Approximate reasoning

computer science
mathematics

elective monographs

Classroom

The lecture is addressed to students of mathematics as well as to students of computer science interested in theoretical or applied aspects of approximate reasoning. Issues and problems discussed in the lecture are considered by many famous mathematicians and computer scientists to be among central problems of the current century, as important as deciphering the genetic code was for the second half of the 20th century. We will discuss problems important for making progress in many projects, in particular, interdisciplinary projects, in which mathematicians and computer scientists work together with specialists from other areas such as neuroscience, bioinformatics, psychology, economy, or complex adaptive systems. Different theoretical and applied aspects of methods of concept approximation from experimental data and domain knowledge will be covered.

1. Selected problems of approximate reasoning in such domains as machine learning, pattern recognition, data mining and knowledge discovery, soft computing, in particular, algorithmic methods in discovery of patterns, laws and approximate reasoning schemes from experimental data and domain knowledge based on non-conventional models of computation (e.g., evolutionary programming, neural networks, rough sets and Boolean reasoning, Bayesian networks, approximate reasoning schemes and granular computing).

2. Strategies in adaptive and autonomic computing, in particular, strategies for learning interactions.

3. Theoretical aspects of approximate reasoning: (i) Vapnik-Chervonenkis dimension and the role of different entropies in concept learning; (ii) logical foundations for approximate reasoning, in particular, in distributed (multiagent systems), non-monotonic reasoning and approximate reasoning from sensory data, reasoning about knowledge, belief revision, conflict analysis and negotiations; (iii) computational complexity of approximate reasoning: heuristics and approximation of NP-hard problems, minimal length principle and its relationship to Kolmogoroff complexity; (iv) selected methods of information compression.

1. T. Baeck: Evolutionary Algorithms in Theory and Practice, Oxford University Press 1996.

2. J. Barwise, J. Seligman: Information flow: The logic of distributed systems, Cambridge University Press 1997.

3. T. Hastie, R. Tibshirani, J. Friedman: The elements of statistical learning. Data mining, inference, and prediction. (2nd edition), Springer 2009.

4. D.S. Hochbaum: Approximation algorithms for NP-hard problems. PWS 1997.

5. A. Skowron: Approximate reasoning, notes prepared for monographic lectures, 2013.

6. V. Vapnik: Statistical learning theory. Wiley 1998.

Final grade: 50% - oral exam (25% - topics covered by lectures and exercises, 25% - papers extending selected topics covered by lectures), 50% - preparing and delivering a presentation (during exercises) on the basis of selected research papers.