Book:Michael R.A. Huth/Logic in Computer Science: Modelling and reasoning about systems

Subject Matter

 * Symbolic Logic
 * Mathematical Logic

Contents

 * Foreword


 * Preface


 * Acknowledgments


 * 1 Propositional logic
 * 1.1 Declarative sentences
 * 1.2 Natural deduction
 * 1.2.1 Rules for natural deduction
 * 1.2.2 Derived rules
 * 1.2.3 Natural deduction in summary
 * 1.2.4 Provable equivalence
 * 1.2.5 An aside: proof by contradiction
 * 1.3 Propositional logic as a formal language
 * 1.4 Semantics of propositional logic
 * 1.4.1 The meaning of logical connectives
 * 1.4.2 Mathematical induction
 * 1.4.3 Soundness of propositional logic
 * 1.4.4 Completeness of propositional logic
 * 1.5 Normal forms
 * 1.5.1 Semantic equivalence, satisfiability and validity
 * 1.5.2 Conjunctive normal forms and validity
 * 1.5.3 Horn clauses and satisfiability
 * 1.6 Bibliographic notes


 * 2 Predicate logic
 * 2.1 The need for a richer language
 * 2.2 Predicate logic as a formal language
 * 2.2.1 Terms
 * 2.2.2 Formulas
 * 2.2.3 Free and bound variables
 * 2.2.4 Substitution
 * 2.3 Proof theory of predicate logic
 * 2.3.1 Natural deduction rules
 * 2.3.2 Quantifier equivalences
 * 2.4 Semantics of predicate logic
 * 2.4.1 Models
 * 2.4.2 Semantic entailment
 * 2.4.3 The semantics of equality
 * 2.5 Undecidability of predicate logic
 * 2.6 Bibliographic notes


 * 3 Verification by model checking
 * 3.1 Motivation for verification
 * 3.2 The syntax of computation tree logic
 * 3.3 Semantics of computation tree logic
 * 3.3.1 Practical patterns of specifications
 * 3.3.2 Important equivalences between CTL formulas
 * 3.4 Example: mutual exclusion
 * 3.4.1 The first modelling attempt
 * 3.4.2 The second modelling attempt
 * 3.5 A model-checking algorithm
 * 3.5.1 The labelling algorithm
 * 3.5.2 The pseudo-code of the model checking algorithm
 * 3.5.3 The 'state explosion' problem
 * 3.6 The SMV system
 * 3.6.1 Modules in SMV
 * 3.6.2 Synchronous and asynchronous composition
 * 3.6.3 Mutual exclusion revisited
 * 3.6.4 The alternating bit protocol
 * 3.7 Model checking with fairness
 * 3.8 Alternatives and extensions of CTL
 * 3.8.1 Linear-time temporal logic
 * 3.8.2 CTL*
 * 3.8.3 The expressive power of CTL
 * 3.9 The fixed-point characterisation of CTL
 * 3.9.1 Monotone functions
 * 3.9.2 The correctness of SATEG
 * 3.9.3 The correctness of SATEU
 * 3.10 Bibliographic notes


 * 4 Program verification
 * 4.1 Why should we specify and verify code?
 * 4.2 A framework for software verification
 * 4.2.1 A core programming language
 * 4.2.2 Hoare triples
 * 4.2.3 Partial and total correctness
 * 4.2.4 Program variables and logical variables
 * 4.3 Proof calculus for partial correctness
 * 4.3.1 Proof rules
 * 4.3.2 Proof tableaux
 * 4.3.3 A case study: minimal-sum section
 * 4.4 Proof calculus for total correctness
 * 4.5 Bibliographic notes


 * 5 Modal logics and agents
 * 5.1 Modes of truth
 * 5.2 Basic modal logic
 * 5.2.1 Syntax
 * 5.2.2 Semantics
 * 5.3 Logic engineering
 * 5.3.1 The stock of valid formulas
 * 5.3.2 Important properties of the accessibility relation
 * 5.3.3 Correspondence theory
 * 5.3.4 Some modal logics
 * 5.3.5 Semantic entailment
 * 5.4 Natural deduction
 * 5.5 Reasoning about knowledge in a multi-agent system
 * 5.5.1 Some examples
 * 5.5.2 The modal logic $$\text{KT45}^n$$
 * 5.5.3 Natural deduction for $$\text{KT45}^n$$
 * 5.5.4 Formalising the examples
 * 5.6 Bibliographic notes


 * 6. Binary decision diagrams
 * 6.1 Representing boolean functions
 * 6.1.1 Propositional formulas and truth tables
 * 6.1.2 Binary decision diagrams
 * 6.1.3 Ordered BDDs
 * 6.2 Algorithms for reduced OBDDS
 * 6.2.1 The algorithm reduce
 * 6.2.2 The algorithm apply
 * 6.2.3 The algorithm restrict
 * 6.2.4 The algorithm exists
 * 6.2.5 Assessment of OBDDs
 * 6.3 Symbolic model checking
 * 6.3.1 Representing subsets of the set of states
 * 6.3.2 Representing the transition relation
 * 6.3.3 Implementing the functions $$\text{pre}_\exists$$ and $$\text{pre}_\forall$$
 * 6.3.4 Synthesising OBDDs
 * 6.4 A relational mu-calculus
 * 6.4.1 Syntax and semantics
 * 6.4.2 Coding CTL models and specifications
 * 6.5 Bibliographic notes


 * Bibliography


 * Index