The Kurt Gödel Society


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Aim of the Workshop

Due mainly to the pioneering work of L. Zadeh, it is widely recognized
that fuzzy logic is the basis for reasoning with vagueness. Nowadays,
the literature on fuzzy logic is nearly unsurmountable.
However, only in recent years a sound mathematical foundation
for this field is emerging. As a consequence of this research,
it has been shown that reasoning in fuzzy logic may be formalized in
certain infinite-valued logics, namely, Lukasiewicz, Gödel and
Product logic.
At the propositional level, these logics jointly allow to represent all
continuous t-norm based logics. The latter are the main tool to deal with imprecise

Most practical and scientific applications require however deduction systems
in first-order logics. In contrast to propositional logic, it has been shown that most
of the above mentioned t-norm based logics are not recursively axiomatizable with respect to the natural first-order extension of their propositional semantics. A denotable exception is Gödel logic which is the logic of ordinal relations of truth-values.
This logic cannot be applied in circumstances, where quantitative
information counts. Therefore various groups of scientists have started to express doubts about the true nature of the underlying semantics, especially in the case of
Lukasiewicz logic which is the most important of the logics considered.

This workshop is intended to bring together the most relevant European
scientists from the fields of logic, mathematics, computer science and engineering.

Their combined knowledge should lead to the developement and standardization
of semantics concepts for fuzzy logic adequate both from the foundational
and applicative point of view.