Logic and Reasoning

Academic year: 2022-23
Course: Foundation Course Science
Credits: 3
Period: Second semester

Number of hours: 24

Teacher(s): Roberto Bruni (

Language of instruction: English

Learning outcomes


Students will learn the syntax and some elementary aspects of the semantics of Set Theory,  Propositional Calculus and First-Order Logic. They will also learn simple but formal proof techniques applicable to the three formalisms.

Assessment criteria of knowledge

Oral exam at the end of the course.


Students will learn how to use logic formulas to formalize simple propositions in the natural language. They will also learn how to use formal proof techniques to prove (or disprove) equivalences among sets, and among propositional or first-order formulas.

Assessment criteria of skills

Continuous evaluation based on on-line tests along the course. If in presence, written exam at the end of the course.   


The students will be encouraged to transfer the acquired knowledge in other contexts.




  1. Introduction: relevance of the Mathematical Language in Science
  2. Examples of discursive and formal proofs of algebraic identities
  3. Notations for sets, comparing sets, composing sets: some laws
  4. Discursive, graphical and formal proofs of set equalities
  5. Syntax and semantics of Propositional Calculus
  6. Syntax and basics of semantics of First Order Logic
  7. Formalization of natural language statements and formal proofs of logical equivalence


Teaching material (in English) will be distributed at the beginning of the module

Assessment methods

Online tests during the course, written exam (if in presence) and oral exam.