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Version vom 8. September 2009, 11:00 Uhr
A categorical view on algebraic lattices in formal concept analysis
A categorical view on algebraic lattices in formal concept analysis
Veröffentlicht: 2006 Juli
Journal: Fundamenta Informaticae
Nummer: 2-3Der Datenwert „-3“ kann einem Attribut des Datentyps Zahl nicht zugeordnet werden sondern bspw. der Datenwert „2“.
Seiten: 301-328
Volume: 74
Referierte Veröffentlichung
Kurzfassung
Formal concept analysis has grown from a new branch of the mathematical
field of lattice theory to a widely recognized tool in Computer Science
and elsewhere. In order to fully benefit from this theory, we believe that it
can be enriched with notions such as approximation by computation or representability. The latter are commonly studied in denotational semantics and domain theory and captured most prominently by the notion of algebraicity, e.g. of lattices. In this paper, we explore the notion of algebraicity in formal concept analysis from a category-theoretical perspective. To this end, we build on the the notion of approximable concept with a suitable category and show that the latter is equivalent to the category of algebraic lattices. At the same time, the paper provides a relatively comprehensive account of the representation theory of algebraic lattices in the framework of Stone duality, relating well-known structures such as Scott information systems with further formalisms from logic, topology, domains and lattice theory.
Download: Media:2006_786_Hitzler_A_categorical_v_1.pdf
Formale Begriffsanalyse, Topologie in der Informatik, Logik, Theoretische Informatik