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Approximable Concepts, Chu spaces, and information systems

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Guo-Qiang Zhang and Gongqin Shen

This paper serves to bring three independent but important areas of
computer science to a common meeting point: Formal Concept Analysis (FCA),
Chu Spaces, and Domain Theory (DT). Each area is given a perspective or
reformulation that is conducive to the flow of ideas and to the
exploration of cross-disciplinary connections. Among other results, we
show that the notion of state in Scott's information system corresponds
precisely to that of formal concepts in FCA with respect to all finite Chu
spaces, and the entailment relation corresponds to ``association rules".
We introduce, moreover, the notion of *approximable concept* and show
that approximable concepts represent algebraic lattices which are
identical to Scott domains except the inclusion of a top element. This
notion serves as a stepping stone in recent work in which a new notion of
morphism on formal contexts results in a category equivalent to (a) the
category of complete algebraic lattices and Scott continuous functions,
and (b) a category of information systems and approximable mappings.

Keywords:
Formal concept analysis, domain theory, Chu spaces

2000 MSC:
03B70, 06A15, 06B23, 08A70, 68P99, 68Q55

*Theory and Applications of Categories,*
Vol. 17, 2006,
No. 5, pp 79-102.

http://www.tac.mta.ca/tac/volumes/17/5/17-05.dvi

http://www.tac.mta.ca/tac/volumes/17/5/17-05.ps

http://www.tac.mta.ca/tac/volumes/17/5/17-05.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/17/5/17-05.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/17/5/17-05.ps

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