Logic and related disciplines, historical development, mathematical logic, logic in computer science. Propositional Logic (ProL): language of ProL, formulas, truth valuation, truth evaluation of formulas, semantic consequence, tautology, satisfiable formulas, table method. Axiomatic system of ProL: axioms, deduction rules, proof, deduction theorem, provable formulas, selected theorems (substitution, equivalence, neutral formulas), theories, consistency, correctness theorem, completeness theorem. Predicate logic (PreL): language, terms, formulas, basic syntactic notions; semantics: structures for PreL, evaluation of terms and formulas, tautologies, satisfiable formulas, semantics consequence, basic semantic concepts, theories, models. Axiomatic system of PreL: axioms, deduction rules, proof, deduction theorem, extension and conservative extension, constants, provable formulas, variants, consistency. Completeness: correctness, Henkin theory, complete theory, completion theorem, models from constants, canonical structure, completeness theorem. Introduction to Goedel's results on incompleteness, the two incompleteness theorems. Undecidability of predicate logic. Introduction to logic programming: resolution, completeness of resolution, relationship to Prolog. Representative examples of Prolog. Introduction to non-classical logics: fuzzy logic, modal logic, temporal logic. Examples and applications.
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