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
- Concept
lattices: examples, basic notions, the algebra of concepts, diagrams of
concept
lattices
- Closure
systems: definitions, examples, computing all closed sets with the Next
Closure
algorithm
- 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
- Implications,
implication inference, closure systems specified by sets of implications
- Pseudo-closed
sets as premises of the canonical basis of implications, computational
complexity issues related to pseudo-closed sets
- Algorithms
for computing the canonical basis
- Attribute
exploration as a knowledge acquisition technique: the idea and the
basic algorithm
- Examples
and potential applications of attribute exploration
- Variations
of the attribute exploration algorithm: object exploration, the use of
"harmless" background knowledge, partially specified examples
- A
case study (attribute exploration of a particular mathematical field):
generating examples, using background knowledge and symmetries
- 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
- Many-valued
contexts and conceptual scaling
- Implications
in scaled many-valued contexts and many-valued attribute exploration
- Rule
exploration: motivation, basic idea, and examples
- Rule
exploration: relational contexts and Horn inference