## An Introduction to Non-Classical LogicThis book is an introduction to non-classical propositional logics. It brings together for the first time in a textbook a range of topics in logic, many of them of relatively recent origin, including modal, conditional, intuitionist, many-valued, paraconsistent, relevant and fuzzy logics. The material is unified by the underlying theme of world-semantics. All of the topics are explained clearly and accessibly, using devices such as tableaux proofs, and their relation to current philosophical issues and debates is discussed. Students with a basic understanding of classical logic will find this an invaluable introduction to an area that has become of central importance in both logic and philosophy, but which, until now, could be studied only through the research literature. It will interest those studying logic, those who need to know about non-classical logics because of their philosophical importance, and, more widely, readers working in mathematics and computer science. |

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Overall, a very good introduction to the topic. Concepts explained well, but not babysitting. Definitely not for students who are not already very comfortable with classical logic.

### Contents

I | 1 |

II | 2 |

III | 3 |

IV | 4 |

V | 8 |

VI | 9 |

VII | 10 |

VIII | 11 |

LXII | 110 |

LXIII | 111 |

LXIV | 114 |

LXVI | 115 |

LXVII | 117 |

LXVIII | 119 |

LXIX | 122 |

LXX | 123 |

IX | 13 |

X | 14 |

XI | 15 |

XII | 17 |

XIV | 18 |

XV | 20 |

XVI | 21 |

XVII | 24 |

XVIII | 28 |

XIX | 29 |

XX | 30 |

XXI | 31 |

XXII | 33 |

XXIII | 35 |

XXIV | 36 |

XXVI | 38 |

XXVII | 40 |

XXVIII | 44 |

XXIX | 47 |

XXX | 48 |

XXXI | 52 |

XXXII | 54 |

XXXIV | 55 |

XXXV | 58 |

XXXVI | 60 |

XXXVII | 62 |

XXXVIII | 63 |

XXXIX | 64 |

XL | 65 |

XLI | 67 |

XLII | 68 |

XLIII | 69 |

XLIV | 71 |

XLV | 72 |

XLVII | 74 |

XLVIII | 77 |

XLIX | 78 |

L | 80 |

LI | 83 |

LII | 88 |

LIII | 91 |

LIV | 93 |

LV | 95 |

LVI | 96 |

LVIII | 99 |

LIX | 101 |

LX | 104 |

LXI | 108 |

LXXI | 125 |

LXXII | 127 |

LXXIII | 128 |

LXXIV | 130 |

LXXV | 131 |

LXXVI | 134 |

LXXVII | 136 |

LXXVIII | 137 |

LXXX | 139 |

LXXXI | 141 |

LXXXII | 144 |

LXXXIII | 147 |

LXXXIV | 151 |

LXXXV | 152 |

LXXXVI | 159 |

LXXXVIII | 160 |

LXXXIX | 162 |

XC | 163 |

XCI | 165 |

XCII | 167 |

XCIII | 168 |

XCIV | 171 |

XCV | 174 |

XCVI | 179 |

XCIX | 182 |

C | 184 |

CI | 188 |

CII | 193 |

CIII | 197 |

CIV | 198 |

CV | 202 |

CVI | 205 |

CVII | 206 |

CVIII | 207 |

CIX | 211 |

CX | 212 |

CXI | 214 |

CXII | 218 |

CXIII | 221 |

CXIV | 222 |

CXV | 225 |

CXVI | 226 |

CXVIII | 229 |

231 | |

237 | |

239 | |

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### Common terms and phrases

A A B A D B antecedent apply the rule argument B A C ceteris paribus chapter classical logic complete with respect Completeness Lemma completeness proofs conditional logics connectives consider construction counter-model definition disjunction example extension fA(w fact faithful finite formula Hence induced interpretation induction hypothesis inference intuitionism intuitionist logic invalid laws logical truth many-valued logic material conditional modus ponens negation node non-normal worlds normal modal logics normal worlds objects obtained occurs open branch possible worlds possible-world semantics premises problem propositional calculus propositional logic propositional parameter relational semantics relevant logics Routley Rxyz sentence similar sorites sound and complete Soundness Lemma SOUNDNESS THEOREM sphere sub-logic suppose tableau rules takes the value terms of truth ternary relation things tion tional true nor false truth conditions truth functions truth preservation truth value truth-value gaps truth-value gluts vw(A