MAT-42106 Applied Logics, 2-6 cr, 2/2011
Lecturer
Associate Professor Esko Turunen, PhD
Office: TD 405
Office hours: Wednesday 13.15-13.00
e-mail: esko.turunen@tut.fi
Schedule
Lectures will start on Wednesday, the 26.th of October at 9:15 in lecture room SJ202 and will last the
teaching period II (6 hours per week). Lectures, demonstrations as well as computer demonstrations will the be held in lecture room
SJ202 on Wednesdays at 9:15 - 12:00 and Thursdays at 8:30 - 11:00. There are no special hours for demonstrations: exercises and
computer tasks will be done during lectures. Each student should write and submit his learning notes. It is recommended to pass the
course by taking partial examinations; there will be two of them during the teaching period II. The first partial examination is on
Monday, the 14.th of November at 15:00-18:00 in TB308 and the second one on Friday, the 2.nd of December at 16:00-19:00 in TB308.
The course in composed of the following two separate topics. It is possible to take only one of them.
1. GUHA method in Data Mining
Knowledge discovery in databases (KDD) is defined to be ‘a non-trivial process of identifying valid,
novel, potentially useful, and ultimately understandable patterns in data’. In practise, we have a huge data matrix and
we are interested in finding some hidden information in this data. The GUHA method is one of the oldest data mining
methods and is based on a special extension of classical logic. We study the mathematical foundations of the
GUHA method and Lisp Miner - a computer implementation of GUHA - and see several real world applications.
The skeleton of this recently updated part can be down loaded here, however, this is just a skeleton that will be
completed during the course.
Part 1
Part 2
Part 3
Part 4
Part 5
Part 6
Part 7
Part 8
Part 9
Part 10
You might also like to have a look at the 2008 implementation of the data mining part, it is here
Data mining - an overview
Introduction to the GUHA method
GUHA - theory 1
GUHA - theory 2
GUHA - theory 3
GUHA - theory 4
GUHA - applications
2. Many-valued Similarity - Theory and Applications of Fuzzy Reasoning
First we show a theoretical basis of fuzzy inference systems, the 6 axioms of
Wajsberg algebras, then we introduce an general algorithm and, finally, we apply this algorithm to construct various
fuzzy inference machines such as traffic signal control, water level control, algorithmic decision making, etc.
Down load the skeleton of the second part here, it is again just an outline to be completed.
Many-valued similarity - theory
Many-valued similarity - applications
3. An algebraic approach to non-classical logics (no included in 2011)
This will be the most abstract part of the course. If you know the relation of Boolean Algberas and classical logic,
then you have a hint of what is comming: non-classical logics have a similar relation to more general algebraic
structures called residuated lattices. We study in detail such algebraic structures and their relation to Monoidal logic,
Linear logic, matematical Fuzzy Logic (also called BL-logic), Lukasiewicz logic, etc. Down load the skeleton
of last part here, however, it is possible that we will not have time to go through all that material. Also notice that this
is just an outline, and will be completed.
Order, posets, lattices and residuated lattices in logic
MacNeille completion of posets
MacNeille completion of residuated lattices
MacNeille completion of some special residuated lattices
MacNeille completion of semi-divisible and prelinear
residuated lattices
Ulrich Höhle's Monoidal Logic
Soundness and completeness of Monoidal Logic
and some of its extensions I
Soundness and completeness of Monoidal Logic
and some of its extensions II
Literature:
Turunen, E.; Mathematics behind Fuzzy Logic, Springer-Verlag, 1999
Hajek, P., Havranek, T. : Mechanizing hypothesis formation (http://www.cs.cas.cz/~hajek/guhabook/)
Rauch, J ; LISpMiner (http://lispminer.vse.cz/ )
Examination
Last updated 18.10.2011.