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 basic aspects of the semantics of Set Theory,  Propositional Calculus and First-Order Logic. They will also learn simple but formal techniques applicable to the three formalisms to state some properties and to prove them.

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.


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

– Prerequisites



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 English) will be distributed at the beginning of the course.

Assessment methods

Online tests during the course, and oral exam.

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