Many-Valued Logics (Oxford Logic Guides, 25)

This book provides an incisive, basic introduction to many-valued logics and to the constructions that are "many-valued" at their origin. Using the matrix method, the author sheds light on the profound problems of many-valuedness criteria and its classical characterizations. The book also includes information concerning the main systems of many-valued logic, related axiomatic constructions, and conceptions inspired by many-valuedness. With its selective bibliography and many useful historical references, this book provides logicians, computer scientists, philosophers, and mathematicians with a valuable survey of the subject. 1. The Classical Logic. 1.1. Truth-tables. 1.2. Propositional Tautologies. 1.3. Functional Completeness. 1.4. Axiomatization Of Cpc. 1.5. Predicate Calculus. 1.6. Algebraization -- 2. The Third Logical Value Of Lukasiewicz. 2.1. Lukasiewicz And The Lvov-warsaw School. 2.2. Three-valued Logic. 2.3. Modality And Three-valuedness. 2.4. Interpretation Difficulties -- 3. Logic Algebras And Matrices. 3.1. Language And Logic Algebras. 3.2. Functional Completeness Of Finite Algebras. 3.3. Logical Matrices -- 4. Many-valuedness. 4.1. Two Criteria. 4.2. Structurality And Many-valuedness. 4.3. Finiteness And Deduction -- 5. Lukasiewicz Logics. 5.1. Fundamental Properties. 5.2. Definability In Lukasiewicz Matrices. 5.3. Axiomatization. 5.4. Algebraic Interpretations -- 6. Post Logics. 6.1. Post Matrices. 6.2. Interpretation. 6.3. Algebraic Form Of Post Logics. 6.4. Axiomatization Of Functionally Complete Systems Of N-valued Logic -- 7. Three-valuedness Of Kleene And Bochvar. 7.1. Logic Of Indeterminacy. 7.2. Bochvar Logic. 7.3. Partial Logics -- 8. Standard Properties Of Many-valued Constructions. 8.1. Standard Conditions. 8.2. Axiomatization. 8.3. Standard Matrix Consequence -- 9. Probability And Many-valuedness. 9.1. Logical Probability. 9.2. Operationalistic Conception Of Subjective Probability -- 10. Classical Characterization Of Many-valued Logics. 10.1. Suszko's Thesis. 10.2. Scott's Method. 10.3. Urquhart's Interpretation -- 11. Quantifiers In Many-valued Logic. 11.1. Ordinary Predicate Calculi. 11.2. Set Theory And Many-valued Logic. 11.3. Generalized Quantifiers -- 12. Intuitionism And The Modal Logics Of Lewis. 12.1. Intuitionistic Logic. 12.2. Modal Logics 54 And 55. 12.3. Remarks On Quantification -- 13. Fuzzy Sets And Zadeh Logic. 13.1. Fuzzy Sets And Logics Of Imprecise Concepts. 13.2. Fuzzy Logic -- 14. Applications And Significance Of The Topic. 14.1. Independence Of Axioms. 14.2. Formalization Of Intensional Functions. 14.3. Many-valued Algebras And Switching Theory. 14.4. Many-valuedness In Computer Science. Grzegorz Malinowski. Includes Bibliographical References And Indexes. 'Many-valued Logics' attempts an elementary exposition of the topics connected with logical many-valueness. It provides readers with a stimulating discussion which focuses on the constructions being "many-valued" at their origin, i.e. those obtained through intended introduction of logical values next to truth and falsity.