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The predicate completion of a partial information system

In: Mathematica Slovaca, vol. 68, no. 2
Zack French - James B. Hart

Details:

Year, pages: 2018, 253 - 270
Keywords:
domain, information system, partial information system, programming semantics
About article:
Originally, partial information systems were introduced as a means of providing a representation of the Smyth powerdomain in terms of order convex substructures of an information-based structure. For every partial information system ${\mathbb{S}}$, there is a new partial information system that is natrually induced by the principal lowersets of the consistency predicate for ${\mathbb{S}}$. In this paper, we show that this new system serves as a completion of the parent system ${\mathbb{S}}$ in two ways. First, we demonstrate that the induced system relates to the parent system ${\mathbb{S}}$ in much the same way as the ideal completion of the consistency predicate for ${\mathbb{S}}$ relates to the consistency predicate itself. Second, we explore the relationship between this induced system and the notion of $D$-completions for posets. In particular, we show that this induced system has a ``semi-universal" property in the category of partial information systems coupled with the preorder analog of Scott-continuous maps that is induced by the universal property of the $D$-completion of the principal lowersets of the consistency predicate for the parent system ${\mathbb{S}}$.
How to cite:
ISO 690:
French, Z., Hart, J. 2018. The predicate completion of a partial information system. In Mathematica Slovaca, vol. 68, no.2, pp. 253-270. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0098

APA:
French, Z., Hart, J. (2018). The predicate completion of a partial information system. Mathematica Slovaca, 68(2), 253-270. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0098
About edition: