A Coherence Space of Rational Intervals for a Construction of IR

A Coherence Space of Rational Intervals for a Construction of IR A constructive computational representation of the space of real intervals IR is introduced, in a way that makes it possible to capture both its information structure relevant from a computational standpoint, and its application features as a mathematical structure. The representation consists of the Coherence Space of Rational Intervals IIQ, introduced by defining the web (IQ, ≈) of rational intervals, which is obtained from the set IQ of rational intervals on which a suitable reflexive and symmetric relation ≈ is defined. A two-fold construction of IIQ is performed, such that the internal construction of its domain-like structure leads the transformation of a suitable external algebraic structure defined on IQ into a certain one on IIQ which, when restricted to the set tot(IIQ) of total objects, becomes a structure which is order and algebraically isomorphic to the complete ordered field of the real numbers, R, and such that the family of quasi-total objects when extended with R is order and algebraically isomorphic to the set of the real intervals R. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

A Coherence Space of Rational Intervals for a Construction of IR

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009913122021
Publisher site
See Article on Publisher Site

Abstract

A constructive computational representation of the space of real intervals IR is introduced, in a way that makes it possible to capture both its information structure relevant from a computational standpoint, and its application features as a mathematical structure. The representation consists of the Coherence Space of Rational Intervals IIQ, introduced by defining the web (IQ, ≈) of rational intervals, which is obtained from the set IQ of rational intervals on which a suitable reflexive and symmetric relation ≈ is defined. A two-fold construction of IIQ is performed, such that the internal construction of its domain-like structure leads the transformation of a suitable external algebraic structure defined on IQ into a certain one on IIQ which, when restricted to the set tot(IIQ) of total objects, becomes a structure which is order and algebraically isomorphic to the complete ordered field of the real numbers, R, and such that the family of quasi-total objects when extended with R is order and algebraically isomorphic to the set of the real intervals R.

Journal

Reliable ComputingSpringer Journals

Published: Oct 7, 2004

References

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