354 Georg Cantor, 245 George Boole, 26 Gerhard Gentzen, 75 Giuseppe Peano, 253 Gottlob Frege, 107 graph of a function, 239 greatest lower bound, 241 Henkin theory, 214 extension of a theory maximal theory, 216 model, 215 Herbrand interpretation, 212 structure, 212 universe, 194, 212 Hilary Putnam, 85 Hilbert-style system, 52 Hugh MacColl, 33 Hyperresolution, 203 Idempotency, 30, 31 identity, 140, 238 implication, contrapositive, 24 converse, 24 falacy, 24 derivative, 24 inverse, 24 falacy, 24 indirect proof, 224 induction principle, 40 inductive hypothesis, 248 inference propositional, 21 inference rule instance, 21 premise of, 21 propositional, 21 infimum, 241 initial elements, 37 injection, 236 Index instance first-order, 105 interpretation, 108 standard, 111 intersection, 234 introduction rule, 69 intuitionistic logic, 70 Jaakko Hintikka, 68 Jacques Herbrand, 208 Jan Łukasiewicz, 94 John Alan Robinson, 209 John Venn, 158 Kurt Găodel, 220 language first-order, 99 propositional, law of excluded middle, 11 of non-contradiction, 11 De Morgan, 28 logical, 11 least upper bound, 241 Leon Henkin, 221 Leonid Levin, 88 Lewis Carroll, 158 linear order, 239 literal, 77 first-order, 187, 190 logic classical, 96 predicate, 96 first-order, 96 logic program, 256 logic programming, 255 rule body, 256 clause-based, 256 head, 256 logical connective propositional, logical consequence first-order, 137 propositional, 18