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1.

電子ジャーナル

EJ
出版情報: ACM Digital Library , UNITED STATES : Association for Computing Machinery
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2.

電子ジャーナル

EJ
出版情報: ACM Digital Library , New York, NY : Association for Computing Machinery
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3.

電子ジャーナル

EJ
出版情報: ACM Digital Library , NETHERLANDS : Springer US
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4.

電子ジャーナル

EJ
出版情報: ACM Digital Library , [New York] : ACM
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5.

電子ジャーナル

EJ
出版情報: ACM Digital Library , New York, N.Y. : Association for Computing Machinery
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6.

電子ジャーナル

EJ
出版情報: ACM Digital Library , [New York, N.Y.] : Association for Computing Machinery
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7.

電子ジャーナル

EJ
出版情報: ACM Digital Library , [New York, N.Y., etc.] : Association for Computing Machinery, Special Interest Group on Computer Science Education.
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8.

電子ジャーナル

EJ
出版情報: ACM Digital Library , UNITED STATES : Association for Computing Machinery
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9.

電子ジャーナル

EJ
出版情報: ACM Digital Library , New York, N.Y. : ACM Special Interest Group on Computer Architecture
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10.

電子ブック

EB
John Harrison
出版情報: Cambridge University Press Online Books , Cambridge University Press, 2009
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目次情報: 続きを見る
Preface
Introduction / 1:
What is logical reasoning? / 1.1:
Calculemus! / 1.2:
Symbolism / 1.3:
Boole's algebra of logic / 1.4:
Syntax and semantics / 1.5:
Symbolic computation and OCaml / 1.6:
Parsing / 1.7:
Prettyprinting / 1.8:
Propositional logic / 2:
The syntax of propositional logic / 2.1:
The semantics of propositional logic / 2.2:
Validity, satisfiability and tautology / 2.3:
The De Morgan laws, adequacy and duality / 2.4:
Simplification and negation normal form / 2.5:
Disjunctive and conjunctive normal forms / 2.6:
Applications of propositional logic / 2.7:
Definitional CNF / 2.8:
The Davis-Putnam procedure / 2.9:
Stålmarck's method / 2.10:
Binary decision diagrams / 2.11:
Compactness / 2.12:
First-order logic / 3:
First-order logic and its implementation / 3.1:
Parsing and printing / 3.2:
The semantics of first-order logic / 3.3:
Syntax operations / 3.4:
Prenex normal form / 3.5:
Skolemization / 3.6:
Canonical models / 3.7:
Mechanizing Herbrand's theorem / 3.8:
Unification / 3.9:
Tableaux / 3.10:
Resolution / 3.11:
Subsumption and replacement / 3.12:
Refinements of resolution / 3.13:
Horn clauses and Prolog / 3.14:
Model elimination / 3.15:
More first-order metatheorems / 3.16:
Equality / 4:
Equality axioms / 4.1:
Categoricity and elementary equivalence / 4.2:
Equational logic and completeness theorems / 4.3:
Congruence closure / 4.4:
Rewriting / 4.5:
Termination orderings / 4.6:
Knuth-Bendix completion / 4.7:
Equality elimination / 4.8:
Paramodulation / 4.9:
Decidable problems / 5:
The decision problem / 5.1:
The AE fragment / 5.2:
Miniscoping and the monadic fragment / 5.3:
Syllogisms / 5.4:
The finite model property / 5.5:
Quantifier elimination / 5.6:
Presburger arithmetic / 5.7:
The complex numbers / 5.8:
The real numbers / 5.9:
Rings, ideals and word problems / 5.10:
Gröbner bases / 5.11:
Geometric theorem proving / 5.12:
Combining decision procedures / 5.13:
Interactive theorem proving / 6:
Human-oriented methods / 6.1:
Interactive provers and proof checkers / 6.2:
Proof systems for first-order logic / 6.3:
LCF implementation of first-order logic / 6.4:
Propositional derived rules / 6.5:
Proving tautologies by inference / 6.6:
First-order derived rules / 6.7:
First-order proof by inference / 6.8:
Interactive proof styles / 6.9:
Limitations / 7:
Hilbert's programme / 7.1:
Tarski's theorem on the undefinability of truth / 7.2:
Incompleteness of axion systems / 7.3:
Gödel's incompleteness theorem / 7.4:
Definability and decidability / 7.5:
Church's theorem / 7.6:
Further limitative results / 7.7:
Retrospective: the nature of logic / 7.8:
Mathematical background / Appendix 1:
OCaml made light of / Appendix 2:
Parsing and printing of formulas / Appendix 3:
References
Index
Preface
Introduction / 1:
What is logical reasoning? / 1.1:
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