Book:M. Ben-Ari/Mathematical Logic for Computer Science

Subject Matter

 * Mathematical Logic
 * Computer Science

Contents

 * Preface


 * 1. Introduction
 * 1.1 The origins of mathematical logic
 * 1.2 Propositional and predicate calculus
 * 1.3 Theorem provers and logic programming
 * 1.4 Non-standard logics


 * 2. Propositional calculus
 * 2.1 Boolean operators
 * 2.2 Propositional formulas
 * 2.3 Boolean interpretations
 * 2.4 Logical equivalence and substitution
 * 2.5 Satisfiability, validity and consequence
 * 2.6 Semantic tableaux
 * 2.7 Deductive proofs
 * 2.8 Gentzen systems
 * 2.9 Hilbert systems
 * 2.10 Resolution
 * 2.11 Variant forms of the deductive systems *
 * 2.12 Complexity *
 * 2.13 Exercises


 * 3. Predicate calculus
 * 3.1 Relations and predicates
 * 3.2 predicate formulas
 * 3.3 Interpretations
 * 3.4 Logical equivalence and substitution
 * 3.5 Semantic tableaux
 * 3.6 Deductive proofs
 * 3.7 Functions and terms
 * 3.8 Clausal form
 * 3.9 Herbrand models
 * 3.10 Finite and infinite models *
 * 3.11 Solvable cases of the decision problem *
 * 3.12 Exercises


 * 4. Resolution and logic programming
 * 4.1 Ground resolution
 * 4.2 Substitution
 * 4.3 Unification
 * 4.4 General resolution
 * 4.5 Theories and theorem proving
 * 4.6 Logic programming
 * 4.7 Prolog
 * 4.8 Parallel logic programming *
 * 4.9 Complete and decidable theories *
 * 4.10 Exercises


 * 5. Temporal logic
 * 5.1 Introduction
 * 5.2 Syntax and semantics
 * 5.3 A deductive system for linear PTL
 * 5.4 Semantic tableaux
 * 5.5 Soundness and completeness
 * 5.6 Applications of temporal logic *
 * 5.7 Extensions of temporal logic *
 * 5.8 Exercises


 * 6. Formalization of programs
 * 6.1 Introduction
 * 6.2 Axiomatisation of a language
 * 6.3 Proving programs
 * 6.4 Formal specification with $Z$
 * 6.5 Exercises


 * 7. Further reading
 * 7.1 Mathematical logic
 * 7.2 Complexity
 * 7.3 Resolution and logic programming
 * 7.4 Temporal logic
 * 7.5 Formalization of programs


 * Bibliography


 * Appendices


 * A. Set theory
 * A.1 Finite and infinite sets
 * A.2 Set operators
 * A.3 Ordered sets
 * A.4 Relations and functions
 * A.5 Cardinality
 * A.6 Proving properties of sets


 * B. Algorithm implementation


 * C. Hints


 * Index