by Lu Zhongwan (Chinese Academy of Science, Beijing)

Mathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic. This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science.

In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new terms and notations.

• Prerequisites:
  • Sets
  • Inductive Definitions and Proofs
  • Notations
• Classical Propositional Logic:
  • Propositions and Connectives
  • Propositional Language
  • Structure of Formulas
  • Semantics
  • Tautological Consequence
  • Formal Deduction
  • Disjunctive and Conjunctive Normal Forms
  • Adequate Sets of Connectives
• Classical First-Order Logic:
  • Proposition Functions and Quantifiers
  • First-Order Language
  • Semantics
  • Logical Consequence
  • Formal Deduction
  • Prenex Normal Form
• Axiomatic Deduction System:
  • Axiomatic Deduction System
  • Relation between the Two Deduction Systems
• Soundness and Completeness:
  • Satisfiability and Validity
  • Soundness
  • Completeness of Propositional Logic
  • Completeness of First-Order Logic
  • Completeness of First-Order Logic with Equality
  • Independence
• Compactness, Löwenheim–Skolem, and Herbrand Theorems:
  • Compactness
  • Löwenheim-Skolem's Theorem
  • Herbrand's Theorem
• Constructive Logic:
  • Constructivity of Proofs
  • Semantics
  • Formal Deduction
  • Soundness
  • Completeness
• Modal Propositional Logic:
  • Modal Propositional Language
  • Semantics
  • Formal Deduction
  • Soundness
  • Completeness of T
  • Completeness of S₄, B, S₅
• Modal First-Order Logic:
  • Modal First-Order Language
  • Semantics
  • Formal Deduction
  • Soundness
  • Completeness
  • Equality