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40
Qualitative Spatial Representation and Reasoning
 An Overview”, Fundamenta Informaticae
, 2001
"... The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related ..."
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Cited by 67 (10 self)
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The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research, such as geographic information science
Constraint Satisfaction with Countable Homogeneous Templates
 IN PROCEEDINGS OF CSL’03
, 2003
"... For a fixed countable homogeneous structure we study the computational problem whether a given finite structure of the same relational signature homomorphically maps to . This problem is known as the constraint satisfaction problem CSP( ) for and was intensively studied for finite . We show that ..."
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Cited by 42 (19 self)
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For a fixed countable homogeneous structure we study the computational problem whether a given finite structure of the same relational signature homomorphically maps to . This problem is known as the constraint satisfaction problem CSP( ) for and was intensively studied for finite . We show that  as in the case of finite  the computational complexity of CSP( ) for countable homogeneous is determinded by the clone of polymorphisms of . To this end we prove the following theorem which is of independent interest: The primitive positive definable relations over an !categorical structure are precisely the relations that are invariant under the polymorphisms of .
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 ..."
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Cited by 34 (23 self)
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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
Constraint Satisfaction Problems with Countable Homogeneous Templates
"... Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a nonuniform constraint satisfaction problem. It turns out that many CSPs over infinite templates can be formulated with templates that are ωcategorical. We survey examples of such problems in ..."
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Cited by 25 (10 self)
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Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a nonuniform constraint satisfaction problem. It turns out that many CSPs over infinite templates can be formulated with templates that are ωcategorical. We survey examples of such problems in temporal and spatial reasoning, infinitedimensional algebra, acyclic colorings in graph theory, artificial intelligence, phylogenetic reconstruction in computational biology, and tree descriptions in computational linguistics. We then give an introduction to the universalalgebraic approach to infinitedomain constraint satisfaction, and discuss how cores, polymorphism clones, and pseudovarieties can be used to study the computational complexity of CSPs with ωcategorical templates. The theoretical results will be illustrated by examples from the mentioned application areas. We close with a series of open problems and promising directions of future research.
The core of a countably categorical structure
 In Proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science (STACS’05), LNCS 3404
, 2005
"... Abstract. A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure S has a core, i.e., S has an endomorphism e such that th ..."
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Cited by 25 (19 self)
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Abstract. A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure S has a core, i.e., S has an endomorphism e such that the structure induced by e(S) is a core; moreover, the core is unique up to isomorphism. We prove that every ωcategorical structure has a core. Moreover, every ωcategorical structure is homomorphically equivalent to a modelcomplete core, which is unique up to isomorphism, and which is finite or ωcategorical. We discuss consequences for constraint satisfaction with ωcategorical templates. 1.
Decidable and undecidable fragments of Halpern and Shoham’s interval temporal logic: towards a complete classification
 In Proc. of the 15th Int. Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), volume 5330 of LNCS
, 2008
"... Abstract. Interval temporal logics are based on temporal structures where time intervals, rather than time instants, are the primitive ontological entities. They employ modal operators corresponding to various relations between intervals, known as Allen’s relations. Technically, validity in interv ..."
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Cited by 20 (14 self)
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Abstract. Interval temporal logics are based on temporal structures where time intervals, rather than time instants, are the primitive ontological entities. They employ modal operators corresponding to various relations between intervals, known as Allen’s relations. Technically, validity in interval temporal logics translates to dyadic secondorder logic, thus explaining their complex computational behavior. The full modal logic of Allen’s relations, called HS, has been proved to be undecidable by Halpern and Shoham under very weak assumptions on the class of interval structures, and this result was discouraging attempts for practical applications and further research in the field. A renewed interest has been recently stimulated by the discovery of interesting decidable fragments of HS. This paper contributes to the characterization of the boundary between decidability and undecidability of HS fragments. It summarizes known positive and negative results, it describes the main techniques applied so far in both directions, and it establishes a number of new undecidability results for relatively small fragments of HS. 1
Variations on an ordering theme with constraints
 Proc. 4th IFIP International Conference on Theoretical Computer Science, TCS 2006 (Springer
"... Abstract. We investigate the problem of nding a total order of a nite set that satises various local ordering constraints. Depending on the admitted constraints, we provide an ecient algorithm or prove NPcompleteness. We discuss several generalisations and systematically classify the problems. Key ..."
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Cited by 10 (0 self)
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Abstract. We investigate the problem of nding a total order of a nite set that satises various local ordering constraints. Depending on the admitted constraints, we provide an ecient algorithm or prove NPcompleteness. We discuss several generalisations and systematically classify the problems. Key words: total ordering, NPcompleteness, computational complexity, betweenness, cyclic ordering, topological sorting
Temporally expressive scenarios in ScenarioML
, 2005
"... Sequential, nonoverlapping events are the norm in traditionallyexpressed scenarios and use cases, but the world is much more fluid. Events have duration and may overlap, be separated in time, begin or end together, or have various other specific temporal relations. The ordering of the events may b ..."
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Cited by 8 (6 self)
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Sequential, nonoverlapping events are the norm in traditionallyexpressed scenarios and use cases, but the world is much more fluid. Events have duration and may overlap, be separated in time, begin or end together, or have various other specific temporal relations. The ordering of the events may be completely known or partially uncertain, resulting in any of a large (but finite) number of relations for any two events. These relations, which can be formally stated and manipulated, are separable in form and meaning from the events themselves, which in requirements are most often expressed in prose. The temporal relations and partial ordering of events can be a significant part of what is specified, and must be inferred by a reader if not explicitly expressed. This paper presents a scenario language, ScenarioML, which expresses requirements scenarios using a broad and effective selection of event relations and structures. ScenarioML scenarios range from concrete scenarios to parameterized schemata that represent large families of scenarios related in a variety of temporal and structural ways. The language is designed for automated analysis and operations on temporal event relations, as well as other aspects of scenarios. An example from aircraft navigation is presented. 1
Determining the consistency of partial tree descriptions
 Artificial Intelligence
"... Abstract. We present an efficient algorithm that decides the consistency of partial descriptions of ordered trees. The constraint language of these descriptions was introduced by Cornell in computational linguistics; the constraints specify for pairs of nodes sets of admissible relative positions in ..."
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Abstract. We present an efficient algorithm that decides the consistency of partial descriptions of ordered trees. The constraint language of these descriptions was introduced by Cornell in computational linguistics; the constraints specify for pairs of nodes sets of admissible relative positions in an ordered tree. Cornell asked for an algorithm to find a tree structure satisfying these constraints. This computational problem generalizes the commonsupertree problem studied in phylogenetic analysis, and also generalizes the network consistency problem of the socalled leftlinear point algebra. We present the first polynomial time algorithm for Cornell’s problem, which runs in time O(mn), where m is the number of constraints and n the number of variables in the constraint.
Spatial and temporal reasoning: beyond Allen's calculus
 AI Communications
"... Temporal knowledge representation and reasoning with qualitative temporal knowledge has now been around for several decades, as formalisms such as Allen’s calculus testify. Now a variety of qualitative calculi, both temporal and spatial, has been developed along similar lines to Allen’s calculus. T ..."
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Cited by 8 (1 self)
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Temporal knowledge representation and reasoning with qualitative temporal knowledge has now been around for several decades, as formalisms such as Allen’s calculus testify. Now a variety of qualitative calculi, both temporal and spatial, has been developed along similar lines to Allen’s calculus. The main object of this paper is to point to open questions which arise when, leaving the now wellchartered waters of Allen’s, we venture into rougher sea of these formalisms. What remains true among the properties of Allen’s calculus? Partial answers are indeed known, but numerous new problems also arise. We try to point to the main issues in this paper.