Reliable Computing

, Volume 6, Issue 2, pp 139–178 | Cite as

A Coherence Space of Rational Intervals for a Construction of IR

  • Graçaliz P. Dimuro
  • Antônio Carlos Da R. Costa
  • Dalcidio M. Claudio
Article

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.

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Graçaliz P. Dimuro
    • 1
  • Antônio Carlos Da R. Costa
    • 2
    • 3
  • Dalcidio M. Claudio
    • 4
  1. 1.Escola de InformáticaUniversidade Católica de PelotasPelotasRS, Brasil
  2. 2.Escola de InformáticaUniversidade Católica de PelotasPelotasRS, Brasil
  3. 3.Curso de Pós-Graduação em Ciência da ComputaçãoUniversidade Federal do Rio Grande do SulPorto AlegreRS, Brasil
  4. 4.Faculdade de Matemática, PontifíciaUniversidade Católica do Rio Grande do SulPorto AlegreRS, Brasil

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