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Representation of algebraic domains by formal association rule systems†

Published online by Cambridge University Press:  15 May 2015

LANKUN GUO ,
QINGGUO LI ,
PETKO VALTCHEV  and
YAPING LIN
LANKUN GUO
Affiliation:
College of Mathematics and Computer Science, Hunan Normal University, Changsha, P.R. China Email: lankun.guo@gmail.com
QINGGUO LI
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China
PETKO VALTCHEV
Affiliation:
Département d'Informatique, Université du Québec à Montréal, Montréal, Canada
YAPING LIN
Affiliation:
College of Information Science and Engineering, Hunan University, Changsha, P.R. China
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Abstract

In this paper, we introduce the notion of consistent F-augmented contexts by adding a special family of finite subsets into the structure of a formal context, which essentially establishes the basis of the representation of general algebraic domains. In particular, we investigate the association rule systems which are derived from the consistent F-augmented contexts and propose the notion of formal association rule systems. By the notion of antecedent connections, we obtain the equivalence between the category of formal association rule systems and that of algebraic domains, which demonstrates that the proposed notion of formal association rule systems provides a concrete approach to representing algebraic domains.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 4: Symposium on Domain Theory (ISDT 2013) , May 2017 , pp. 470 - 490
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

†

This manuscript is submitted to Mathematical Structures in Computer Science for possible publication in the special issue of ISDT 2013. It is an extension of our conference paper in ISDT 2013 and our earlier work (Guo et al. 2013).

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