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. |
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 |
LXIX | 119 |
LXX | 122 |
LXXI | 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 |
LXXII | 125 |
LXXIII | 127 |
LXXIV | 128 |
LXXV | 130 |
LXXVI | 131 |
LXXVII | 134 |
LXXVIII | 136 |
LXXIX | 137 |
LXXXI | 139 |
LXXXII | 141 |
LXXXIII | 144 |
LXXXIV | 147 |
LXXXV | 151 |
LXXXVI | 152 |
LXXXVII | 159 |
LXXXIX | 160 |
XC | 162 |
XCI | 163 |
XCII | 165 |
XCIII | 167 |
XCIV | 168 |
XCV | 171 |
XCVI | 174 |
XCVII | 179 |
C | 182 |
CI | 184 |
CII | 188 |
CIII | 193 |
CIV | 197 |
CV | 198 |
CVI | 202 |
CVII | 205 |
CVIII | 206 |
CIX | 207 |
CX | 211 |
CXI | 212 |
CXII | 214 |
CXIII | 218 |
CXIV | 221 |
CXV | 222 |
CXVI | 225 |
CXVII | 226 |
CXIX | 229 |
| 231 | |
| 237 | |
| 239 | |
Other editions - View all
Common terms and phrases
antecedent apply the rule argument ceteris paribus chapter classical logic complete with respect Completeness Lemma conditional logics consider construction counter-model definition disjunction example extension f₁(w fa(w fact faithful false at w₁ finite formula Hence induced interpretation induction hypothesis inference intuitionism intuitionist logic 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 q is true 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 at f(i true at w₁ true nor false truth conditions truth functions truth preservation truth value truth-value gaps truth-value gluts vw(A