Ateneo - UPO

Propositional logic and relative calculation of the natural deduction. Introduction to the Logic of Predicates.

"Logica a Informatica" di A. Asperti e A. Ciabattoni, Mc Grow Hill Education (1997)

Introduce the elementary notions of logic of propositions and of the first order with particular attention to the relationship between truth and derivability and to representability in the calculation of predicates.

Basic mathematical knowledge

Frontal lessons including exercises.

The grade of the logic module is a weighted average with the grade of the algebra and geometry module to obtain the final grade of discrete mathematics.

The final exam consists of a written test lasting half an hour and an optional oral test.

Propositional Logic:
• Syntax.
• Semantics: interpretation, definitions of satisfiable, contradictory, tautology, semantic consequence and related results, semantic equivalence, functional completeness and normal form.
• Natural deduction: rules and proofs, correctness, completeness statement.
Logic of Predicates:
• Syntax: free and bound variables, substitution.
• Semantics: Interpretation, definitions of satisfiable, contradictory, tautology, semantic consequence and related results.

The skills to be tested, and necessary for passing the course, consist in the understanding of the basic concepts of propositional logic (both as regards semantics and as regards test methods) and predicate logic.