Abstract Concept Lattices

Abstract : We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language of terms and the powerset of a set of instances O. Such a relation is materialized as an extension-intension lattice, namely a concept lattice when L is the powerset of a set P of attributes. We define and characterize an abstraction A as some part of either the language or the powerset of O, defined in such a way that the extension-intension latticial structure is preserved. Such a structure is denoted for short as an abstract lattice. We discuss the extensional abstract lattices obtained by so reducing the powerset of O, together together with the corresponding abstract implications, and discuss alpha lattices as particular abstract lattices. Finally we give formal framework allowing to define a generalized abstract lattice whose language is made of terms mixing abstract and non abstract conjunctions of properties.
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Communication dans un congrès
Petko Valtchev. International Conference on Formal Concept Analysis, May 2011, Nicosia, Cyprus. Springer, 6628/2011, pp.235-250, 2011, Lecture Notes in Computer Science. 〈10.1007/978-3-642-20514-9_18〉
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Henry Soldano, Veronique Ventos. Abstract Concept Lattices. Petko Valtchev. International Conference on Formal Concept Analysis, May 2011, Nicosia, Cyprus. Springer, 6628/2011, pp.235-250, 2011, Lecture Notes in Computer Science. 〈10.1007/978-3-642-20514-9_18〉. 〈hal-00642105〉

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