Many-valued logics were developed as an attempt to handlephilosophical doubts about the "law of excluded middle" inclassical logic. The first many-valued formal systems weredeveloped by J. Lukasiewicz in Poland and E.Post in theU.S.A. in the 1920s, and since then the field has expandeddramatically as the applicability of the systems to otherphilosophical and semantic problems was recognized.Intuitionisticlogic, for example, arose from deep problemsin the foundations of mathematics. Fuzzy logics,approximation logics, and probability logics all addressquestions that classical logic alone cannot answer. Allthese interpretations of many-valued calculi motivatespecific formal systems thatallow detailed mathematicaltreatment.In this volume, the authors are concerned with finite-valuedlogics, and especially with three-valued logical calculi.Matrix constructions, axiomatizations of propositional andpredicate calculi, syntax, semantic structures, andmethodology are discussed. Separate chapters deal withintuitionistic logic, fuzzy logics, approximation logics,and probability logics. These systems all find applicationin practice, in automatic inference processes, which havebeen decisive for the intensive development of these logics.This volume acquaints the reader with theoreticalfundamentals of many-valued logics. It is intended to be thefirst of a two-volume work. The second volume will deal withpractical applications and methods of automated reasoningusing 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 handlephilosophical doubts about the "law of excluded middle" inclassical logic. The first many-valued formal systems weredeveloped by J. Lukasiewicz in Poland and E.Post in theU.S.A. in the 1920s, and since then the field has expandeddramatically as the applicability of the systems to otherphilosophical and semantic problems was recognized.Intuitionisticlogic, for example, arose from deep problemsin the foundations of mathematics. Fuzzy logics,approximation logics, and probability logics all addressquestions that classical logic alone cannot answer. Allthese interpretations of many-valued calculi motivatespecific formal systems thatallow detailed mathematicaltreatment.In this volume, the authors are concerned with finite-valuedlogics, and especially with three-valued logical calculi.Matrix constructions, axiomatizations of propositional andpredicate calculi, syntax, semantic structures, andmethodology are discussed. Separate chapters deal withintuitionistic logic, fuzzy logics, approximation logics,and probability logics. These systems all find applicationin practice, in automatic inference processes, which havebeen decisive for the intensive development of these logics.This volume acquaints the reader with theoreticalfundamentals of many-valued logics. It is intended to be thefirst of a two-volume work. The second volume will deal withpractical applications and methods of automated reasoningusing 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 handlephilosophical doubts about the "law of excluded middle" inclassical logic. The first many-valued formal systems weredeveloped by J. Lukasiewicz in Poland and E.Post in theU.S.A. in the 1920s, and since then the field has expandeddramatically as the applicability of the systems to otherphilosophical and semantic problems was recognized.Intuitionisticlogic, for example, arose from deep problemsin the foundations of mathematics. Fuzzy logics,approximation logics, and probability logics all addressquestions that classical logic alone cannot answer. Allthese interpretations of many-valued calculi motivatespecific formal systems thatallow detailed mathematicaltreatment.In this volume, the authors are concerned with finite-valuedlogics, and especially with three-valued logical calculi.Matrix constructions, axiomatizations of propositional andpredicate calculi, syntax, semantic structures, andmethodology are discussed. Separate chapters deal withintuitionistic logic, fuzzy logics, approximation logics,and probability logics. These systems all find applicationin practice, in automatic inference processes, which havebeen decisive for the intensive development of these logics.This volume acquaints the reader with theoreticalfundamentals of many-valued logics. It is intended to be thefirst of a two-volume work. The second volume will deal withpractical applications and methods of automated reasoningusing 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 handlephilosophical doubts about the "law of excluded middle" inclassical logic. The first many-valued formal systems weredeveloped by J. Lukasiewicz in Poland and E.Post in theU.S.A. in the 1920s, and since then the field has expandeddramatically as the applicability of the systems to otherphilosophical and semantic problems was recognized.Intuitionisticlogic, for example, arose from deep problemsin the foundations of mathematics. Fuzzy logics,approximation logics, and probability logics all addressquestions that classical logic alone cannot answer. Allthese interpretations of many-valued calculi motivatespecific formal systems thatallow detailed mathematicaltreatment.In this volume, the authors are concerned with finite-valuedlogics, and especially with three-valued logical calculi.Matrix constructions, axiomatizations of propositional andpredicate calculi, syntax, semantic structures, andmethodology are discussed. Separate chapters deal withintuitionistic logic, fuzzy logics, approximation logics,and probability logics. These systems all find applicationin practice, in automatic inference processes, which havebeen decisive for the intensive development of these logics.This volume acquaints the reader with theoreticalfundamentals of many-valued logics. It is intended to be thefirst of a two-volume work. The second volume will deal withpractical applications and methods of automated reasoningusing 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.