| Preface | p. xi |
| Introduction | p. 1 |
| Issues of Vagueness | p. 1 |
| Vagueness Defined | p. 5 |
| The Problem of the Fringe | p. 6 |
| Preview of the Rest of the Book | p. 7 |
| History and Scope of Fuzzy Logic | p. 8 |
| Tall People | p. 10 |
| Exercises | p. 10 |
| Review of Classical Propositional Logic | p. 12 |
| The Language of Classical Propositional Logic | p. 12 |
| Semantics of Classical Propositional Logic | p. 13 |
| Normal Forms | p. 18 |
| An Axiomatic Derivation System for Classical Propositional Logic | p. 21 |
| Functional Completeness | p. 32 |
| Decidability | p. 35 |
| Exercises | p. 36 |
| Review of Classical First-Order Logic | p. 39 |
| The Language of Classical First-Order Logic | p. 39 |
| Semantics of Classical First-Order Logic | p. 42 |
| An Axiomatic Derivation System for Classical First-Order Logic | p. 49 |
| Exercises | p. 55 |
| Alternative Semantics for Truth-Values and Truth-Functions: Numeric Truth-Values and Abstract Algebras | p. 57 |
| Numeric Truth-Values for Classical Logic | p. 57 |
| Boolean Algebras and Classical Logic | p. 59 |
| More Results about Boolean Algebras | p. 63 |
| Exercises | p. 69 |
| Three-Valued Propositional Logics: Semantics | p. 71 |
| Kleene's "Strong" Three-Valued Logic | p. 71 |
| Lukasiewicz's Three-Valued Logic | p. 76 |
| Bochvar's Three-Valued Logics | p. 80 |
| Evaluating Three-Valued Systems; Quasi-Tautologies and Quasi-Contradictions | p. 84 |
| Normal Forms | p. 89 |
| Questions of Interdefinability between the Systems and Functional Completeness | p. 90 |
| Lukasiewicz's System Expanded | p. 94 |
| Exercises | p. 96 |
| Derivation Systems for Three-Valued Propositional Logic | p. 100 |
| An Axiomatic System for Tautologies and Validity in Three-Valued Logic | p. 100 |
| A Pavelka-Style Derivation System for L[subscript 3] | p. 114 |
| Exercises | p. 126 |
| Three-Valued First-Order Logics: Semantics | p. 130 |
| A First-Order Generalization of L[subscript 3] | p. 130 |
| Quantifiers Based on the Other Three-Valued Systems | p. 137 |
| Tautologies, Validity, and "Quasi-" Semantic Concepts | p. 140 |
| Exercises | p. 143 |
| Derivation Systems for Three-Valued First-Order Logic | p. 146 |
| An Axiomatic System for Tautologies and Validity in Three-Valued First-Order Logic | p. 146 |
| A Pavelka-Style Derivation System for L[subscript 3 for all] | p. 153 |
| Exercises | p. 159 |
| Alternative Semantics for Three-Valued Logic | p. 161 |
| Numeric Truth-Values for Three-Valued Logic | p. 161 |
| Abstract Algebras for L[subscript 3], K[superscript S subscript 3], B[superscript I subscript 3], and B[superscript E subscript 3] | p. 163 |
| MV-Algebras | p. 167 |
| Exercises | p. 172 |
| The Principle of Charity Reconsidered and a New Problem of the Fringe | p. 174 |
| Fuzzy Propositional Logics: Semantics | p. 176 |
| Fuzzy Sets and Degrees of Truth | p. 176 |
| Lukasiewicz Fuzzy Propositional Logic | p. 178 |
| Tautologies, Contradictions, and Entailment in Fuzzy Logic | p. 180 |
| N-Tautologies, Degree-Entailment, and N-Degree-Entailment | p. 183 |
| Fuzzy Consequence | p. 190 |
| Fuzzy Generalizations of K[superscript S subscript 3], B[superscript I subscript 3], and B[superscript E subscript 3]; the Expressive Power of Fuzzy[subscript L] | p. 192 |
| T-Norms, T-Conorms, and Implication in Fuzzy Logic | p. 194 |
| Godel Fuzzy Propositional Logic | p. 199 |
| Product Fuzzy Propositional Logic | p. 202 |
| Fuzzy External Assertion and Negation | p. 203 |
| Exercises | p. 206 |
| Fuzzy Algebras | p. 212 |
| More on MV-Algebras | p. 212 |
| Residuated Lattices and BL-Algebras | p. 214 |
| Zero and Unit Projections in Algebraic Structures | p. 219 |
| Exercises | p. 220 |
| Derivation Systems for Fuzzy Propositional Logic | p. 223 |
| An Axiomatic System for Tautologies and Validity in Fuzzy[subscript L] | p. 223 |
| A Pavelka-Style Derivation System for Fuzzy[subscript L] | p. 229 |
| An Alternative Axiomatic System for Tautologies and Validity in Fuzzy[subscript L], Based on BL-Algebras | p. 245 |
| An Axiomatic System for Tautologies and Validity in Fuzzy[subscript G] | p. 249 |
| An Axiomatic System for Tautologies and Validity in Fuzzy[subscript P] | p. 252 |
| Summary: Comparision of Fuzzy[subscript L], Fuzzy[subscript G], and Fuzzy[subscript P] and Their Derivation Systems | p. 254 |
| External Assertion Axioms | p. 254 |
| Exercises | p. 256 |
| Fuzzy First-Order Logics: Semantics | p. 262 |
| Fuzzy Interpretations | p. 262 |
| Lukasiewicz Fuzzy First-Order Logic | p. 263 |
| Tautologies and Other Semantic Concepts | p. 266 |
| Lukasiewicz Fuzzy Logic and the Problems of Vagueness | p. 268 |
| Godel Fuzzy First-Order Logic | p. 278 |
| Product Fuzzy First-Order Logic | p. 280 |
| The Sorites Paradox: Comparison of Fuzzy[subscript L for all], Fuzzy[subscript G for all], and Fuzzy[subscript P for all] | p. 282 |
| Exercises | p. 282 |
| Derivation Systems for Fuzzy First-Order Logic | p. 287 |
| Axiomatic Systems for Fuzzy First-Order Logic: Overview | p. 287 |
| A Pavelka-Style Derivation System for Fuzzy[subscript L for all] | p. 288 |
| An Axiomatic Derivation System for Fuzzy[subscript G for all] | p. 294 |
| Combining Fuzzy First-Order Logical Systems; External Assertion | p. 297 |
| Exercises | p. 298 |
| Extensions of Fuzziness | p. 300 |
| Fuzzy Qualifiers: Hedges | p. 300 |
| Fuzzy "Linguistic" Truth-Values | p. 303 |
| Other Fuzzy Extensions of Fuzzy Logic | p. 305 |
| Exercises | p. 306 |
| Fuzzy Membership Functions | p. 309 |
| Defining Membership Functions | p. 309 |
| Empirical Construction of Membership Functions | p. 312 |
| Logical Relevance? | p. 313 |
| Exercises | p. 313 |
| Basics of Countability and Uncountability | p. 315 |
| Bibliography | p. 321 |
| Index | p. 327 |
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