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| Anil Nerode 康奈尔大学数学系的创始人和教授，于1956年在芝加哥大学获得博士学位。他的研究领域包括数理逻辑、自动机、可计算理论、混合系统等。除本书外，他还与其他人合著了《Effective Completeness Theorems for Modal Logic》、《Tableaux for Constructive Concurrent Dynamic Logic》、《Logic，Categories，Lambda Calculus》等书。. Richard A．Shore 康奈尔大学数学教授，于1972年在麻省理工学院获得博士学位。他的研究领域包括数理逻辑、递归论、集合论等。... .. << 查看详细 |
| preface introduction. i propositional logic 1 orders and trees 2 propositions. connectives and truth tables 3 truth assignments and valuations 4 tableau proofs in propositional calculus 5 soundness and completeness of tableau proofs 6 deductions from premises and compactness 7 an axiomatic approach* 8 resolution 9 refining resolution 10 linear resolution. horn clauses and prolog ii predicate logic 1 predicates and quantifiers 2 the language: terms and formulas 3 formation trees. structures and lists 4 semantics: meaning and truth 5 interpretations of prolog programs 6 proofs: complete systematic tableaux .7 soundness and completeness of tableau proofs 8 an axiomatic approach* 9 prenex normal form and skolemization 10 herbrand's theorem 11 unification 12 the unification algorithm 13 resolution 14 refining resolution: linear resolution iii prolog 1 sld-resolution 2 implementations: searching and backtracking 3 controlling the implementation: cut 4 termination conditions for prolog programs 5 equality 6 negation as failure 7 negation and nonmonotonic logic 8 computability and undecidability iv modal logic.. 1 possibility and necessity; knowledge or belief 2 frames and forcing 3 modal tableaux 4 soundness and completeness 5 modal axioms and special accessibility relations 6 an axiomatic approach* v intuitionistic logic 1 intuitionism and constructivism 2 frames and forcing 3 intuitionistic tableaux 4 soundness and completeness 5 decidability and undecidability 6 a comparative guide vi elements of set theory 1 some basic axioms of set theory 2 boole's algebra of sets 3 relations. functions and the power set axiom 4 the natural numbers. arithmetic and infinity 5 replacement. choice and foundation 6 zermelo-fraenkel set theory in predicate logic 7 cardinality: finite and countable 8 ordinal numbers 9 ordinal arithmetic and transfinite induction 10 transfinite recursion. choice and the ranked universe 11 cardinals and cardinal arithmetic appendix a: an historical overview 1 calculus 2 logic 3 leibniz's dream 4 nineteenth century logic 5 nineteenth century foundations of mathematics 6 twentieth century foundations of mathematics 7 early twentieth century logic 8 deduction and computation 9 recent automation of logic and prolog 10 the future appendix b: a genealogical database bibliography index of symbols index of terms... |
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