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Mathematical logic and foundations


Handbook of Mathematical Fuzzy Logic. Volume 1

Petr Cintula, Petr Hájek and Carles Noguera, eds

Originating as an attempt to provide solid logical foundations
for fuzzy set theory, and motivated also by philosophical
and computational problems of vagueness and imprecision,
Mathematical Fuzzy Logic (MFL) has become a significant
subfield of mathematical logic. Research in this area focuses
on many-valued logics with linearly ordered truth values and
has yielded elegant and deep mathematical theories and
challenging problems, thus continuing to attract an ever
increasing number of researchers.

This two-volume handbook provides an up-to-date systematic
presentation of the best-developed areas of MFL. Its intended
audience is researchers working on MFL or related fields, who
may use the text as a reference book, and anyone looking for
a comprehensive introduction to MFL. Despite being located
in the realm of pure mathematical logic, this handbook will
also be useful for readers interested in logical foundations of
fuzzy set theory or in a mathematical apparatus suitable for
dealing with some philosophical and linguistic issues related
to vagueness.

The first volume contains a gentle introduction to MFL, a
presentation of an abstract algebraic framework for MFL,
chapters on proof theory and algebraic semantics of fuzzy
logics, and, finally, an algebraic study of Hájek’s logic BL.
The second volume is devoted to Łukasiewicz logic and MValgebras,
Gödel-Dummett logic and its variants, fuzzy logics
in expanded propositional languages, studies of functional
representations for fuzzy logics and their free algebras,
computational complexity of propositional logics, and
arithmetical complexity of first-order logics.

See inside

21 December 2011


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