Fuzzy logics are many-valued logics that are well suited to
reasoning in the context of vagueness. They provide the basis for
the wider field of Fuzzy Logic, encompassing diverse areas such as
fuzzy control, fuzzy databases, and fuzzy mathematics. This book
provides an accessible and up-to-date introduction to this
fast-growing and increasingly popular area. It focuses in
particular on the development and applications of "proof-theoretic"
presentations of fuzzy logics; the result of more than ten years of
intensive work by researchers in the area, including the authors.
In addition to providing alternative elegant presentations of fuzzy
logics, proof-theoretic methods are useful for addressing
theoretical problems (including key standard completeness results)
and developing efficient deduction and decision algorithms.
Proof-theoretic presentations also place fuzzy logics in the
broader landscape of non-classical logics, revealing deep relations
with other logics studied in Computer Science, Mathematics, and
Philosophy. The book builds methodically from the semantic origins
of fuzzy logics to proof-theoretic presentations such as Hilbert
and Gentzen systems, introducing both theoretical and practical
applications of these presentations.
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