Many-Valued Logics 1

Many-valued logics were developed as an attempt to handle
philosophical doubts about the "law of excluded middle" in
classical logic. The first many-valued formal systems were
developed by J. Lukasiewicz in Poland and E.Post in the
U.S.A. in the 1920s, and since then the field has expanded
dramatically as the applicability of the systems to other
philosophical and semantic problems was recognized.
Intuitionisticlogic, for example, arose from deep problems
in the foundations of mathematics. Fuzzy logics,
approximation logics, and probability logics all address
questions that classical logic alone cannot answer. All
these interpretations of many-valued calculi motivate
specific formal systems thatallow detailed mathematical
treatment.
In this volume, the authors are concerned with finite-valued
logics, and especially with three-valued logical calculi.
Matrix constructions, axiomatizations of propositional and
predicate calculi, syntax, semantic structures, and
methodology are discussed. Separate chapters deal with
intuitionistic logic, fuzzy logics, approximation logics,
and probability logics. These systems all find application
in practice, in automatic inference processes, which have
been decisive for the intensive development of these logics.
This volume acquaints the reader with theoretical
fundamentals of many-valued logics. It is intended to be the
first of a two-volume work. The second volume will deal with
practical applications and methods of automated reasoning
using many-valued logics.