Course language: English
This course aims to deepen understanding of knowledge representation principles beyond the predicate logic formalism. Firstly, the course presents ontologies and description logic, the principle elements of semantic web. Then, attention will be paid to statements whose validity varies in time. Uncertainty makes the next issue to be discussed. Modal logic extends the classical logic with additional modalities, namely, possibility, probability, and necessity. Probabilistic graphical models associate the classical probabilistic theory with the graph theory. Fuzzy sets allow to represent vagueness.
ontology, description logic, conditional independence, bayesian network, fuzzy set and operation.
1. Introduction frames and ontologies.
2. Description logic language and its expressivity, interactions with rule-based systems.
3. Description logic inference, tableuax method.
4. Description queries forming and evaluation. Inconsistency in ontologies.
5. Tractable fragments of description logic. Present and future of semantic web.
6. Uncertainty and conditional independence introduction to probabilistic networks.
7. Bayesian networks -- inference.
8. Learning Bayesian networks from data.
9. Dynamic models applications of probabilistic networks.
10. Uncertainty and its representation in knowledge-based systems.
11. Fuzzy sets and their representations.
12. Fuzzy numbers and operations with them.
13. Operations with fuzzy sets.
14. Algebra of fuzzy logical operations.
1. Introduction, ontological editor Protege. OWL language modeling, examples. The first assignment.
2. Inference engine Pellet. The first assignment -- autonomous working.
3. Query language SPARQL. The first assignment -- autonomous working.
4. Overview of modeling faults. Test.
5. Modalities and time in logic systems -- reminder.
6. SW probabilistic modeling tools (Bayes Net Toolbox for Matlab). The second assignment.
7. Inference in probabilistic models. The second assignment -- autonomous working.
8. Learning probabilistic models from data. The second assignment -- autonomous working.
9. Overview of probabilistic models. Test.
10. Conversion between representations of fuzzy sets.
11. Fuzzy numbers and operations with them; the third assignment: computing with fuzzy numbers.
12. Operations with fuzzy sets.
13. Properties of fuzzy logical operations, test.
14. Backup, credits.
 Franz Baader , Diego Calvanese , Deborah L. McGuinness , Daniele Nardi , Peter F. Patel-Schneider, The Description Logic Handbook, Cambridge University Press, New York, NY, 2007.
 Baader, F., Sattler U.: An overview of tableau algorithms for description logics ; Studia Logica, 69:5-40, 2001.
 Charniak, E.: Bayesian Networks without Tears. AI Magazine 12(4): 50-63, 1991.
 Pearl , J.: Causality: Models, Reasoning and Inference. Cambridge University Press, 2001.
 Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. 3rd ed., Cha- pman & Hall/CRC, Boca Raton/London/New York/Washington, 2005.