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Efficient Algorithms for Qualitative Reasoning about Time
 Artificial Intelligence
, 1995
"... Reasoning about temporal information is an important task in many areas of Artificial Intelligence. In this paper we address the problem of scalability in temporal reasoning by providing a collection of new algorithms for efficiently managing large sets of qualitative temporal relations. We focus on ..."
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Cited by 35 (6 self)
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Reasoning about temporal information is an important task in many areas of Artificial Intelligence. In this paper we address the problem of scalability in temporal reasoning by providing a collection of new algorithms for efficiently managing large sets of qualitative temporal relations. We focus on the class of relations forming the Point Algebra (PArelations) and on a major extension to include binary disjunctions of PArelations (PAdisjunctions). Such disjunctions add a great deal of expressive power, including the ability to stipulate disjointness of temporal intervals, which is important in planning applications. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a metagraph data structure. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms herein enable construction of a timegraph from a given set of PAr...
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...
Combining Topological and Qualitative Size Constraints for Spatial Reasoning
, 1998
"... . Information about the relative size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we combine a simple framework for reasoning about qualitative size relations with the Region Connection Cal ..."
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Cited by 19 (4 self)
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. Information about the relative size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we combine a simple framework for reasoning about qualitative size relations with the Region Connection Calculus RCC8, a widely studied approach for qualitative spatial reasoning with topological relations. Reasoning about RCC8 relations is NPhard, but a large maximal tractable subclass of RCC8 called b H8 was identified. Interestingly, any constraint in RCC8 \Gamma b H8 can be consistently reduced to a constraint in b H8 , when an appropriate size constraint between the spatial regions is supplied. We propose an O(n 3 ) time pathconsistency algorithm based on a novel technique for combining RCC8 constraints and relative size constraints, where n is the number of spatial regions. We prove its correctness and completeness for deciding consistency when the input contains topological ...
Combining Topological and Size Information for Spatial Reasoning
 Artificial Intelligence
, 2000
"... Information about the size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we introduce four classes of qualitative and metric size constraints, and we study their integration with the Regi ..."
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Cited by 18 (7 self)
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Information about the size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we introduce four classes of qualitative and metric size constraints, and we study their integration with the Region Connection Calculus RCC8, a widely studied approach for qualitative spatial reasoning with topological relations. Reasoning about RCC8 relations is NPhard, but three large maximal tractable subclasses of RCC8, called b H8 , C8 and Q8 respectively, have been identied. We propose an O(n 3 ) time pathconsistency algorithm based on a novel technique for combining RCC8 relations and qualitative size relations forming a Point Algebra, where n is the number of spatial regions. This algorithm is correct and complete for deciding consistency when the topological relations are either in b H8 , C8 or Q8 , and has the same complexity as the best known method for deciding consistency...
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 7 (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 . .
On Pointbased Temporal Disjointness
 Artificial Intelligence
, 1994
"... We address the problems of determining consistency and of finding a solution for sets of 3point relations expressing exclusion of a point from an interval, and for sets of 4point relations expressing interval disjointness. Availability of these relations is an important requirement for dealing wit ..."
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Cited by 6 (0 self)
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We address the problems of determining consistency and of finding a solution for sets of 3point relations expressing exclusion of a point from an interval, and for sets of 4point relations expressing interval disjointness. Availability of these relations is an important requirement for dealing with the sorts of temporal constraints encountered in many AI applications such as plan reasoning. We prove that consistency testing is NPcomplete and finding a solution is NPhard. Keywords: temporal reasoning, complexity of reasoning, planning, reasoning with disjunctions The work of the first author was carried out in part during a visit at the Computer Science Department of the University of Rochester (NY) supported by the Italian National Research Council (CNR), and in part at IRST in the context of the MAIA project and CNR projects "Sistemi Informatici e Calcolo Parallelo" and "Pianificazione Automatica". The second author was supported by Rome Lab Contract F3060291C0010. 1 Introd...
Fuzzy extension of intervalbased temporal subalgebras
 in ‘Proceedings of IPMU 2002
, 2002
"... In a previous paper, we have proposed a fuzzy extension of Allen’s Interval Algebra, called IA fuz,which is able to model soft temporal constraints and uncertainty in a unified way. In this paper, we address the problem of finding tractable subalgebras of IA fuz, as it has been done in the classical ..."
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In a previous paper, we have proposed a fuzzy extension of Allen’s Interval Algebra, called IA fuz,which is able to model soft temporal constraints and uncertainty in a unified way. In this paper, we address the problem of finding tractable subalgebras of IA fuz, as it has been done in the classical case. In particular, we show that the fuzzy extensions of classical SAc and SA subalgebras are tractable subalgebras of IA fuz.
Incremental Tractable Reasoning about Qualitative Temporal Constraints
, 2003
"... In many applications of temporal reasoning we are interested in reasoning incrementally In particular, given a CSP of temporal constrains and a new constraint, we want to maintain certain properties in the extended CSP (e.g., a solution), rather than recomputing them from scratch. The Point Algebra ..."
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In many applications of temporal reasoning we are interested in reasoning incrementally In particular, given a CSP of temporal constrains and a new constraint, we want to maintain certain properties in the extended CSP (e.g., a solution), rather than recomputing them from scratch. The Point Algebra (PA) and the Interval Algebra (IA) are two wellknown frameworks for qualitative temporal reasoning. Most of the existing algorithms for PA and the known tractable fragments of IA, such as ORDHorn, has been designed for &quot;static &quot; reasoning. In this paper we study the incremental version of some fundamental problems of temporal reasoning, proposing new algorithms that amortize their complexity when processing a sequence of input constraints. After analyzing the role of pathconsistency for incremental satisfiability, we propose algorithms for maintaining a solution of a CSP over either PA or ORDHorn, and the minimal labels of a CSP over PA. Our algorithms improve the complexity of using existing techniques by a factor of where n is the number of variables involved in the CSP. 1
Efficient Computation of Minimal Point Algebra Constraints by Metagraph Closure
"... Abstract. Computing the minimal network (or minimal CSP) representation of a given set of constraints over the Point Algebra (PA) is a fundamental reasoning problem. In this paper we propose a new approach to solving this task which exploits the timegraph representation of a CSP over PA. A timegraph ..."
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Abstract. Computing the minimal network (or minimal CSP) representation of a given set of constraints over the Point Algebra (PA) is a fundamental reasoning problem. In this paper we propose a new approach to solving this task which exploits the timegraph representation of a CSP over PA. A timegraph is a graph partitioned into a set of chains on which the search is supported by a metagraph data structure. We introduce a new algorithm that, by making a particular closure of the metagraph, extends the timegraph with information that supports the derivation of the strongest implied constraint between any pair of point variables in constant time. The extended timegraph can be used as a representation of the minimal CSP. We also compare our method and known techniques for computing minimal CSPs over PA. For CSPs that are sparse or exhibit chain structure, our approach has a better worstcase time complexity. Moreover, an experimental analysis indicates that the performance improvements of our approach are practically very significant. This is the case especially for CSPs with a chain structure, but also for randomly generated (both sparse and dense) CSPs. 1