Table of Contents for: Handbook of practical logic and automate

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Handbook of practical logic and automated reasoning /

John Harrison.

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