Mathematical logic

A.Y. 2020/2021
6
Max ECTS
64
Overall hours
SSD
INF/01 MAT/01
Language
Italian
Learning objectives
The course has the purpose of introducing the fundamental principles of rational inquiry, by means of the formal approach provided by mathematical logic, both at the propositional and predicative levels.
Expected learning outcomes
The student should be able to formalise rational arguments via the formal proof techniques imparted in the course. Moreover, she should be able to construct counterexamples for fallacious arguments.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Videorecordings of the lectures will be made available.
Course syllabus
The mathematical logic course for the first degree is meant as an introductory course to logic, and to its relationship with language and concept formalisation.
The course is naturally articulated into two main sections: propositional logic and first-order logic. Furthermore, the subject of induction principle is investigated, in particular in the context of Peano arithmetic.
Syntax and semantics of logic are introduced, both at the propositional and the first-order level, and the use of a natural-deduction calculus.
Special attention is dedicated to the effective use of logic, starting from translation and formalisation of natural-language sentences.
The course is supplemented with lab class exercises, where a dedicated software is used.
Prerequisites for admission
None
Teaching methods
Lectures.
The course is supplemented with lab class exercises, where a dedicated software is used.

The Logic lab course is supplementary, as a lab class exercise course, to the Mathematical Logic course. Classes use a dedicated software that provides the students with tools to test comprehension of semantics concepts, and to write formal proofs in a natural-deduction calculus.
Teaching Resources
See the web page of the course: https://homes.di.unimi.it/aguzzoli/logicatriennale.html

Bibliography:
Dave Barker-Plummer, Jon Barwise, John Etchemendy: Language, Proof and Logic, 2nd Edition. CSLI Publications, 2011.
Assessment methods and Criteria
The exam consists in a written test and in a possible oral interview.
The written test is structured in two parts:
- "laboratory" exercises, to be done using the dedicated software;
- "theory" exercises, that aims to ascertain if concepts introduced in the lectures have been understood.
The final evaluation, expressed on a scale from 1 to 30. keeps into account how the student masters the concepts, of the exhibition clarity and property of language.
INF/01 - INFORMATICS - University credits: 0
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
Laboratories: 16016 hours
Lessons: 32 hours
Shifts:
Professor: Aguzzoli Stefano
Lab. parte 1 - Turno A
Professor: Aguzzoli Stefano
Lab. parte 1 - Turno B
Professor: Aguzzoli Stefano
Lab. parte 1 - Turno C
Professor: Fiorentini Camillo
Lab. parte 2 - Turno A
Professor: Aguzzoli Stefano
Lab. parte 2 - Turno B
Professor: Fiorentini Camillo