Mathematical Logic For Computer Science (2nd Edition)

Part 1 Prerequisites: sets; inductive definitions and proofs; notations. Part 2 Classical propositional logic: propositions and connectives; propositional language; semantics; tautological consequence; formal deduction; disjunctive and conjunctive normal forms; adequate sets of connectives. Part 3 Classical first-order logic: proposition functions and quantifiers; first-order language; semantics; logical consequence; formal deduction; prenex normal form. Part 4 Axiomatic deduction system: axiomatic deduction system; relation between the two deduction systems. Part 5 Soundness and completeness: satisfiability and validity; soundness; completeness of propositional logic; completeness of first-order logic; completeness of first-order logic with equality; independence. Part 6 Compactness, Lowenheim-Skolem, and Herbrand theorems: compactness; Lowenheim-Skolem's theorem; Herbrand's theorem. Part 7 Constructive logic: constructivity of proofs; semantics; formal deduction; soundness; completeness. Part 8 Modal propositional logic: modal propositional language; semantics; formal deduction; soundness; completeness of T; completeness of S4, B, S5. Part 9 Modal first-order logic: modal first-order language; semantics; formal deduction; soundness; completeness; equality.