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42046 - Fuzzy Logic (LD) [UB]


Type: S3 Course
Semester: Spring (not offered in course 2010/2011)
ECTS: 6
Teaching Points: 15
Offer: Annual
Responsible Unit: UB
Responsible: Ventura Verdú
Language: English
Requirements:
GOALS

  • To introduce the basic concepts and techniques of Fuzzy Logic.
  • To present Fuzzy Logic as a plausible model for the treatment of vagueness.
  • To obtain a well founded logic theoretic background for approximate reasoning.
  • To present some applications of fuzzy logic to the approximate reasoning


CONTENTS

1. Introduction. Background on Classical logic

2. Classical logic and many-valued logics

3. Two versions of Fuzzy Logic: The wide sense (Zadeh) and the narrow sense (Hájek).

4. The real interval [0,1] as a set of truth values for fuzzy logics. Triangular norms and their residua.

5. Distinct views of fuzzy logics based on triangular norms: Tautologies and consequence relations.

6. The three main basic logics: Gödel logic, Lukasiewicz logic and Product logic.

7. The calculi. Axiomatic extensions

8. Application to fuzzy rules.

9. Complexity of the three main basic logics.

10. First order Fuzzy Logic

11. Fuzzy Prolog.

12. Description Logics and web semantics.


BIBLIOGRAPHY

  • S. Aguzzoli, B. Gerla and Z. Haniková. Complexity issues in basic logic. Soft Computing 9: 919-934, 2004.
  • D. Dubois, F. Esteva, L. Godo, and H. Prade. Fuzzy-set Based Logics- An History-oriented Presentation of their Main Developments, in Handbook of the History of Logic, volume 8. The many Valued and Non-monotonic Turn in Logic. D. M. Gabbay and J. Woods, eds., pp. 325-449. Elsevier, 2007.
  • S. Gotwald and P. Hájek. Triangular norm based mathematical fuzzy logic. In E. P. Klement nad R. Mesiar, editors, Logical Algebraic, Analytic and Probabilistic Aspects of Triangular Norms, pages 275-300, Elsevier, Amsterdam, 2005.
  • P. Hájek. Metamathematics of Fuzzy Logic, Trend in Logic, vol. 4, Kluwer, Dodrecht, 1998.
  • P. Kájek. Making fuzzy description logic more general. Fuzzy Sets and Systems, 154, 1-15, 2005.
  • P. Hájek. What does mathematical fuzzy logic offer to description logic? In Capturing Intelligence: Fuzzy Logic and the Semantical We, Elie Sanchez, ed., Elsevier, 91-100, 2006.
  • V. Nóvak, I. Perfilieva, and J. Mockor. Mathematical Principles of Fuzzy Logic. Kluwe, Dordrech, 1999.
  • U. Straccia. Reasoning within fuzzy description logics. J. Of Artif. Intellig. Research, 14:137-166, 2001.
  • U. Straccia. A fuzzy description logic for the semantic web. In Capturing Intelligence: Fuzzy Logic and the Semantic Web, E. Sánchex, ed, Elsevier, 2006.
  • U. Straccia. Uncertainty and description logic programs over lattices. In Capturing Intelligence: Fuzzy Logic and the Semantic Web, E. Sánchex, ed, Elsevier, 2006.
  • P. Vojtás. Fuzzy reasoning with tunable t-operators. Journal for Advanced Computer Intelligence, 2:121-127, 1998.
  • P. Vojtás. Fuzzy logic programing. Fuzzy Sets and Systems, 124 (3):361-370, 2001.
  • L. A. Zadeh. Fuzzy Sets, Information and Control, 8:338-353, 1965.
  • L. A. Zadeh. Fuzzy Logic. IEEE Computer 21(4): 83-93, 1988.
  • L. A. Zadeh. Fuzzy Logic = Computing with words. IEEE Trans. On Fuzzy Systems, 4: 103-111, 1995.
  • L. A. Zadeh. A New Direction in A. I.: Toward a Computational Theory of Perceptions. A. I. Magazine 22 (1): 73-84, 2001.