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

Subject Matter

 * Mathematical Logic
 * Computer Science

Contents

 * 1 Introduction
 * 1.1 The Origins of Mathematical Logic
 * 1.2 Propositional Logic
 * 1.3 First-Order Logic
 * 1.4 Modal and Temporal Logics
 * 1.5 Program Verification
 * 1.6 Summary
 * 1.7 Further Reading
 * 1.8 Exercise
 * References


 * 2 Propositional Logic: Formulas, Models, Tableaux
 * 2.1 Propositional Formulas
 * 2.2 Interpretations
 * 2.3 Logical Equivalence
 * 2.4 Sets of Boolean Operators $^*$
 * 2.5 Satisfiability, Validity and Consequence
 * 2.6 Semantic Tableaux
 * 2.7 Soundness and Completeness
 * 2.8 Summary
 * 2.9 Further Reading
 * 2.10 Exercises
 * References


 * 3 Propositional Logic: Deductive Systems
 * 3.1 Why Deductive Proofs?
 * 3.2 Gentzen System $\mathscr G$
 * 3.3 Hilbert System $\mathscr H$
 * 3.4 Derived Rules in $\mathscr H$
 * 3.5 Theorems for Other Operators
 * 3.6 Soundness and Completeness of $\mathscr H$
 * 3.7 Consistency
 * 3.8 Strong Completeness and Compactness $^*$
 * 3.9 Variant Forms of the Deductive Systems $^*$
 * 3.10 Summary
 * 3.11 Further Reading
 * 3.12 Exercises
 * References


 * 4 Propositional Logic: Resolution
 * 4.1 Conjunctive Normal Form
 * 4.2 Clausal Form
 * 4.3 Resolution Rule
 * 4.4 Soundness and Completeness of Resolution $^*$
 * 4.5 Hard Examples for Resolution $^*$
 * 4.6 Summary
 * 4.7 Further Reading
 * 4.8 Exercises
 * References


 * 5 Propositional Logic: Binary Decision Diagrams
 * 5.1 Motivation Through Truth Tables
 * 5.2 Definition of Binary Decision Diagrams
 * 5.3 Reduced Binary Decision Diagrams
 * 5.4 Ordered Binary Decision Diagrams
 * 5.5 Applying Operators to BDDs
 * 5.6 Restriction and Quantification $^*$
 * 5.7 Summary
 * 5.8 Further Reading
 * 5.9 Exercises
 * References


 * 6 Propositional Logic: SAT Solvers
 * 6.1 Properties of Clausal Form
 * 6.2 Davis-Putnam Algorithm
 * 6.3 DPLL Algorithm
 * 6.4 An Extended Example of the DPLL Algorithm
 * 6.5 Improving the DPLL Algorithm
 * 6.6 Stochastic Algorithm
 * 6.7 Complexity of SAT $^*$
 * 6.8 Summary
 * 6.9 Further Reading
 * 6.10 Exercises
 * References


 * 7 First-Order Logic: Formulas, Models, Tableaux
 * 7.1 Relations and Predicates
 * 7.2 Formulas in First-Order Logic
 * 7.3 Interpretations
 * 7.4 Logical Equivalences
 * 7.5 Semantic Tableaux
 * 7.6 Soundness and Completeness of Semantic Tableaux
 * 7.7 Summary
 * 7.8 Further Reading
 * 7.9 Exercises
 * References


 * 8 First-Order Logic: Deductive Systems
 * 8.1 Gentzen System $\mathscr G$
 * 8.2 Hilbert System $\mathscr H$
 * 8.3 Equivalence of $\mathscr H$ and $\mathscr G$
 * 8.4 Proofs of Theorems in $\mathscr H$
 * 8.5 The C-Rule $^*$
 * 8.6 Summary
 * 8.7 Further Reading
 * 8.8 Exercises
 * References


 * 9 First-Order Logic: Terms and Normal Forms
 * 9.1 First-Order Logic with Functions
 * 9.2 PCNF and Clausal Form
 * 9.3 Herbrand Models
 * 9.4 Herbrand's Theorem $^*$
 * 9.5 Summary
 * 9.6 Further Reading
 * 9.7 Exercises
 * References


 * 10 First-Order Logic: Resolution
 * 10.1 Ground Resolution
 * 10.2 Substitution
 * 10.3 Unification
 * 10.4 General Resolution
 * 10.5 Soundness and Completeness of General Resolution $^*$
 * 10.6 Summary
 * 10.7 Further Reading
 * 10.8 Exercises
 * References


 * 11 First-Order Logic: Logic Programming
 * 11.1 From Formulas in Logic to Logic Programming
 * 11.2 Horn Clauses and SLD-Resolution
 * 11.3 Search Rules in SLD-Resolution
 * 11.4 Prolog
 * 11.5 Summary
 * 11.6 Further Reading
 * 11.7 Exercises
 * References


 * 12 First-Order Logic: Undecidability and Model Theory $^*$
 * 12.1 Undecidability of First-Order Logic
 * 12.2 Decidable Cases of First-Order Logic
 * 12.3 Finite and Infinite Models
 * 12.4 Complete and Incomplete Theories
 * 12.5 Summary
 * 12.6 Further Reading
 * 12.7 Exercises
 * References


 * 13 Temporal Logic: Formulas, Models, Tableaux
 * 13.1 Introduction
 * 13.2 Syntax and Semantics
 * 13.3 Models of Time
 * 13.4 Linear Temporal Logic
 * 13.5 Semantic Tableaux
 * 13.6 Binary Temporal Operators $^*$
 * 13.7 Summary
 * 13.8 Further Reading
 * 13.9 Exercises
 * References


 * 14 Temporal Logic: A Deductive System
 * 14.1 Deductive System $\mathscr L$
 * 14.2 Theorems of $\mathscr L$
 * 14.3 Soundness and Completeness of $\mathscr L$ $^*$
 * 14.4 Axioms for the Binary Temporal Operators $^*$
 * 14.5 Summary
 * 14.6 Further Reading
 * 14.7 Exercises
 * References


 * 15 Verification of Sequential Programs
 * 15.1 Correctness Formulas
 * 15.2 Deductive System $\mathscr{HL}$
 * 15.3 Program Verification
 * 15.4 Program Synthesis
 * 15.5 Formal Semantics of Programs $^*$
 * 15.6 Soundness and Completeness of $\mathscr{HL}$ $^*$
 * 15.7 Summary
 * 15.8 Further Reading
 * 15.9 Exercises
 * References


 * 16 Verification of Concurrent Programs
 * 16.1 Definition of Concurrent Programs
 * 16.2 Formalization of Correctness
 * 16.3 Deductive Verification of Concurrent Programs
 * 16.4 Programs as Automata
 * 16.5 Model Checking of Invariance Properties
 * 16.6 Model Checking of Liveness Properties
 * 16.7 Expressing an LTL Formula as an Automaton
 * 16.8 Model Checking Using the Synchronous Automaton
 * 16.9 Branching-Time Temporal Logic $^*$
 * 16.10 Symbolic Model Checking $^*$
 * 16.11 Summary
 * 16.12 Further Reading
 * 16.13 Exercises
 * References


 * Appendix Set Theory
 * A.1 Finite and Infinite Sets
 * A.2 Set Operators
 * A.3 Sequences
 * A.4 Relations and Functions
 * A.5 Cardinality
 * A.6 Proving Properties of Sets
 * References


 * Index of Symbols


 * Name Index


 * Subject Index



In Appendix:



Source work progress
* : $\S 3.3$: Theorem $3.10$