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Linear Approximation of Semi-algebraic Spatial Databases Using Transitive Closure Logic, in Arbitrary Dimension
[chapter]
2002
Lecture Notes in Computer Science
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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
2000
Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '00
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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]
2007
Handbook of Spatial Logics
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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
1999
Journal of Geographical Systems
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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
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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]
2005
Foundations of Artificial Intelligence
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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
2017
Logical Methods in Computer Science
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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
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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
1986
The American mathematical monthly
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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
2019
Sensors
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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]
2012
Lecture Notes in Computer Science
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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]
2021
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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
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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]
Finite and Algorithmic Model Theory
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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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