ICFCA06 - Invited Lectures
Talk: Methods of Conceptual Knowledge Processing - Rudolf
Wille (Technische Universität
Abstract.
The offered methods of Conceptual Knowledge Processing are procedures
which are well-planed to mean and purpose and therewith lead to skills for
solving practical tasks. The used means and skills have been mainly created as
translations of mathematical means and skills of Formal Concept Analysis.
Those transdisciplinary translations may be understood as transformations from
mathematical thinking, dealing with potential realities, to logical thinking,
dealing with actual realities. Each of the 38 presented methods is discussed in
a general language of logical nature, while citations give links to the
underlying mathematical background. Applications of the methods are
demonstrated by concrete examples mostly taken from the literature to which
explicit references are given.
Talk: An Enumeration Problem in Ordered Sets Leads to
Possible Benchmarks for Run-Time Prediction Algorithms - Tushar S. Kulkarni, Bernd S. W.
Schröder (
Abstract.
Motivated by the desire to estimate the number of order-preserving self maps of
an ordered set, we compare three algorithms (Simple Sampling, Partial
Backtracking and Heuristic Sampling) which predict how many nodes of a search
tree are visited. The comparison is for the original algorithms that apply to
backtracking and for modifications that apply to forward checking. We identify
generic tree types and concrete, natural problems on which the algorithms
predict incorrectly. We show that incorrect predictions not only occur because of
large statistical variations but also because of (perceived) systemic biases of
the prediction. Moreover, the quality of the prediction depends on the order of
the variables. Our observations give new benchmarks for
estimation and seem to make heuristic sampling the estimation algorithm of
choice.
Talk: Attribute Implications in a Fuzzy Setting - Radim
Bělohlávek (
Abstract.
The paper is an overview of recent developments concerning attribute
implications in a fuzzy setting. Attribute implications are formulas of the
form A Þ B, where A and B are collections of attributes, which describe
dependencies between attributes. Attribute implications are studied in several
areas of computer science and mathematics. We focus on two of them, namely,
formal concept analysis and databases.
Talk: The Assessment of Knowledge, in Theory and in
Practice
Jean-Claude Falmagne, Eric Cosyn, Jean-Paul
Doignon (Free University of Brussels), Nicolas Thiéry
Abstract.
This paper is adapted from a book and many scholarly articles. It reviews the
main ideas of a theory for the assessment of a student’s knowledge in a topic
and gives details on a practical implementation in the form of a software. The basic concept of the theory is the
‘knowledge state,’ which is the complete set of problems that an individual is
capable of solving in a particular topic, such as Arithmetic or Elementary
Algebra. The task of the assessor - which is always a computer - consists in
uncovering the particular state of the student being assessed, among all the
feasible states. Even though the number of knowledge states for a topic may
exceed several hundred thousand, these large numbers are well within the
capacity of current home or school computers. The result of an assessment
consists in two short lists of problems which may be labelled: ‘What the
student can do’ and ‘What the student is ready to learn.’ In the most important
applications of the theory, these two lists specify the exact knowledge state
of the individual being assessed. Moreover, the family of feasible states is
specified by two combinatorial axioms which are pedagogically sound from the
standpoint of learning. The resulting mathematical structure is related to
closure spaces and thus also to concept lattices. This work is presented
against the contrasting background of common methods of assessing human
competence through standardized tests providing numerical scores. The
philosophy of these methods, and their scientific origin in nineteenth century
physics, are briefly examined.