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Qualitative Spatial Representation and Reasoning: An Overview
 FUNDAMENTA INFORMATICAE
, 2001
"... The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning inclu ..."
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Cited by 178 (16 self)
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The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning including reasoning about spatial change. Finally there is a discussion of theoretical results and a glimpse of future work. The paper is a revised and condensed version of [33, 34].
Combining Qualitative and Quantitative Constraints in Temporal Reasoning
 Artificial Intelligence
, 1996
"... This paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information. This model allows the representation and processing of many types of constraints discussed in the literature to date, including metric constraints (restricting the ..."
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Cited by 139 (0 self)
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This paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information. This model allows the representation and processing of many types of constraints discussed in the literature to date, including metric constraints (restricting the distance between time points) and qualitative, disjunctive constraints (specifying the relative position of temporal objects). Reasoning tasks in this unified framework are formulated as constraint satisfaction problems and are solved by traditional constraint satisfaction techniques, such as backtracking and path consistency. New classes of tractable problems are characterized, involving qualitative networks augmented by quantitative domain constraints, some of which can be solved in polynomial time using arc and path consistency. This work was supported in part by grants from the Air Force Office of Scientific Research, AFOSR 900136, and the National Science Foundation, IRI 8815522...
On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus
 Artificial Intelligence
, 1997
"... The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. ..."
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Cited by 108 (22 self)
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The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. We extend Bennett's encoding of RCC8 in modal logic. Based on this encoding, we prove that reasoning is NPcomplete in general and identify a maximal tractable subset of the relations in RCC8 that contains all base relations. Further, we show that for this subset pathconsistency is sufficient for deciding consistency. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. One particular approach in this context has been developed by Randell, Cui, and Cohn [20], the socalled Region Connecti...
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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Cited by 106 (2 self)
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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...
Temporal Query Languages: a Survey
, 1995
"... We define formal notions of temporal domain and temporal database, and use them to survey a wide spectrum of temporal query languages. We distinguish between an abstract temporal database and its concrete representations, and accordingly between abstract and concrete temporal query languages. We als ..."
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Cited by 106 (11 self)
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We define formal notions of temporal domain and temporal database, and use them to survey a wide spectrum of temporal query languages. We distinguish between an abstract temporal database and its concrete representations, and accordingly between abstract and concrete temporal query languages. We also address the issue of incomplete temporal information. 1 Introduction A temporal database is a repository of temporal information. A temporal query language is any query language for temporal databases. In this paper we propose a formal notion of temporal database and use this notion in surveying a wide spectrum of temporal query languages. The need to store temporal information arises in many computer applications. Consider, for example, records of various kinds: financial [37], personnel, medical [98], or judicial. Also, monitoring data, e.g., in telecommunications network management [4] or process control, has often a temporal dimension. There has been a lot of research in temporal dat...
Solving Hard Qualitative Temporal Reasoning Problems: Evaluating the Efficiency of Using the ORDHorn Class
 Constraints
, 1997
"... While the worstcase computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. ..."
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Cited by 59 (6 self)
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While the worstcase computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. In this paper, we will demonstrate that using the ORDHorn class in Ladkin and Reinefeld's backtracking algorithm leads to performance improvements when deciding consistency of hard instances in Allen's calculus. For this purpose, we prove that Ladkin and Reinefeld's algorithm is complete when using the ORDHorn class, we identify phase transition regions of the reasoning problem, and compare the improvements of ORDHorn with other heuristic methods when applied to instances in the phase transition region. Finally, we give evidence that combining search methods orthogonally can dramatically improve the performance of the backtracking algorithm. Contents 1 Introduction 1 2 Allen's...
EXPTIME tableaux for ALC
 ARTIFICIAL INTELLIGENCE
, 2000
"... The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reaso ..."
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Cited by 51 (3 self)
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The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for PSPACEcomplete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on treeautomata, which are used to prove EXPTIMEcompleteness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableaubased decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.
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 this mat ..."
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Cited by 50 (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
Tractable Disjunctions of Linear Constraints: Basic Results and Applications to Temporal Reasoning
 Theoretical Computer Science
, 1996
"... We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez an ..."
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Cited by 49 (2 self)
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We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez and McAloon. We show that deciding consistency of a set of constraints in this class can be done in polynomial time. We also present a variable elimination algorithm which is similar to Fourier's algorithm for linear inequalities. Finally, we use these results to provide new temporal reasoning algorithms for the OrdHorn subclass of Allen's interval formalism. We also show that there is no low level of local consistency that can guarantee global consistency for the OrdHorn subclass. This property distinguishes the OrdHorn subclass from the pointizable subclass (for which strong 5consistency is sufficient to guarantee global consistency), and the continuous endpoint subclass (for whi...
Spatial Reasoning with Topological Information
 Ph.D. thesis, Institut fur Informatik, AlbertLudwigsUniversitat Freiburg
, 1998
"... . This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the re ..."
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Cited by 45 (1 self)
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. This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the required dimension of the applied space. Further, it includes computational issues, e.g., how hard is it to reason with the calculus and are there efficient algorithms. Finally, we also address cognitive issues, i.e., is the calculus cognitively adequate. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. Different aspects of space can be treated in a qualitative way. Among others there are approaches considering orientation, distance, shape, topology, and combinations of these. A summary o...