Logic: 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, normal forms, 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 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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