Advanced Logic

A.Y. 2020/2021
9
Max ECTS
60
Overall hours
SSD
MAT/01
Language
English
Learning objectives
The course aims to provide students with an overview of the most important formal systems that have been put forward as extensions of, or alternatives to classical logic. More specifically, students will acquire a basic knowledge of the following topics:
- intuitionistic logic
- informational view of logical consequence
- modal and epistemic logics
- non-monotonic logics
The acquired knowledge will be fruitfully employed in teaching, and in all activities requiring the usage of a variety of reasoning tools that are more powerful than elementary logic and more suited to problem-solving in a variety of applications.
Expected learning outcomes
Knowledge and understanding:
- knowledge of the foundations of non-monotonic reasoning;
- knowledge of the main extensions of, and alternatives to classical logic.
- knowledge of the most recent investigations into the relationship between logic and information.
Ability to apply knowledge and understanding

At the end of the course students are expected to be able to apply the acquired knowledge in order to:
- read and understand original scientific contributions in the field of logic;
- analyze and solve scientific, philosophical and practical problems that do not admit of natural solutions in terms of standard logic.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Two of the three weekly lectures will be in asynchronous, voice-over-slide mode, and will be uploaded to the Ariel site of the course; one will be a synchronous 2-hour online lecture via Teams which will be also recorded and uploaded to the Ariel site.
Course syllabus
Topics:
1 Intuitionistic Logic
2 Logic and Information
3 Modal Logic 1 (S4,S5)
4 Modal Logic 2 (general theory)
5 Epistemic Logics
6 Non-monotonic Logics

Prof. D'Agostino will lecture on topics 1-3, while Prof. Hosni will lecture on topics 4-6.

The 6 CFU exam will concern the first four topics (first 20 lectures) and the 9 CFU will concern all the six topics (30 lectures).
Prerequisites for admission
The "Logical Methods" course.
Teaching methods
Frontal lectures. The approach will be problem-oriented and students will be trained to solve basic logical problems through exercises.
Teaching Resources
Handouts provided by the lectures that will be uploaded to the Ariel site for the course. No additional reading material will be necessary for students who cannot attend the lectures regularly. These students will be able to ask the lecturers for clarifications via the forum in the Ariel site.
Assessment methods and Criteria
Learning assessment will be articulated in a written part and an oral part. The written part will consist in a short essay (max 5000 words) on one of the topics of the course that will be agreed upon with the lecturer; the oral part will consist in a discussion of the essay and on some questions on the other topics of the course. The assessment will depend on the level of understanding of both the conceptual and the formal aspects of the topics presented in the lectures and in the reading material.
The methods of assessment will be the same for all students, including those who do not regularly attend the lectures.
Unita' didattica A
MAT/01 - MATHEMATICAL LOGIC - University credits: 3
Lessons: 20 hours
Unita' didattica B
MAT/01 - MATHEMATICAL LOGIC - University credits: 3
Lessons: 20 hours
Unita' didattica C
MAT/01 - MATHEMATICAL LOGIC - University credits: 3
Lessons: 20 hours
Professor(s)
Reception:
Until the end of the COVID-19 emergency, students can request clarifications via Skype in all working days (please write to marcello.dagostino@unimi.it to make an appointment).
Department of Philosophy 2nd floor (Cortile della Ghiacciaia)