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G.: Approximable concepts, Chu spaces, and information systems. Theory and Applications of Categories (200x
"... ABSTRACT. 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 ..."
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Cited by 12 (8 self)
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ABSTRACT. 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 crossdisciplinary 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 the recent work [Hitzler and Zhang, 2004] 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. 1.
Demonic Operators and Monotype Factors
, 1993
"... This paper tackles the problem of constructing a compact, pointfree proof of the associativity of demonic composition of binary relations and its distributivity through demonic choice. In order to achieve this goal a definition of demonic composition is proposed in which angelic composition is r ..."
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Cited by 5 (1 self)
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This paper tackles the problem of constructing a compact, pointfree proof of the associativity of demonic composition of binary relations and its distributivity through demonic choice. In order to achieve this goal a definition of demonic composition is proposed in which angelic composition is restricted by means of a socalled "monotype factor". Monotype factors are characterised by a Galois connection similar to the Galois connection between composition and factorisation of binary relations. The identification of such a connection is argued to be highly conducive to the desired compactness of calculation. Nothing delights a mathematician more than to discover that two things, previously regarded as entirely distinct, are mathematicaly identical. W. W. Sawyer La math'ematique est l'art de donner le meme nom `a des choses diff'erentes. [J.] H. Poincar'e The term "Galois connexion" was coined by Oystein Ore [20] almost fifty years ago in order to describe a particularly si...