Distributive Concept Exploration - A Knowledge Acquisition Tool in Formal Concept Analysis

Introduction Formal Concept Analysis ([9], [1]) provides a mathematical model of the concept `concept' which is used in data analysis for examining conceptual hierarchies in data tables. If these data tables are too large to be completely given, then the conceptual structure has to be determined in an interactive knowledge acquisition process from an expert of the domain. Exploration tools suggest, starting with the concepts to be examined, hierarchical relationships. The expert is asked either to confirm them or to provide typical counter-examples. The result of the exploration is a lattice that is generated by adding all largest common subconcepts and/or least common superconcepts. In [12] and [4], an overview over different exploration tools in Formal Concept Analysis is given. While Attribute Exploration considers largest common subconcepts only and Object Exploration least common superconcepts only ([1]), Concept Exploration treats largest common subconcepts (infima) and least

Formal Concept Analysis Methods for Description Logics

This work presents mainly two contributions to Description Logics (DLs) research by means of Formal Concept Analysis (FCA) methods: supporting bottom-up construction of DL knowledge bases, and completing DL knowledge bases. Its contribution to FCA research is on the computational complexity of computing generators of closed sets

Learning Terminological Knowledge with High Confidence from Erroneous Data

Description logics knowledge bases are a popular approach to represent terminological and assertional knowledge suitable for computers to work with. Despite that, the practicality of description logics is impaired by the difficulties one has to overcome to construct such knowledge bases. Previous work has addressed this issue by providing methods to learn valid terminological knowledge from data, making use of ideas from formal concept analysis. A basic assumption here is that the data is free of errors, an assumption that can in general not be made for practical applications. This thesis presents extensions of these results that allow to handle errors in the data. For this, knowledge that is "almost valid" in the data is retrieved, where the notion of "almost valid" is formalized using the notion of confidence from data mining. This thesis presents two algorithms which achieve this retrieval. The first algorithm just extracts all almost valid knowledge from the data, while the second algorithm utilizes expert interaction to distinguish errors from rare but valid counterexamples