Published online by Cambridge University Press: 15 May 2015
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.
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).