by Lu Zhongwan (Academia Sinica, Beijing)

This book describes the aspects of mathematical logic related to computer sciences. The materials adopted in this book are intended to attend to both the peculiarities of logical systems and the requirements of computer science.

• Prerequisites:
  • Sets
  • Inductive Definitions and Proofs
  • Notations
• Propositional Logic:
  • Propositions and Connectives
  • Propositional Language
  • Semantics
  • Tautological Consequence
  • Formal Deducibility
  • Disjunctive and Conjunctive Normal Forms
  • Adequate Sets of Connectives
• First-Order Logic:
  • Proposition Functions and Quantifiers
  • First-Order Language
  • Semantics
  • Logical Consequence
  • Formal Deducibility
  • Prenex Normal Form
• Formal Deducibility — Another Type:
  • Formal Deducibility of Another Type
  • Relation between the Two Types
• Soundness and Completeness:
  • Satisfiability and Validity
  • Soundness
  • Completeness of Propositional Logic
  • Completeness of First-Order Logic
  • Completeness of First-Order Logic with Equality
  • Independence
• Applications of Soundness and Completeness:
  • Compactness
  • L_wenheim-Skolem's Theorem
  • Herbrand's Theorem
  • Some Basic Notions of Model Theory
  • Constructive Logic: Logic for Constructive Reasoning
  • Semantics
  • Formal Deducibility
  • Soundness
  • Completeness
• Modal Propositional Logic:
  • Modal Propositional Language
  • Semantics
  • Formal Deducibility
  • Soundness
  • Completeness of T
  • Completeness of S₄, B, S₅
• Modal First-Order Logic:
  • Modal First-Order Language
  • Semantics
  • Formal Deducibility
  • Soundness
  • Completeness
  • Equality