The Resource Handbook of practical logic and automated reasoning, John Harrison

Handbook of practical logic and automated reasoning, John Harrison

Label
Handbook of practical logic and automated reasoning
Title
Handbook of practical logic and automated reasoning
Statement of responsibility
John Harrison
Title variation
Handbook of Practical Logic & Automated Reasoning
Creator
Author
Subject
Language
eng
Summary
The sheer complexity of computer systems has meant that automated reasoning, i.e. the ability of computers to perform logical inference, has become a vital component of program construction and of programming language design. This book meets the demand for a self-contained and broad-based account of the concepts, the machinery and the use of automated reasoning. The mathematical logic foundations are described in conjunction with practical application, all with the minimum of prerequisites. The approach is constructive, concrete and algorithmic: a key feature is that methods are described with reference to actual implementations (for which code is supplied) that readers can use, modify and experiment with. This book is ideally suited for those seeking a one-stop source for the general area of automated reasoning. It can be used as a reference, or as a place to learn the fundamentals, either in conjunction with advanced courses or for self study
Cataloging source
UkCbUP
http://library.link/vocab/creatorDate
1966-
http://library.link/vocab/creatorName
Harrison, J.
Dewey number
006.333
Index
index present
LC call number
QA76.9.L63
LC item number
H38 2009
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
Computer logic
Label
Handbook of practical logic and automated reasoning, John Harrison
Link
https://doi.org/10.1017/CBO9780511576430
Instantiates
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Extent
1 online resource (xix, 681 pages)
Form of item
online
Isbn
9780511576430
Isbn Type
(ebook)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote
System control number
(UkCbUP)CR9780511576430
Label
Handbook of practical logic and automated reasoning, John Harrison
Link
https://doi.org/10.1017/CBO9780511576430
Publication
Note
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Extent
1 online resource (xix, 681 pages)
Form of item
online
Isbn
9780511576430
Isbn Type
(ebook)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
digital, PDF file(s).
Specific material designation
remote
System control number
(UkCbUP)CR9780511576430

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