Logic and the set theory - Lecture 9: Predicate Calculus

More documents

Recommendations

Info

Inference rules for the universal quantifiersInference rules for the universal quantifiersThe inferences rules of propositional calculus hold here also.Here we use ⊢ since this is an inference without models.Universal elimination or universal instantiation ∀E:Given a wff ∀βφ, we may infer φ α/β replacing each occurence of βwith some name letter α. (could be a new one withoutassumptions.)Example: ∀x(M 1 x → M 2 x), M 1 S ⊢ M 2 S.S. Choi (KAIST) Logic and set theory October 7, 2012 5 / 26
Inference rules for the universal quantifiersInference rules for the universal quantifiersThe inferences rules of propositional calculus hold here also.Here we use ⊢ since this is an inference without models.Universal elimination or universal instantiation ∀E:Given a wff ∀βφ, we may infer φ α/β replacing each occurence of βwith some name letter α. (could be a new one withoutassumptions.)Example: ∀x(M 1 x → M 2 x), M 1 S ⊢ M 2 S.1. ∀x(M 1 x → M 2 x). A, 2. M 1 S A, 3. M 1 S → M 2 S. 4. M 2 S.S. Choi (KAIST) Logic and set theory October 7, 2012 5 / 26
Page 2 and 3: IntroductionAbout this lectureReaso
Page 10 and 11: IntroductionSome helpful references
Page 18 and 19: Inference rules for the universal q
Page 66 and 67: Inference rules for existential qua
Page 72 and 73:
Inference rules for existential qua
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
show all

Logic and the set theory - Lecture 9: Predicate Calculus

Create successful ePaper yourself

Delete template?

Save as template?