We apply mathematical concept analysis to the problem of reengineering configurations. Concept analysis will reconstruct a taxonomy of concepts from a relation between objects and attributes. We use concept analysis to infer configuration structures from existing source code. Our tool NORA/RECS will accept source code, where configuration-specific code pieces are controlled by the preprocessor. The algorithm will compute a so-called concept lattice, which —when visually displayed — offers remarkable insight into the structure and properties of possible configurations. The lattice not only displays tine-grained dependencies between configurations, but also visualizes the overall quality of configuration structures according to software engineering principles. In a second step, interferences between configurations can be analyzed in order to restructure or simplify configurations. Interferences showing up in the lattice indicate high coupling and low cohesion between configuration concepts. Source files can then be simplified according to the lattice structure. Finally, we show how governing expressions can be simplified by utilizing an isomorphism theorem of mathematical concept analysis.

this article is to describe a generalized version of a well known knowledge acquistion method, called attribute exploration. To get a rough idea of what these explorations are about, imagine you want to classify some collection G of items according to selected properties. For example, G could be a class of mathematical structures, e.g. groups, to be classified by structural properties like "commutative", "nilpotent", etc. Or G could consist of technical devices, car engines for example, and the attributes may reflect properties such as reliability, weight, price, and so on. But G might also be a set of persons, perhaps the students of your university, and the classifying attributes may be field of study, age, degree, etcetera. Attribute exploration then would help you to explore the implicational logic of these attributes.

Concept exploration is a knowledge acquisition tool for interactively exploring the hierarchical structure of finitely generated lattices. Applications comprise the support of knowledge engineers by constructing a type lattice for conceptual graphs, and the exploration of large formal contexts in formal concept analysis.

We present a new topological representation and Stone-type duality for general (non-distributive) lattices. The dual objects of lattices are triples (X,r,Y ), where X, Y are the filter and ideal spaces of the lattice, endowed with a natural topology, and r is a relation from X to Y .

Lattice-Ordered Stone Spaces are shown to be the dual spaces of partial orders or meet semilattices. These results are subsequently extended to obtain a duality between galois connections and ?-frames. Galois connections are viewed as negation-like operators. The representation of galois connections leads us to a representation theorem for lattices, using the identity homomorphism on a lattice L. Rephrased, the representation theorem for lattices asserts that for any lattice L there is a complete, concrete Boolean algebra B, and a closure operator c : B ! B, such that L can be imbedded in the complete lattice of stable elements of B. B can be taken to be the powerset of a lattice-ordered Stone Space, in which case L is identified as the lattice of all clopen and stable subsets of the space. Representation is subsequently extended to a duality theorem for lattices and canonical L-frames. . Duality Theorems for Partial Orders, Semilattices, Galois Connections and Lattices Chrysafis H...