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Linear Approximation of Semi-algebraic Spatial Databases Using Transitive Closure Logic, in Arbitrary Dimension [chapter]

Floris Geerts
2002 Lecture Notes in Computer Science  
We compute in first-order logic extended with a transitive closure operator, a linear spatial database which characterizes the semi-algebraic spatial database up to a homeomorphism.  ...  We consider n-dimensional semi-algebraic spatial databases.  ...  Fig. 3 . 3 Illustration of the algorithm Linearize. Theorem 5 . 5 Rational linearizations of spatial databases are expressible in the transitive closure logic FO+TC.  ... 
doi:10.1007/3-540-46093-4_11 fatcat:q5uf5lnvgvdinhr6i4e2ob7kwu

Linear approximation of planar spatial databases using transitive-closure logic

Floris Geerts, Bart Kuijpers
2000 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '00  
Furthermore, we introduce an extension of transitive-closure logic and show that this logic is complete for the computable queries on linear spatial databases.  ...  This result together with our first result implies that this extension of transitive-closure logic can express all computable topological queries on arbitrary spatial databases in the plane.  ...  ACKNOWLEDGEMENTS The authors are grateful to Jan Van den Bussche and Leonid Libkin for helpful comments on issues of completeness.  ... 
doi:10.1145/335168.335215 dblp:conf/pods/GeertsK00 fatcat:yacih2vhkjbd5i3bspdfhvdi74

Real Algebraic Geometry and Constraint Databases [chapter]

Floris Geerts, Bart Kuijpers
2007 Handbook of Spatial Logics  
The constraint database model can be seen as a generalization of the classical relational database model that was introduced by Codd in the 1970s to deal with the management of alpha-numerical data, typically  ...  A relational database is usually modeled following a database schema. A schema contains information on the relation names and on the names of the attributes appearing in relation.  ...  The linear analog of the previous theorem also holds for the language FO(+, <, 0, 1) + T.  ... 
doi:10.1007/978-1-4020-5587-4_13 fatcat:5oemzcnwe5egnkkrjxquwsl5ve

On the design of formal theories of geographic space

Thomas Bittner, Andrew U. Frank
1999 Journal of Geographical Systems  
This is used to provide (1) a classi®cation of formal theories of geographic space, (2) criteria of their adequacy, and (3) an evaluation of design decisions in the process of formalization.  ...  Other designs are possible and a systematic exploration of alternative types of GIS, for example, based on constraints or based on stored spatial relations, becomes necessary.  ...  Semi-linear sets are semi-algebraic sets that can be represented by linear polynomials (e.g., F 1 and F 3 ).  ... 
doi:10.1007/s101090050014 fatcat:3xgxevlhhvcpbgcnvufafimpo4

Subject index volumes 1–200

1999 Theoretical Computer Science  
2583 transitive, 2197, 2644 binary relations, 3404 transitive closure, 78, 364,893, 929, 1324, 1375, 2225,2428,3030,3173 algebraic structures for -, 78 transitive closure of an acyclic digraph,  ...  dependencies, 1857 interpretations, 88 intuitionistic linear logic, 3257 linear logic, 3580 matrix equivalence problem, 355 monadic logic, 1802 parallelism, 493 full principal cones, 1088 semi-AFL  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Time Granularity [chapter]

Jérôme Euzenat, Angelo Montanari
2005 Foundations of Artificial Intelligence  
As an example, the representations associated with the different layers can use the same temporal logic or the same algebra of relations.  ...  and de Rijke, 1997], as well as by combining linear and branching temporal logics in a suitable way Franceschet and Montanari, 2004] .  ...  Answering a query q against a database with granularities D and hypotheses H consists in answering the query against the closure of the database (D H |= q).  ... 
doi:10.1016/s1574-6526(05)80005-7 fatcat:jgytu4xfljdfdoso56gucfk2ya

Model Checking Spatial Logics for Closure Spaces

Vincenzo Ciancia, Diego Latella, Michele Loreti, Mieke Massink, Alexandra Silva
2017 Logical Methods in Computer Science  
The latter are interpreted over arbitrary sets of points instead of individual points in space.  ...  Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space  ...  For this reason, we consider it a fundamental collective property, deserving special treatment in the field of spatial logics, akin to the notion of transition in models of modal logics.  ... 
doi:10.2168/lmcs-12(4:2)2016 fatcat:q4irnsavp5dr3luph7rl5ptpaa

Real algebraic geometry

2014 ChoiceReviews  
the pool of the Real Algebraic Geometry of tomorrow.  ...  We also wish to thank the numerous sponsors who allowed us to welcome so many participants under proper conditions, in particular a large number of PhD students and post-PhD students called to constitute  ...  In [6] Theorem 2.22 is used to prove the equivalence of two different semantics and in the theory of constraint databases. However, it also has applications in logic.  ... 
doi:10.5860/choice.51-3296 fatcat:xm5l6ieafzewtfpuegkxsbtzhy

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
41A45 Approximation by arbitrary linear expressions 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy 41A50 Best approximation, Chebyshev systems 41A52 Uniqueness of  ...  as readily as possible-in products derived from the Mathematical Reviews Database (MRDB), in Zentralblatt MATH (ZMATH), or anywhere else where this classification scheme is used.  ...  geometry [See also 58B34] 83C75 Space-time singularities, cosmic censorship, etc. 83C80 Analogues in lower dimensions 83C99 None of the above, but in this section 83Dxx Relativistic gravitational theories  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis

Wenjuan Gong, Bin Zhang, Chaoqi Wang, Hanbing Yue, Chuantao Li, Linjie Xing, Yu Qiao, Weishan Zhang, Faming Gong
2019 Sensors  
Geometric methods that exploit the applications of geometrics, e.g., geometric features, are widely used in computer graphics and computer vision problems.  ...  Considering the broad applications of deep learning methods, this review also studies geometric deep learning, which has recently become a popular topic of research.  ...  Therefore, we see that for fixed py, vq the transition functions are linear in pξ, wq P R mˆV .  ... 
doi:10.3390/s19122809 fatcat:nrnq4vrj7bfv7iv4aem5g6k4zu

Data Models and Query Languages for Linked Geospatial Data [chapter]

Manolis Koubarakis, Manos Karpathiotakis, Kostis Kyzirakos, Charalampos Nikolaou, Michael Sioutis
2012 Lecture Notes in Computer Science  
databases and artificial intelligence.  ...  The recent availability of geospatial information as linked open data has generated new interest in geospatial query processing and reasoning, a topic with a long tradition of research in the areas of  ...  We thank all the participants and the reviewers of these projects for many interesting discussions on the area covered by this survey paper.  ... 
doi:10.1007/978-3-642-33158-9_8 fatcat:tlyz4vsnpjevxchysoqiyrrrbi

On closures for reduced order models - A spectrum of first-principle to machine-learned avenues [article]

Shady E. Ahmed, Suraj Pawar, Omer San, Adil Rasheed, Traian Iliescu, Bernd R. Noack
2021 arXiv   pre-print
Specifically, we focus on ROM closures, which are correction terms that are added to classical ROMs in order to model the effect of the discarded ROM modes in under-resolved simulations.  ...  In early POD modeling, available data was used to build an optimal basis, which was then utilized in a classical Galerkin procedure to construct the ROM.  ...  In order to build the projection-based ROM, the solution u is approximated in a low-dimensional affine subspace of dimension r via the Galerkin ansatz as follows: u(t) ≈ū + Ψa(t), (30) whereū ∈ R n is  ... 
arXiv:2106.14954v2 fatcat:q6jzbxfjabc3vg3nsn24z4lbyy

Spacetimes with Semantics [article]

Mark Burgess
2014 arXiv   pre-print
Semantics make up the essential difference in how one describes and uses the concept of space in physics, chemistry, biology and technology.  ...  The aim of this exercise is to apply related tools and ideas to an initial unification of real and artificial spaces, e.g. databases and information webs with natural spacetime.  ...  Acknowledgement I am grateful to Paul Borrill for interesting discussions on the nature of time.  ... 
arXiv:1411.5563v1 fatcat:lo6gml2axbbhtluxjwiiearzny

Lossy Image Compression [chapter]

2017 Encyclopedia of GIS  
Three-Dimensional City Models High point density laser scanner data contains detailed information on the shapes of building roofs and can be used to produce 3D city models (Haala and Brenner 1999).  ...  Corridor Mapping Laser scanning has also proven useful for largescale mapping around linear infrastructure such as roads, rail roads and power lines.  ...  Also in the context of linear constraints, there is a closure property: any FO C lin query, when evaluated on a spatial database in the linear constraint model, yields a spatial database in the linear  ... 
doi:10.1007/978-3-319-17885-1_100712 fatcat:wyr6e3phbjgmhfeu57dockc5om

Logical aspects of spatial databases [chapter]

Bart Kuijpers, Jan Van den Bussche, Javier Esparza, Christian Michaux, Charles Steinhorn
Finite and Algorithmic Model Theory  
Viewing R as a structure R = (R, 0, 1, +, ·, <) over the language of ordered fields, we can then use first-order logic to express properties of spatial datasets.  ...  In most general terms, a spatial dataset is any set S ⊂ R n for some n. Equivalently, we can view such a set as an n-ary relation S over R (using Cartesian coordinates).  ...  computationally complete on linear or arbitrary (semi-algebraic) datasets.  ... 
doi:10.1017/cbo9780511974960.003 fatcat:tlb23rm6drft5jnyzyqcx5qcve
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