On a tree-like representation for symbolic-numeric data and its use in Galois lattice method

The authors propose a knowledge representation system that combines a greater expressive richness than that of the Boolean or attribute frameworks, and an analogous treatment complexity. This system can be used in symbolic-numerical clustering analysis and will be used to build a Galois (concept) lattice. Data and data classes are described by labelled, recursive trees called genterms. The set of these are generated with an algebraic signature. In addition, it is ordered by a generalization relation inducing a semilattice and easily extending to a lattice. Genterm node labels belong to numerical or symbolic sets of type. Each of these sets is a semilattice in which the order relation can also be viewed as a generalization relation. The used formalism is similar to those of abstract data type signatures and offers an alternative to the description logic formalisms. The elements of the Galois lattice between a genterm lattice and a power set of objects are couples (concepts) containing one set of objects and its description by a unique genterm