[FOM] Book announcement: Handbook of Practical Logic and Automated Reasoning

John R Harrison johnh at ichips.intel.com
Mon Apr 20 14:30:10 EDT 2009

```I'm pleased to announce the availability of my new book on logic and
automated theorem proving. This is intended to be both a survey of the
central results in automated theorem proving and a basic introduction
to mathematical logic, closely intertwined. A notable characteristic
is that all the automated theorem proving techniques described are
accompanied by actual code that the reader can use, or even modify and
otherwise experiment with.

Handbook of Practical Logic and Automated Reasoning

John Harrison

Cambridge University Press 2009

ISBN: 9780521899574

Publisher's Web page: http://www.cambridge.org/9780521899574
Code and resources:   http://www.cl.cam.ac.uk/~jrh13/atp/

You can already get the book from several sellers, and it should be
generally available very soon. Currently the price and availability
seems a bit better in Europe (it was on offer for 56 pounds last

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 Davis-Putnam procedure
2.10 Staalmarck'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 Groebner 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  Goedel'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

John Harrison.

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