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On the Computability of RegionBased Euclidean Logics
"... Abstract. By a Euclidean logic, we understand a formal language whose variables range over subsets of Euclidean space, of some fixed dimension, and whose nonlogical primitives have fixed meanings as geometrical properties, relations and operations involving those sets. In this paper, we consider fi ..."
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Abstract. By a Euclidean logic, we understand a formal language whose variables range over subsets of Euclidean space, of some fixed dimension, and whose nonlogical primitives have fixed meanings as geometrical properties, relations and operations involving those sets. In this paper, we consider
Euclidean Hierarchy in Modal Logic
 Studia Logica
, 2002
"... For an Euclidean space R , let L n denote the modal logic of chequered . For every n 1, we characterize L n using the more familiar Kripke semantics, thus implying that each L n is a tabular logic over the wellknown modal system Grz of Grzegorczyk. ..."
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Cited by 3 (2 self)
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For an Euclidean space R , let L n denote the modal logic of chequered . For every n 1, we characterize L n using the more familiar Kripke semantics, thus implying that each L n is a tabular logic over the wellknown modal system Grz of Grzegorczyk.
Interpreting Topological Logics over Euclidean Spaces
 IN PROCEEDINGS OF KR2010
, 2010
"... Topological logics are a family of languages for representing and reasoning about topological data. The nonlogical primitives of these languages stand for various topological relations and operations, and their valid formulas encode our ..."
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Cited by 9 (4 self)
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Topological logics are a family of languages for representing and reasoning about topological data. The nonlogical primitives of these languages stand for various topological relations and operations, and their valid formulas encode our
A Topological logics with connectedness over Euclidean spaces
"... We consider the quantifierfree languages, Bc and Bc ◦ , obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected interior. These languages are interpreted over the regular clos ..."
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closed sets of R n (n ≥ 2) and, additionally, over the regular closed semilinear sets of R n. The resulting logics are examples of formalisms that have recently been proposed in the Artificial Intelligence literature under the rubric Qualitative Spatial Reasoning. We prove that the satisfiability problem
Different conceptions of Euclidean geometry
, 2007
"... Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In Erepresentation there are three basic elements (point, segment, angle) and no additional structures. Vrepresentation c ..."
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Cited by 9 (2 self)
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Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In Erepresentation there are three basic elements (point, segment, angle) and no additional structures. V
Heat kernels on Euclidean complexes
, 2006
"... In this thesis we describe a type of metric space called an Euclidean polyhedral complex. We define a Dirichlet form on it; this is used to give a corresponding heat kernel. We provide a uniform small time Poincaré inequality for complexes with bounded geometry and use this to determine uniform smal ..."
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Cited by 2 (2 self)
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In this thesis we describe a type of metric space called an Euclidean polyhedral complex. We define a Dirichlet form on it; this is used to give a corresponding heat kernel. We provide a uniform small time Poincaré inequality for complexes with bounded geometry and use this to determine uniform
FOUNDATIONS OF EUCLIDEAN CONSTRUCTIVE GEOMETRY
"... Abstract. Euclidean geometry, as presented by Euclid, consists of straightedgeandcompass constructions and rigorous reasoning about the results of those constructions. A consideration of the relation of the Euclidean “constructions ” to “constructive mathematics” leads to the development of a first ..."
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Abstract. Euclidean geometry, as presented by Euclid, consists of straightedgeandcompass constructions and rigorous reasoning about the results of those constructions. A consideration of the relation of the Euclidean “constructions ” to “constructive mathematics” leads to the development of a
EUCLIDEAN DISTANCE GEOMETRY AND APPLICATIONS
"... Abstract. Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the inputdataconsistsofanincompleteset of distances, and the output is a set of points in Euclidean space that realizes the given distances. We surv ..."
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Cited by 6 (1 self)
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Abstract. Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the inputdataconsistsofanincompleteset of distances, and the output is a set of points in Euclidean space that realizes the given distances. We
LOGICAL
"... Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose F04JGF finds the solution of a linear leastsquares problem, Ax b, where A is a real m by nðm nÞ matrix an ..."
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Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose F04JGF finds the solution of a linear leastsquares problem, Ax b, where A is a real m by nðm nÞ matrix and b is an m element vector. If the matrix of observations is not of full rank, then the minimal leastsquares solution is returned.
LOGICAL
"... Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose F04JGF finds the solution of a linear leastsquares problem, Ax b, where A is a real m by nm ð nÞ matrix a ..."
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Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose F04JGF finds the solution of a linear leastsquares problem, Ax b, where A is a real m by nm ð nÞ matrix and b is an m element vector. If the matrix of observations is not of full rank, then the minimal leastsquares solution is returned.
Results 1  10
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49,703