Abstract
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.
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