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36
Finitely Representable Databases
, 1995
"... : We study classes of infinite but finitely representable databases based on constraints, motivated by new database applications such as geographical databases. We formally define these notions and introduce the concept of query which generalizes queries over classical relational databases. We prove ..."
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Cited by 55 (8 self)
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: We study classes of infinite but finitely representable databases based on constraints, motivated by new database applications such as geographical databases. We formally define these notions and introduce the concept of query which generalizes queries over classical relational databases. We prove that in this context the basic properties of queries (satisfiability, containment, equivalence, etc.) are nonrecursive. We investigate the theory of finitely representable models and prove that it differs strongly from both classical model theory and finite model theory. In particular, we show that most of the well known theorems of either one fail (compactness, completeness, locality, 0/1 laws, etc.). An immediate consequence is the lack of tools to consider the definability of queries in the relational calculus over finitely representable databases. We illustrate this very challenging problem through some classical examples. We then mainly concentrate on dense order databases, and exhibit...
On the Structure of Queries in Constraint Query Languages
 In Proceedings of IEEE Symposium on Logic in Computer Science
, 1996
"... We study the structure of firstorder and secondorder queries over constraint databases. Constraint databases are formally modeled as finite relational structures embedded in some fixed infinite structure. We concentrate on problems of elimination of constraints, reducing quantification range to the ..."
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Cited by 28 (11 self)
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We study the structure of firstorder and secondorder queries over constraint databases. Constraint databases are formally modeled as finite relational structures embedded in some fixed infinite structure. We concentrate on problems of elimination of constraints, reducing quantification range to the active domain of the database and obtaining new complexity bounds. We show that for a large class of signatures, including real arithmetic constraints, unbounded quantification can be eliminated. That is, one can transform a sentence containing unrestricted quantification over the infinite universe of discourse to get an equivalent sentence in which quantifiers range over the finite relational structure. We use this result to get a new complexity upper bound on the evaluation of real arithmetic constraints. We also expand upon techniques in [20] and [4] for getting upper bounds on the expressiveness of constraint query languages, and apply it to a number of firstorder and secondorder quer...
Moving objects: Logical relationships and queries
 In Proc. 7th Int. Symp. on Spatial and Temporal Databases (SSTD
, 2001
"... Abstract. In moving object databases, object locations in some multidimensional space depend on time. Previous work focuses mainly on moving object modeling (e.g., using ADTs, temporal logics) and ad hoc query optimization. In this paper we investigate logical properties of moving objects in connect ..."
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Cited by 23 (0 self)
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Abstract. In moving object databases, object locations in some multidimensional space depend on time. Previous work focuses mainly on moving object modeling (e.g., using ADTs, temporal logics) and ad hoc query optimization. In this paper we investigate logical properties of moving objects in connection with queries over such objects using tools from differential geometry. In an abstract model, object locations can be described as vectors of continuous functions of time. Using this conceptual model, we examine the logical relationships between moving objects, and between moving objects and (stationary) spatial objects in the database. We characterize these relationships in terms of position, velocity, and acceleration. We show that these fundamental relationships can be used to describe natural queries involving time instants and intervals. Based on this foundation, we develop a concrete data model for moving objects which is an extension of linear constraint databases. We also present a preliminary version of a logical query language for moving object databases. 1
On Topological Elementary Equivalence of Spatial Databases
 In ICDT'97
, 1997
"... . We consider spatial databases and queries definable using firstorder logic and real polynomial inequalities. We are interested in topological queries: queries whose result only depends on the topological aspects of the spatial data. Two spatial databases are called topologically elementary equiva ..."
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Cited by 22 (5 self)
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. We consider spatial databases and queries definable using firstorder logic and real polynomial inequalities. We are interested in topological queries: queries whose result only depends on the topological aspects of the spatial data. Two spatial databases are called topologically elementary equivalent if they cannot be distinguished by such topological firstorder queries. Our contribution is a natural and effective characterization of topological elementary equivalence of closed databases in the real plane. As far as topological elementary equivalence is concerned, it does not matter whether we use firstorder logic with full polynomial inequalities, or firstorder logic with simple order comparisons only. 1 Introduction and summary Spatial database systems [5, 12, 1, 9] are concerned with the representation and manipulation of data that have a geometrical or topological interpretation. In this paper, we are interested in planar spatial databases; the conceptual view of such a data...
MODAL LOGICS OF TOPOLOGICAL RELATIONS
 ACCEPTED FOR PUBLICATION IN LOGICAL METHODS IN COMPUTER SCIENCE
, 2006
"... Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham’s modal logic of time intervals based on the Allen relations, we int ..."
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Cited by 18 (6 self)
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Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham’s modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the EgenhoferFranzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the twovariable fragment of firstorder logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to Π 1 1hard, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity.
dedale, A Spatial Constraint Database
, 1997
"... This paper presents a first prototype of a constraint database for spatial information, dedale. Implemented on top of the O2 DBMS, data is stored in an objectoriented framework, with spatial data represented using linear constraints over a dense domain. The query language is the standard OQL, with ..."
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Cited by 17 (6 self)
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This paper presents a first prototype of a constraint database for spatial information, dedale. Implemented on top of the O2 DBMS, data is stored in an objectoriented framework, with spatial data represented using linear constraints over a dense domain. The query language is the standard OQL, with special functions for constraint solving and geometric operations. A simple geographical application from the French Institute for Geography, IGN, is running on dedale. The data initially in vector mode was loaded into the database after a translation to constraint representation. Although it is too early to speak of performance since not all operations have been optimized yet, our experience with dedale demonstrates already the advantages of the constraint approach for spatial manipulation.
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 17 (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...
Querying Spatial Databases via Topological Invariants
 In PODS'98
, 1998
"... The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of topological queries against the spatial database into queries against the topological invariant. The languages considered ..."
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Cited by 17 (2 self)
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The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of topological queries against the spatial database into queries against the topological invariant. The languages considered are firstorder on the spatial database side, and fixpoint + counting, fixpoint, and firstorder on the topological invariant side. In particular, it is shown that fixpoint + counting expresses precisely all the ptime queries on topological invariants; if the regions are connected, fixpoint expresses all ptime queries on topological invariants. 1 Introduction Spatial data is an increasingly important part of database systems. It is present in a wide range of applications: geographic information systems, video databases, medical imaging, CADCAM, VLSI, robotics, etc. Different applications pose different requirements on query languages and therefore on the kind of spatial information th...
Reachability and Connectivity Queries in Constraint Databases
"... It is known that standard query languages for constraint databases lack the power to express connectivity properties. Such properties are important in the context of geographical databases, where one naturally wishes to ask queries about connectivity (what are the connected components of a given set ..."
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Cited by 14 (2 self)
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It is known that standard query languages for constraint databases lack the power to express connectivity properties. Such properties are important in the context of geographical databases, where one naturally wishes to ask queries about connectivity (what are the connected components of a given set?) or reachability (is there a path from A to B that lies entirely in a given region?). No existing constraint query languages that allow closed form evaluation can express these properties. In the rst part of the paper, we show that in principle there is no obstacle to getting closed languages that can express connectivity and reachability queries. In fact, we show that adding any topological property to standard languages like FO+Lin and FO+Poly results in a closed language. In the second part of the paper, we look for tractable closed languages for expressing reachability and connectivity queries. We introduce path logic, which allows one to state properties of paths with respect to given regions. We show that it is closed, has polynomial time data complexity for linear and polynomial constraints, and can express a large number of reachability properties beyond simple connectivity. Query evaluation in the logic involves obtaining a discrete abstraction of a continuous path,
Complete Geometric Query Languages
, 1999
"... We extend Chandra and Harel's seminal work on computable queries for relational databases to a setting in which also spatial data may be present, using a constraintbased data model. Concretely, we introduce both coordinatebased and pointbased query languages that are complete in the sense that th ..."
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Cited by 14 (1 self)
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We extend Chandra and Harel's seminal work on computable queries for relational databases to a setting in which also spatial data may be present, using a constraintbased data model. Concretely, we introduce both coordinatebased and pointbased query languages that are complete in the sense that they can express precisely all computable queries that are generic with respect to certain classes of transformations of space, corresponding to certain geometric interpretations of spatial data. The languages we introduce are obtained by augmenting basic languages with a while construct. We also show that the respective basic pointbased languages are complete relative to the subclass of the corresponding generic queries consisting of those that are expressible in the relational calculus with real polynomial constraints.