."
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Cited by 15 (0 self)
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bliekQilog.fr Among the local consistency techniques used in the resolution of constraint satisfaction problems (CSPs), path consistency (PC) has received a great deal of attention. A constraint graph G is PC if for any valuation of a pair of variables that satisfy the constraint in G between them, one can find values for the intermediate variables on any other path in G between those variables so that all the constraints along that path are satisfied. On complete graphs, Montanari showed that PC holds if and only if each path of length two is PC. By convention, it is therefore said that a CSP is PC if the completion of its constraint graph is PC. In this paper, we show that Montanari's theorem extends to triangulated graphs. One can therefore enforce PC on sparse graphs by triangulating instead of completing them. The advantage is that with triangulation much less universal constraints need to be added. We then compare the pruning capacity of the two approaches. We show that when the constraints are convex, the pruning capacity of PC on triangulated graphs and their completion are identical on the common edges. Furthermore, our experiments show that there is little difference for general nonconvex problems. 1
Temporal Reasoning and Constraint Programming  A Survey
 CWI Quarterly
, 1998
"... Contents 1 Introduction 6 1.1 Temporal Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Constraint Programming . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Constraint problems and constraint satisfaction . . . . . . 7 1.2.2 Algorithms to solve constraints . . . . . . . . . ..."
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Cited by 8 (1 self)
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Contents 1 Introduction 6 1.1 Temporal Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Constraint Programming . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Constraint problems and constraint satisfaction . . . . . . 7 1.2.2 Algorithms to solve constraints . . . . . . . . . . . . . . . 9 1.3 Temporal reasoning and Constraint Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.1 Temporal Reasoning with metric information . . . . . . . 14 1.3.2 Qualitative approach based on Allen's interval algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.3 Mixed approaches . . . . . . . . . . . . . . . . . . . . . . 15 2 Temporal Reasoning and Constraint Programming 16 2.1 Temporal Constraints with metric information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 A first order language . . . . . . . . . . . . . . . . . . . . 16 2.1.2 The original Temporal Constraint Problem . .
Reasoning with Disjunctive Fuzzy Temporal Constraint Networks
, 2002
"... The Disjunctive Fuzzy Temporal Constraint Network (DFTCN) model is a framework that allows reasoning with fuzzy qualitative and quantitative complex temporal constraints. However, its general complexity is exponential. ..."
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Cited by 7 (2 self)
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The Disjunctive Fuzzy Temporal Constraint Network (DFTCN) model is a framework that allows reasoning with fuzzy qualitative and quantitative complex temporal constraints. However, its general complexity is exponential.
Satisfiability of Quantitative Temporal Constraints With Multiple Granularities
 IN PROC. CP
, 1997
"... Most work on temporal constraints has ignored the subtleties involved in dealing with multiple time granularities. This paper considers a constraint satisfaction problem (CSP) where binary quantitative constraints in terms of different time granularities can be specified on a set of variables, an ..."
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Cited by 7 (3 self)
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Most work on temporal constraints has ignored the subtleties involved in dealing with multiple time granularities. This paper considers a constraint satisfaction problem (CSP) where binary quantitative constraints in terms of different time granularities can be specified on a set of variables, and unary constraints are allowed to limit the domain of variables. Such a CSP cannot be trivially reduced to one of the known CSP problems. The main result of the paper is a complete algorithm for checking consistency and finding a solution. The complexity of the algorithm is studied in the paper under di#erent assumptions about the granularities involved in the CSP, and a second algorithm is proposed to improve the efficiency of the backtracking process needed to obtain all the solutions of the CSP.
On nonbinary temporal relations
 In Proc. of ECAI98
, 1998
"... I present a new approach towards temporal reasoning that generalizes from the temporal relations commonly used in Allen's qualitative interval calculus and in quantitative temporal constraint satisfaction problems and includes interval relations with distances, temporal rules and other nonbina ..."
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Cited by 7 (2 self)
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I present a new approach towards temporal reasoning that generalizes from the temporal relations commonly used in Allen's qualitative interval calculus and in quantitative temporal constraint satisfaction problems and includes interval relations with distances, temporal rules and other nonbinary relations into the reasoning scheme. Moreover, I investigate how several factors underlying my generalization influence the reasoning process. Appeared in: