22 March 2004, Mathematical Principles of Fuzzy Logic, Vilem Novak (University of Ostrava)

This talk is a brief overview of fundamental concepts of the mathematical fuzzy logic. The key idea behind fuzzy logic is the idea of grades standing behind our reasoning when dealing with various aspects of the vagueness phenomenon.

Mathematical fuzzy logic is not a unique theory but a group of formal theories based on various kinds of structures of truth values. The starting point is the structure of residuated lattice. Its extensions provide various kinds of fuzzy logics. In the talk, we will briefly characterize the fundamental structures of truth values. Then, we will focus on three essential formal systems:

1. Basic fuzzy propositional and predicate logic (BL-logic)
2. Fuzzy propositional and predicate logic with evaluated syntax (based on Lukasiewicz MV-algebra of truth values)
3. Higher order fuzzy logics (fuzzy type theory)

All fuzzy logics enjoy the completeness property. Because of the completeness, fuzzy logic is suitable for various kinds of applications. We will only mention formalisation of the sorites paradox which plays a crucial role in a ll discussions on the vagueness phenomenon.

For more information, or contact either Jan van Eijck (Jan.van.Eijck at cwi.nl) or Benedikt Löwe (bloewe at science.uva.nl).