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Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen's Interval Algebra
 Journal of the ACM
, 1995
"... We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient ..."
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Cited by 189 (9 self)
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We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient for deciding satisfiability. Further, using an extensive machinegenerated case analysis, we show that the ORDHorn subclass is a maximal tractable subclass of the full algebra (assuming<F NaN> P6=NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations. This work has been supported by the German Ministry for Research and Technology (BMFT) under grant ITW 8901 8 as part of the WIP project and under grant ITW 9201 as part of the TACOS project. 1 1 Introduction Temporal information is often conveyed qualitatively by specifying the relative positions of time intervals such as ". . . point to the figure while explaining the performance of the system . . . "...
Representation and Control in Ixtet, a Temporal Planner
 In AIPS
, 1994
"... This paper presents a temporal planner, called IxTeT. It focuses on the representation and control issues, arguing for a compromise between the expressiveness and the ei~ciency of the search. The representation relies on a pointbased reified logic, associated to mldtivalued domain attributes. Hie ..."
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Cited by 141 (3 self)
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This paper presents a temporal planner, called IxTeT. It focuses on the representation and control issues, arguing for a compromise between the expressiveness and the ei~ciency of the search. The representation relies on a pointbased reified logic, associated to mldtivalued domain attributes. Hieraxchical planning operators ot~er an expressive description, with parallelism, durations, effects and conditions at various moments of the action. Time in the input scenario enables to take into account predicted forthcoming events and to plan in a dynamic world. A compilation procedure checks the consistency of the operators specified by the user. The control relies on the use of causallinks, A, algorithm, and an extended leastcommitment strategy. It uses two important procedures, called C~feasibility " and "satisfiability =, dealing respectively with goal decomposition and conflict resolution:
A Survey on Temporal Reasoning in Artificial Intelligence
, 1994
"... The notion of time is ubiquitous in any activity that requires intelligence. In particular, several important notions like change, causality, action are described in terms of time. Therefore, the representation of time and reasoning about time is of crucial importance for many Artificial Intelligenc ..."
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Cited by 49 (4 self)
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The notion of time is ubiquitous in any activity that requires intelligence. In particular, several important notions like change, causality, action are described in terms of time. Therefore, the representation of time and reasoning about time is of crucial importance for many Artificial Intelligence systems. Specifically during the last 10 years, it has been attracting the attention of many AI researchers. In this survey, the results of this work are analysed. Firstly, Temporal Reasoning is defined. Then, the most important representational issues which determine a Temporal Reasoning approach are introduced: the logical form on which the approach is based, the ontology (the units taken as primitives, the temporal relations, the algorithms that have been developed,. . . ) and the concepts related with reasoning about action (the representation of change, causality, action,. . . ). For each issue the different choices in the literature are discussed. 1 Introduction The notion of time i...
Temporal Constraints: A Survey
, 1998
"... . Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about the times of events and the temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints re ..."
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Cited by 23 (1 self)
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. Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about the times of events and the temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints represent the possible temporal relations between them. The main tasks are two: (i) deciding consistency, and (ii) answering queries about scenarios that satisfy all constraints. This paper overviews results on several classes of Temporal CSPs: qualitative interval, qualitative point, metric point, and some of their combinations. Research has progressed along three lines: (i) identifying tractable subclasses, (ii) developing exact search algorithms, and (iii) developing polynomialtime approximation algorithms. Most available techniques are based on two principles: (i) enforcing local consistency (e.g. pathconsistency), and (ii) enhancing naive backtracking search. Keywords: Temporal Constra...
Timed Possibilistic Logic
 Handbook of logic in Artificial Intelligence and logic programming
, 1991
"... . This paper is an attempt to cast both uncertainty and time in a logical framework. It generalizes possibilistic logic, previously developed by the authors, where each classical formula is associated with a weight which obeys the laws of possibility theory. In the possibilistic temporal logic we pr ..."
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Cited by 16 (4 self)
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. This paper is an attempt to cast both uncertainty and time in a logical framework. It generalizes possibilistic logic, previously developed by the authors, where each classical formula is associated with a weight which obeys the laws of possibility theory. In the possibilistic temporal logic we present here, each formula is associated with a time set (a fuzzy set in the more general case) which represents the set of instants where the formula is certainly true (more or less certainly true in the general case). When a particular instant is fixed we recover possibilistic logic. Timed possibilistic logic generalizes possibilistic logic also in the sense that we substitute the lattice structure of the set of the (fuzzy) subsets of the temporal scale to the lattice structure underlying the certainty weights in possibilistic logic. Thus many results from possibilistic logic can be straightforwardly generalized to timed possibilistic logic. Illustrative examples are given. 1. Introduction ...
Hierarchisation of the Search Space in Temporal Planning
, 1996
"... . Hierarchical problem solving with abstraction is a widely adopted strategy to explore very large search trees. In this paper we describe the automatic generation of abstraction hierarchies for the I X T E T planner. Two points are mainly developped. First, we extend the classical STRIPSlike abstr ..."
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Cited by 15 (2 self)
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. Hierarchical problem solving with abstraction is a widely adopted strategy to explore very large search trees. In this paper we describe the automatic generation of abstraction hierarchies for the I X T E T planner. Two points are mainly developped. First, we extend the classical STRIPSlike abstraction formalism to the I X T E T representation, which allows the use of multivalued variables, resources and temporal constraints. Second, we describe a new way of dynamically managing abstraction hierarchies during planning. In our approach, the definition of the abstraction levels depends not only on the planning problem, but also on the current partial plan in the search. This leastcommited hierarchy has been implemented on the I X T E T planner and its interest in terms of reduction of backtracking and global efficiency has been clearly established on several realistic domains. 1 Introduction Hierarchical problem solving is a widely adopted strategy to explore very large search tree...
Time in Automated Legal Reasoning
"... Despite the ubiquity of time and temporal references in legal texts, their formalization has often been either disregarded or addressed in an ad hoc manner. In this paper we address this issue from the standpoint of the research done on temporal representation and reasoning in AI. We identify the ..."
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Cited by 5 (0 self)
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Despite the ubiquity of time and temporal references in legal texts, their formalization has often been either disregarded or addressed in an ad hoc manner. In this paper we address this issue from the standpoint of the research done on temporal representation and reasoning in AI. We identify the temporal requirements of legal domains and propose a temporal representation framework for legal reasoning which is independent of (i) the underlying representation language and (ii) the specific legal reasoning application. The approach is currently being used in a rulebased language for an application in commercial law. 1 Introduction Automated legal reasoning systems require a proper formalization of time and temporal information [40, 29]. Quoting L. Thorne McCarty [29]: ". . . time and action are both ubiquitous in legal domains. . . . " Notions related to time are found in major legal areas such as labor law (e.g. the time conditions to compute benefit periods), commercial law...
A Comparison of PointBased Approaches to Qualitative Temporal Reasoning
 In Proceedings of the AAAI National Conference on Artificial Intelligence
, 1999
"... We address the problem of implementing general, qualitative, pointbased temporal reasoning. Given a database of assertions concerning relative occurrences of points in time, we are interested in various operations on this database, including compiling the assertions into a representation that su ..."
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Cited by 3 (0 self)
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We address the problem of implementing general, qualitative, pointbased temporal reasoning. Given a database of assertions concerning relative occurrences of points in time, we are interested in various operations on this database, including compiling the assertions into a representation that supports efficient reasoning, determining whether a database is consistent, and computing the strongest entailed relation between two points. We begin by specifying a set of operations and their corresponding algorithms, applicable to general pointbased temporal domains. We next consider a specialpurpose reasoner, based on seriesparallel graphs, which performs very well in a temporal domain with a particular restricted structure. We discuss the notion of a metagraph, which encapsulates local structure inside metaedges and uses special purpose algorithms within such local structures, to obtain a fast general pointbased reasoner. That is, specifically, we use a very fast, seriesparallel graph reasoner to speed up general pointbased reasoning. We also analyse the TimeGraph reasoner of Gerevini and Schubert. For purposes of comparison, we have implemented four approaches: a generic pointbased reasoner, the generic pointbased reasoner with a ranking heuristic, a reasoner based on seriesparallel graphs, and a version of Gerevini and Schubert's TimeGraph reasoner. We compare these different approaches, as well as the original TimeGraphII reasoner of Gerevini and Schubert, on different data sets. We conclude that the seriesparallel graph reasoner provides the best overall performance: our results show that it dominated on domains exhibiting structure, and it degraded gracefully when conditions were less than ideal, in that it did worse than the generic appr...
PointBased Approaches to Qualitative Temporal Reasoning
 Proceedings of 16th National Conference on Artificial Intelligence and Eleventh Conference on Innovative Applications of Artificial Intelligence (AAAI/IAAI’99
, 1999
"... We address the general problem of finding algorithms for efficient, qualitative, pointbased temporal reasoning over a set of operations. We consider general reasoners tailored for temporal domains that exhibit a particular structure and introduce such a reasoner based on the seriesparallel graph r ..."
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Cited by 3 (1 self)
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We address the general problem of finding algorithms for efficient, qualitative, pointbased temporal reasoning over a set of operations. We consider general reasoners tailored for temporal domains that exhibit a particular structure and introduce such a reasoner based on the seriesparallel graph reasoner of Delgrande and Gupta; this reasoner is also an extension of the TimeGraph reasoner of Gerevini and Schubert. Test results indicate that for data with underlying structure, our reasoner performs better than other approaches. When there is no underlying structure in the data, our reasoner still performs better for query answering.