Students will learn the syntax and some elementary aspects of the semantics of Propositional Calculus and First-Order Logic. They will use logic formulas to formalize propositions in the natural language. They will learn simple but formal proof techniques, and will use them to prove (or disprove) equivalences among sets and among predicate calculus or first-order logic formulas.
- Lectures are carried out using slides and a blackboard.
are carried out in the classroom: students will practice the
exercises, even in groups, under the supervision of the lecturer.
- Interaction with the lecturer is done through meetings (on fixed office hours or by appointment) and by e-mail.
- Introduction: relevance of the Mathematical Language in Science
- Examples of discursive and formal proofs of algebraic identities
- Notations for sets, comparing sets, composing sets: some laws
- Discursive, graphical and formal proofs of set equalities
- Syntax and semantics of Propositional Calculus
- Syntax and basics of semantics of First Order Logic
- Formalization of natural language statements and formal proofs of logical equivalence
Teaching material (in Italian) will be distributed at the beginning of the module
Written test, consisiting of a few problems to be solved.