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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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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.
The Largest Cartesian Closed Category of Stable Domains
 Theoretical Computer Science
"... This paper shows that Axiom d and Axiom I are important when one works within the realm of Scottdomains. In particular, it has been shown that (i) if [D ! s D] has a countable basis, then D must be finitary, for any Scottdomain D; (ii) if [D ! s D] is bounded complete, then D must be distributive, ..."
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This paper shows that Axiom d and Axiom I are important when one works within the realm of Scottdomains. In particular, it has been shown that (i) if [D ! s D] has a countable basis, then D must be finitary, for any Scottdomain D; (ii) if [D ! s D] is bounded complete, then D must be distributive, for any finitary Scottdomain D. Therefore, the category of dIdomains is the largest cartesian closed category within omegaalgebraic, bounded complete domains, with the exponential being the stable function space. 1 Introduction Among Scott's many insights which shaped the whole area of domain theory, one is that the partial ordering of a domain should be interpreted as the ordering about information. "Thus," wrote Scott [16], "x v y means that
A Decomposition Theorem for Domains
, 1995
"... A domain constructor that generalizes the product is defined. It is shown that with this constructor exactly the primealgebraic coherent Scottdomains and the empty set can be generated from twochains and boolean flat domains. 3 List of Symbols I am identifying the symbols by the corresponding ..."
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A domain constructor that generalizes the product is defined. It is shown that with this constructor exactly the primealgebraic coherent Scottdomains and the empty set can be generated from twochains and boolean flat domains. 3 List of Symbols I am identifying the symbols by the corresponding Latex(+Amssymb)symbols. " uparrow # downarrow ! rightarrow ? bot ? top leq geq 2 in W bigvee V bigwedge S bigcup Q prod L bigoplus \Theta times OE phi / psi IB Bbb B IN Bbb N hyp normalshape sf hyp (normalshape sans serif) Prime normalshape sf Prime (normalshape sans serif) t normalshape sf t (normalshape sans serif) f normalshape sf f (normalshape sans serif) m normalshape sf m (normalshape sans serif) M cal M (calligraphic) ~ A tilde A 4 1 Introduction This work was motivated by the idea of understanding a database as a subset of a product of flat domains. In relational database theory a database is understood as a relation, i.e. a subset of a product o...