A Computational Logic Handbook
Formerly Notes and Reports in Computer Science and Applied Mathematics
Published on 10. May 2014
426 pages
978-1-4832-7778-3 (ISBN)
Description
Perspectives in Computing: A Computational Logic Handbook contains a precise description of the logic and a detailed reference guide to the associated mechanical theorem proving system, including a primer for the logic as a functional programming language, an introduction to proofs in the logic, and a primer for the mechanical theorem. The publication first offers information on a primer for the logic, formalization within the logic, and a precise description of the logic. Discussions focus on induction and recursion, quantification, explicit value terms, dealing with features and omissions, elementary mathematical relationships, Boolean operators, and conventional data structures. The text then takes a look at proving theorems in the logic, mechanized proofs in the logic, and an introduction to the system. The text examines the processes involved in using the theorem prover, four classes of rules generated from lemmas, and aborting or interrupting commands. Topics include executable counterparts, toggle, elimination of irrelevancy, heuristic use of equalities, representation of formulas, type sets, and the crucial check points in a proof attempt. The publication is a vital reference for researchers interested in computational logic.
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Robert S. Boyer | J. Strother Moore
The Computational Logic Handbook
Book
11/1997
Academic Press
€74.22
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Content
¿Part I. The Logic 1. Introduction 1.1. A Summary of the Logic and Theorem Prover 1.2. Some Interesting Applications 1.3. The Organization of this Handbook 2. A Primer for the Logic 2.1. Syntax 2.2. Boolean Operators 2.3. Data Types 2.4. Extending the Syntax 2.5. Conventional Data Structures 2.6. Defining Functions 2.7. Recursive Functions on Conventional Data Structures 2.8. Ordinals 2.9. Useful Functions 2.10. The Interpreter 2.11. The General Purpose Quantifier 3. Formalization Within the Logic 3.1. Elementary Programming Examples 3.2. Elementary Mathematical Relationships 3.3. Dealing with Omissions 3.4. Dealing with Features 3.5. Nondeterminism 3.6. Embedded Formal Systems 4. A Precise Description of the Logic 4.1. Apologia 4.2. Outline of the Presentation 4.3. Formal Syntax 4.4. Embedded Propositional Calculus and Equality 4.5. The Shell Principle and the Primitive Data Types 4.6. Explicit Value Terms 4.7. The Extended Syntax-Abbreviations I 4.8. Ordinals 4.9. Useful Function Definitions 4.10. The Formal Metatheory 4.11. Quantification 4.12. Subrps and Non-Subrps 4.13. Induction and Recursion 5. Proving Theorems in the Logic 5.1. Propositional Calculus with Equality 5.2. Theorems about If and Propositional Functions 5.3. Simple Theorems about Nil, Cons, and Append 5.4. The Associativity of Append 5.5. Simple Arithmetic 5.6. Structural InductionPart II. Using the System 6. Mechanized Proofs in the Logic 6.1. The Organization of Our Theorem Prover 6.2. An Example Proof-Associativity of Times 6.3. An Explanation of the Proof 7. An Introduction to the System 7.1. The Data Base of Rules 7.2. Logical Events 7.3. A Summary of the Commands 7.4. Errors 7.5. Aborting a Command 7.6. Syntax and the User Interface 7.7. Confusing Lisp and the Logic 8. A Sample Session with the Theorem Prover 9. How to Use the Theorem Prover 9.1. Reverse-Reverse Revisited-Cooperatively 9.2. Using Lisp and a Text Editor as the Interface 9.3. The Crucial Check Points in a Proof Attempt 10. How the Theorem Prover Works 10.1. The Representation of Formulas 10.2. Type Sets 10.3. Simplification 10.4. Elimination of Destructors 10.5. Heuristic Use of Equalities 10.6. Generalization 10.7. Elimination of Irrelevancy 10.8. Induction 11. The Four Classes of Rules Generated from Lemmas 11.1. Rewrite 11.2. Meta 11.3. Elim 11.4. Generalize 12. Reference Guide 12.1. Aborting or Interrupting Commands 12.2. Accumulated-Persistence 12.3. Add-Axiom 12.4. Add-Shell 12.5. Boot-Strap 12.6. Break-Lemma 12.7. Break-Rewrite 12.8. Ch 12.9. Chronology 12.10. Compile-Uncompiled-Defns 12.11. Data-Base 12.12. Dcl 12.13. Defn 12.14. Disable 12.15. Do-Events 12.16. Elim 12.17. Enable 12.18. Errors 12.19. Event Commands 12.20. Events-Since 12.21. Executable Counterparts 12.22. Explicit Values 12.23. Extensions 12.24. Failed-Events 12.25. File Names 12.26. Generalize 12.27. Maintain-Rewrite-Path 12.28. Make-Lib 12.29. Meta 12.30. Names-Events, Functions, and Variables 12.31. Note-Lib 12.32. Nqthm Mode 12.33. Ppe 12.34. Prove 12.35. Proveall 12.
