Results 1  10
of
23
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 ..."
Abstract

Cited by 117 (2 self)
 Add to MetaCart
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...
Reasoning About Temporal Relations: The Tractable Subalgebras Of Allen's Interval Algebra
 Journal of the ACM
, 2001
"... Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra c ..."
Abstract

Cited by 42 (2 self)
 Add to MetaCart
(Show Context)
Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalgebras is NPcomplete. We obtain this result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using an algebraic technique for identifying maximal subalgebras with a given property.
A Unifying Approach to Temporal Constraint Reasoning
 Artificial Intelligence
"... We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs ..."
Abstract

Cited by 37 (10 self)
 Add to MetaCart
(Show Context)
We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs, which have a polynomialtime satisfiability problem. We prove that most approaches to tractable temporal constraint reasoning can be encoded as Horn DLRs, including the ORDHorn algebra by Nebel and Burckert and the simple temporal constraints by Dechter et al. Thus, DLRs is a suitable unifying formalism for reasoning about temporal constraints. 1 Introduction Reasoning about temporal knowledge abounds in artificial intelligence applications and other areas, such as planning [4], natural language understanding [25] and molecular biology [6, 13]. In most applications, knowledge of temporal constraints is expressed in terms of collections of relations between time intervals or time po...
The complexity of temporal constraint satisfaction problems
 J. ACM
"... A temporal constraint language is a set of relations that has a firstorder definition in (Q; <), the dense linear order of the rational numbers. We present a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint langu ..."
Abstract

Cited by 34 (23 self)
 Add to MetaCart
(Show Context)
A temporal constraint language is a set of relations that has a firstorder definition in (Q; <), the dense linear order of the rational numbers. We present a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint language is contained in one out of nine temporal constraint languages, then the CSP can be solved in polynomial time; otherwise, the CSP is NPcomplete. Our proof combines modeltheoretic concepts with techniques from universal algebra, and also applies the socalled product Ramsey theorem, which we believe will useful in similar contexts of
Temporal Representation and Reasoning in Artificial Intelligence: Issues and Approaches
, 2002
"... this paper, we survey a wide range of research in temporal representation and reasoning, without committing ourselves to the point of view of any speci c application ..."
Abstract

Cited by 26 (1 self)
 Add to MetaCart
this paper, we survey a wide range of research in temporal representation and reasoning, without committing ourselves to the point of view of any speci c application
Towards a Comprehensive Treatment of Temporal Constraints
 International Journal of Intelligent Systems
, 2002
"... In this paper, we focus on an application and extension of Artificial Intelligence temporal reasoning techniques in order to represent and reason with temporal constraints in clinical guidelines. Particular attention is dedicated to the treatment of repeated (periodic) events, which play a major rol ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
In this paper, we focus on an application and extension of Artificial Intelligence temporal reasoning techniques in order to represent and reason with temporal constraints in clinical guidelines. Particular attention is dedicated to the treatment of repeated (periodic) events, which play a major role in clinical therapies. We also discuss some limitations of our current approach, highlighting possible future enhancements. The work in this paper has been developed in the GLARE project, meant to realize a prototype of a domainindependent manager of clinical guidelines. The GLARE system has been built in cooperation with Azienda Ospedaliera S. Giovanni Battista of Turin, and has been successfully tested on different clinical domains.
The Complexity of Reasoning about Spatial Congruence
 Journal of Artificial Intelligence Research
, 1999
"... In the recent literature of Artificial Intelligence, an intensive research effort has been spent, for various algebras of qualitative relations used in the representation of temporal and spatial knowledge, on the problem of classifying the computational complexity of reasoning problems for subset ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
(Show Context)
In the recent literature of Artificial Intelligence, an intensive research effort has been spent, for various algebras of qualitative relations used in the representation of temporal and spatial knowledge, on the problem of classifying the computational complexity of reasoning problems for subsets of algebras. The main purpose of these researches is to describe a restricted set of maximal tractable subalgebras, ideally in an exhaustive fashion with respect to the hosting algebras. In this paper we introduce a novel algebra for reasoning about Spatial Congruence, show that the satisfiability problem in the spatial algebra MC4 is NPcomplete, and present a complete classification of tractability in the algebra, based on the individuation of three maximal tractable subclasses, one containing the basic relations. The three algebras are formed by 14, 10 and 9 relations out of 16 which form the full algebra. 1. Introduction Qualitative spatial reasoning has received an increasin...
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 . . . . . . . . . ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
(Show Context)
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 . .
A Complete Classification of Tractability in Allen's Algebra Relative to Subsets of Basic Relations
 Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI '97
, 1998
"... We characterise the set of subalgebras of Allen's algebra which have a tractable satisfiability problem, and in addition contain certain basic relations. The conclusion is that no tractable subalgebra that is not known in the literature can contain more than the three basic relations (j), (b) a ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
We characterise the set of subalgebras of Allen's algebra which have a tractable satisfiability problem, and in addition contain certain basic relations. The conclusion is that no tractable subalgebra that is not known in the literature can contain more than the three basic relations (j), (b) and (b ), where b 2 fd; o; s; fg. This means that concerning algebras for specifying complete knowledge about temporal information, there is no hope of finding yet unknown classes with much expressivity. We also classify completely some cases where we cannot even express complete information (but close to complete), showing that there are exactly two maximal tractable algebras containing the relation (OE ), exactly two containing the relation (OE m m ), and exactly three containing the relation (OE m). The algebras containing (OE ) can express the notion of sequentiality; thus we have a complete characterisation of tractable inference using that notion. 1 Introduction This paper improves o...
A FAST ALGORITHM AND DATALOG INEXPRESSIBILITY FOR TEMPORAL REASONING
, 2009
"... We introduce a new tractable temporal constraint language, which strictly contains the OrdHorn language of Bürkert and Nebel and the class of AND/OR precedence constraints. The algorithm we present for this language decides whether a given set of constraints is consistent in time that is quadratic ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
We introduce a new tractable temporal constraint language, which strictly contains the OrdHorn language of Bürkert and Nebel and the class of AND/OR precedence constraints. The algorithm we present for this language decides whether a given set of constraints is consistent in time that is quadratic in the input size. We also prove that (unlike OrdHorn) the constraint satisfaction problem of this language cannot be solved by Datalog or by establishing local consistency.