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Representation Theorems and Locality for Subsumption Testing and Interpolation in the Description Logics εL; εL+ and their Extensions with n-ary Roles and Numerical Domains

Sofronie-Stokkermans V.

Fundamenta Informaticae

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2017

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Vol. 156, nr 3/4

361--411

EN

In this paper we show that subsumption problems in lightweight description logics (such as εL and εL+) can be expressed as uniform word problems in classes of semilattices with monotone operators. We use possibilities of efficient local reasoning in such classes of algebras, to obtain uniform PTIME decision procedures for CBox subsumption in εL, εL+ and extensions thereof. These locality considerations allow us to present a new family of (possibly many-sorted) logics which extend εL and εL+ with n-ary roles and/or numerical domains. As a by-product, this allows us to show that the algebraic models of εL and εL+ have ground interpolation and thus that εL, εL+, and their extensions studied in this paper have interpolation.

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Typografowie, programiści i matematycy, czyli przypadek estetycznie zadowalającej interpolacji

Jackowski B.

Acta Poligraphica

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2013

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Vol. 1

11--30

EN

The reason for preparing this report is that the author has been convinced or many years that John D. Hobby’s algorithm or connecting Bézier segments, implemented by Donald E. Knuth in METAFONT and later transferred by Hobby to METAPOST, based on the notion o a “mock curvature”, is a genuine pearl which deserves both proper acknowledgement and a far wider awareness of its existence. Of course, one can find nearly all the necessary details in the relevant papers by Hobby and in the METAFONT source, but, needless to say, it is not easy to dig through the publications. The present paper provides a full mathematical description of Hobby’s interpolation algorithm, discusses its advantages and disadvantages (in particular, its instability) and compares Hobby’s approach with a few selected simpler approaches.

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Analiza dokładności interpolacyjnych modeli powierzchni typu grid

Gościewski D.

Acta Scientiarum Polonorum. Geodesia et Descriptio Terrarum

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2007

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Vol. 6, nr 4

11-21

PL

Za pomocą większości systemów oprogramowania z grupy GIS można wygenerować numeryczny model powierzchni na podstawie regularnej siatki kwadratów typu GRID. Do utworzenia takiej siatki wykorzystuje się algorytmy interpolacyjne pozwalające na obliczenie wartości w punktach węzłowych na podstawie wybranych punktów pomiarowych. Dokładność tworzonych modeli powierzchni zależy w głównej mierze od doboru algorytmów interpolacji oraz ich parametrów obliczeniowych. Istotnym zagadnieniem staje się porównanie jakości i dokładności modeli powierzchni tworzonych za pomocą różnych algorytmów. W tym celu wykorzystać można współczynniki statystyczne. W artykule wykorzystano wybrane współczynniki statystyczne do porównania dokładności modeli interpolacyjnych utworzonych przez różne algorytmy.

EN

The majority of GIS type software systems allow generating numerical surface models on the basis of GRID type regular network of squares. Interpolation algorithms allowing computation of values at nodal points on the basis of selected measurement points are used for establishment of such a grid. The accuracy of generated surface models depends mainly on the choice of the interpolation algorithms and their computation parameters. Comparison of quality and accuracy of surface models generated by application of different algorithms seems an important issue. Statistical coefficients can be used for that purpose. The paper uses selected statistical coefficients for comparison of accuracy of interpolation models generated by application of different algorithms.