A construction of an optimal base for conditional attribute and attributional condition implications in triadic contexts

This article studies implications in triadic contexts. Specifically, we focus on those introduced by Ganter and Obiedkov, namely conditional attribute and attributional condition implications. Our aim is to construct an optimal base for these implications.

Mining Generalized Patterns from Large Databases using Ontologies

Formal Concept Analysis (FCA) is a mathematical theory based on the formalization of the notions of concept and concept hierarchies. It has been successfully applied to several Computer Science fields such as data mining,software engineering, and knowledge engineering, and in many domains like medicine, psychology, linguistics and ecology. For instance, it has been exploited for the design, mapping and refinement of ontologies. In this paper, we show how FCA can benefit from a given domain ontology by analyzing the impact of a taxonomy (on objects and/or attributes) on the resulting concept lattice. We willmainly concentrate on the usage of a taxonomy to extract generalized patterns (i.e., knowledge generated from data when elements of a given domain ontology are used) in the form of concepts and rules, and improve navigation through these patterns. To that end, we analyze three generalization cases and show their impact on the size of the generalized pattern set. Different scenarios of simultaneous generalizations on both objects and attributes are also discussed