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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Abstract Concept Lattices
verfasst von : Henry Soldano, Véronique Ventos
Erschienen in: Formal Concept Analysis
Verlag: Springer Berlin Heidelberg
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We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language
$\cal L$
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.