Fuzzy Description Logics

Fuzzy Description Logics

Technische Universität Dresden
Institut für Theoretische Informatik
Lehrstuhl für Automatentheorie

Rafael Peñaloza

Course Description

The course covers the study of fuzzy Description Logics as a formalism for representing--and reasoning with--vague or imprecise knowledge.
We will study several variants of fuzzy DLs, that differentiate from each other by their expressivity and their fuzzy semantics. These will mainly be extensions of the classical DLs EL and ALC.
For the logics where this is possible, we will cover practical methods for reasoning over them. However, we will also show that these logics easily become undecidable.

Prerequisites:

basic knowledge of propositional and first order logic
knowledge of fuzzy and/or Description Logics is helpful, but not mandatory

Organization

The lecture takes place weekly in room E05: Thursdays 13:00-14:30 (DS 4)

Announcements

Important! The Questions-and-Answers session has been cancelled.

Credits / Examinations

Students can earn 3 SWS (2/1/0) by attending this lecture.

Please contact me for fixing a date for your examinations.

Modules

Students from the Bachelor Informatik program can use this lecture for the modules INF-B-510 and INF-B-520
Students from the Master Informatik and Diplom Informatik (Ordnung 2010) programs can use this lecture for the modules INF-BAS6 and INF-VERT6
Students from the Computational Logic program can use this lecture for the modules KR and TCSL

In order to get the credits, students must pass an oral examination at the end of the semester.

Exercises

An exercise session will be held by Felix Distel every second week on Tuesdays 07:30-09:00 (DS 1) in E05 (starting from October 11).

All students are encouraged to present their solutions to the exercises, as they are useful for a better understanding of the lecture material.

Exercise sheets will be available online approx. one week before the session.

Challenging Exercises

A few "challenging" exercises will be proposed during the lecture and tutorials. These can range from finding examples for some of the less intuitive notions presented, to proving further results not covered in the lecture. Students are encouraged to try to work on them and send their solutions to Rafael Peñaloza. The first correct solution will be posted here.

Lecture Notes

A pdf version of the lecture notes is now available. Please notice that these are incomplete and contain several errors; they do not replace the material presented during the course. Use them with care.

Literature

All the material necessary for successfully aproving the course will be presented during the lectures. As there is no available script, students are strongly recommended to copy the material written on the blackboard during lecture time. For getting familiar with Description Logics, consult:

F. Baader, D. Calvanese, D. McGuinness, D. Nardi, and P. F. Patel-Schneider, editors. The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, 2003.
Franz Baader. Description Logics. In Reasoning Web: Semantic Technologies for Information Systems, 5th International Summer School 2009, volume 5689 of Lecture Notes in Computer Science, pages 1--39. Springer-Verlag, 2009.

For getting familiar with Fuzzy Logic, consult:

P. Hajek. Metamathematics of Fuzzy Logic. Springer-Verlag. 1998.

Rafael Peñaloza