|Flow||M - Mathematics|
|Category||Obligatory by selection|
|Class Hours - Lab Hours||4 - 0|
|Lecturers||Giorgos Koletsos, Petros Potikas (T & R Associates)|
Propositional calculus: Language, unique readability, propositional connectives, truth assignments, semantic concepts, completeness of connectives, disjunctive and conjunctive normal forms, compactness theorem of propositional calculus, applications. First-order predicate calculus: Language, variables, free and bound occurrences of variables, substitution, programming analogies, the concept of structure and interpretation of a language, Tarski’s definition of truth, models. Axiomatization of first-order logic: Formal axiom system, analogies with algorithmic concepts, consistency, soundness and Godel’s completeness theorem, undecidability and incompleteness, compactness and Lowenheim-Skolem theorems. Proof theory of propositional and predicate calculus: Gentzen’s sequent calculus, cut elimination, resolution, semantic tableaux, The completeness theorem for predicate calculus via semantic tableaux. Applications to computer science.