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Many-valued logics are becoming increasingly important in all areas
of computer science. This is the second volume of an authoritative
two-volume handbook on many valued logics by two leading figures in
the field. While the first volume was mainly concerned with
theoretical foundations, this volume emphasizes automated
reasoning, practical applications, and the latest developments in
fuzzy logic and rough set theory. Among the applications presented
are those in software specification and electronic circuit
verification.
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.
Many-valued logics is becoming increasingly important in many branches of science. This is the second volume of a comprehensive two-volume handbook on many-valued logics by two leading members of the famous Polish school of logic. While the first volume of 1992 was mainly concerned with theoretical foundations, this volume emphasizes automated reasoning, practical applications, and latest developments in closely related fields, such as fuzzy logics and rough set theory. It offers an extensive overview of Gentzen deduction systems and multi-sequential systems in many-valued logics and shows the application of the resolution principle to this logics. It discusses applications in such areas as software specification and electronic circuit verification and presents fuzzy logics and rough set theory in detail.
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.
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