CSE4401 3.0  Conceptual Knowledge Acquisition and Processing

(Held at WUT, Warsaw, May 2011)

Professor Sergei Obiedkov

Abstract

Formal Concept Analysis (FCA) is a mathematical theory of concepts and conceptual hierarchies. FCA offers several highly practical methods to work with concrete qualitative data, studying how objects can be hierarchically grouped together according to their common attributes. Thus, one of the aspects of FCA is attribute logic, the study of possible attribute combinations. FCA approach differs from the traditional mathematical logic in that FCA adopts a contextual viewpoint, which means that we are interested in the logical structure of concrete data (of the context). In this course, we focus on the theoretical foundations and algorithmic issues of knowledge representation methods offered by FCA, as well as on a particular knowledge acquisition technique, attribute exploration, and some of its extensions, including the use of background knowledge and rule exploration.

Contents

1. Concept lattices: examples, basic notions, the algebra of concepts, diagrams of concept lattices
2. Closure systems: definitions, examples, computing all closed sets with the Next Closure algorithm
3. Modifications and generalizations of Next Closure for computing closed sets under constraints: closed sets (not) containing certain elements, closed sets of size below or above a fixed threshold, "frequent" closed sets; computing the order relation of the lattice diagram
4. Implications, implication inference, closure systems specified by sets of implications
5. Pseudo-closed sets as premises of the canonical basis of implications, computational complexity issues related to pseudo-closed sets
6. Algorithms for computing the canonical basis
7. Attribute exploration as a knowledge acquisition technique: the idea and the basic algorithm
8. Examples and potential applications of attribute exploration
9. Variations of the attribute exploration algorithm: object exploration, the use of "harmless" background knowledge, partially specified examples
10. A case study (attribute exploration of a particular mathematical field): generating examples, using background knowledge and symmetries
11. Non-implicational background knowledge in attribute exploration: clauses and cumulated clauses, models and pseudo-models, algorithms for computing models and pseudo-models, implication inference with background knowledge
12. Many-valued contexts and conceptual scaling
13. Implications in scaled many-valued contexts and many-valued attribute exploration
14. Rule exploration: motivation, basic idea, and examples
15. Rule exploration: relational contexts and Horn inference