cherubino

Logic and Reasoning

Academic year: 2023-24
Course: Foundation Course Science
Credits: 3
Period: Second semester

Number of hours: 24

Teacher(s): Roberto Bruni (roberto.bruni@unipi.it)

Language of instruction: English

Learning outcomes

Knowledge

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.

Skills

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.

Behaviors

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

Assessment criteria of behaviors

Classroom discussion of examples and exercises.

Prerequisites

None

Co-requisites

None

Prerequisites for further study

None

Teaching methods

Learning activities:

attending lectures

participation in discussions

home assignments, to be solved together in the next lecture

individual study

Attendance: Advised

Teaching methods:

Lectures

Self-assesment tests

Recommended readings

Syllabus

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.

Bibliography

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

Non-attending students info

Recorded streaming of lectures will be available upon request

Assessment methods

Online tests during the course, and oral exam.

Work placement

None

Class web page

http://www.di.unipi.it/~bruni

Additional web pages

None

Notes

None

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