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A Coherence Space of Rational Intervals for a Construction of IR

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Reliable Computing

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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Authors and Affiliations

  1. Escola de Informática, Universidade Católica de Pelotas, R. Félix da Cunha 412, Pelotas, 96010-000, RS, Brasil

    Graçaliz P. Dimuro

  2. Escola de Informática, Universidade Católica de Pelotas, R. Félix da Cunha 412, Pelotas, 96010-000, RS, Brasil

    Antônio Carlos Da R. Costa

  3. Curso de Pós-Graduação em Ciência da Computação, Universidade Federal do Rio Grande do Sul, Av. Bento Goncalves 9500, Bl IV, 91501-970, Porto Alegre, RS, Brasil

    Antônio Carlos Da R. Costa

  4. Faculdade de Matemática, Pontifícia, Universidade Católica do Rio Grande do Sul, Av. Ipiranga 6681, Porto Alegre, 90430-900, RS, Brasil

    Dalcidio M. Claudio

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  1. Graçaliz P. Dimuro
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  2. Antônio Carlos Da R. Costa
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  3. Dalcidio M. Claudio
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Dimuro, G.P., Costa, A.C.D.R. & Claudio, D.M. A Coherence Space of Rational Intervals for a Construction of IR. Reliable Computing 6, 139–178 (2000). https://doi.org/10.1023/A:1009913122021

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