Mathematical Logic For Computer Science (2Nd Edition) (World Scientific Computer Science)

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. Introduction. 1. Prerequisites. 1.1. Sets. 1.2. Inductive definitions and proofs. 1.3. Notations -- 2. Classical Propositional Logic. 2.1. Propositions and connectives. 2.2. Propositional language. 2.3. Structure of formulas. 2.4. Semantics. 2.5. Tautological consequence. 2.6. Formal deduction. 2.7. Disjunctive and conjunctive normal forms. 2.8. Adequate sets of connectives -- 3. Classical First-Order Logic. 3.1. Proposition functions and quantifiers. 3.2. First-order language. 3.3. Semantics. 3.4. Logical consequence. 3.5. Formal deduction. 3.6. Prenex normal form ... -- 9.2. Semantics. 9.3. Formal deduction. 9.4. Soundness. 9.5. Completenes. 9.6. Equality Describes the aspects of mathematical logic which are related to computer science. This book deals with both the peculiarities of logical systems and the requirements of computer science. In this edition, the proofs and explanations have been increased and rewritten, with new terms and notations. The only prerequisite for reading this book is familiarity with the basic notions of sets, inductive definitions, and inductive proofs. Lu Zhongwan. Includes Bibliographical References (p. 227-228) And Index.