The computation and the working out of the knowledge rely on the distinction between syntax and semantic. The goal of this course is to study the relationship between syntax and semantic, by showing the potentialities and the limits of formal languages.
First order languages, validity and completeness. Compactness theorem and the strengthening of the completeness theorem. The problem of the decidability of the syntactic check of validity. Lowenheim and Skolem theorems and non categorical theories. Skolem paradox. Categoricity of the theory of a finite structure. Confutation trees for denumerable languages. Sequents, natural deduction, and the syntactic analysis of validity. Hilbert style deduction and the relative theorems of validity and completeness. Propositional calculus. Higher order logics. Hint to non classical logics. An overview to Gödel’s incompleteness theorems.
Open questions written test, and possible oral integration.
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