## Many-Valued Logics 2: Automated Reasoning and Practical ApplicationsMany-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. |

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### Contents

III | 5 |

IV | 12 |

V | 19 |

VI | 31 |

VII | 37 |

X | 41 |

XI | 42 |

XII | 52 |

XLIV | 178 |

XLV | 181 |

XLVI | 183 |

XLVII | 185 |

XLVIII | 189 |

L | 192 |

LI | 194 |

LII | 195 |

XIII | 54 |

XIV | 67 |

XV | 69 |

XVII | 73 |

XVIII | 80 |

XIX | 88 |

XX | 97 |

XXII | 98 |

XXIII | 99 |

XXIV | 100 |

XXV | 102 |

XXVI | 115 |

XXVII | 117 |

XXVIII | 118 |

XXIX | 119 |

XXX | 122 |

XXXI | 129 |

XXXII | 135 |

XXXIII | 137 |

XXXIV | 147 |

XXXVI | 152 |

XXXVII | 158 |

XXXVIII | 162 |

XXXIX | 167 |

XL | 170 |

XLI | 171 |

XLII | 177 |

### Common terms and phrases

antichain applications arbitrary assume axioms classes classical logic clause Cn-inconsistent Cn(X completes the proof condition attributes connectives Consider consistent contains corresponding decision logic deducible defined as follows definition denoted disjunction Dp(a elements end sequent equivalence relations example exists finite set finite-valued functionally complete fuzzy logic fuzzy set theory Gentzen Hence homomorphism implies inductive assumption inference rules interpretation introduced knowledge base knowledge reduction knowledge representation label language lattice Lemma logical values many-valued logics matrix membership function method Moreover n-valued logics notions O'Hearn operation p-diagram Post algebra predicate calculus premise prenex problem proof tree propositional calculus propositional logic propositional variables prove quantifiers r-basic r-designated represented resolution principle Resolution Proof Systems resolution rule resolutional counterpart respect rough set satisfies semantic tree sequence of formulae set of formulae Stachniak subset substitution symbols tautological Theorem tree TX valuation verifiers

### Popular passages

Page 300 - WA Carnielli. Systematization of finite many-valued logics through the method of tableaux. Journal of Symbolic Logic, 52(2):473-493, 1987. [Carnielli 1991] WA Carnielli. On sequents and tableaux for many-valued logics.

Page v - We hope that the two volumes of the monograph will indeed give the reader an overview of the state of the art...