Logical Methods
A.Y. 2025/2026
Learning objectives
Logic, in its broad sense, can be seen on the one hand as a set of unifying languages for the systematization of scientific knowledge, on the other as a set of tools for any practical application based on information processing. This course will provide students with an overview of logical methods useful for both theoretical and practical applications. Students will learn how to design formal languages and compute with them for the resolution of theoretical and practical problems. The approach is thus at the same time abstract and practically oriented, so as to make the course useful for science as well as philosophy students.
Expected learning outcomes
Knowledge acquisition and understanding
Students are expected to acquire a full understanding of the formal notions presented and master basic knowledge of the following topics:
- Formal Methods and their applications:
- Basic mathematical notions (sets and their operations, relations, functions)
- Basic data structures (lists, trees, graphs)
- Regular Expressions
- Finite State Machines
- Classical logic and its applications:
- The semantics of classical logic
- Proof systems for classical logic
- Main applications of classical logic (automated theorem proving, logic programming)
- Non-classical logics and their applications:
- Modal and epistemic logics
- Many-valued logics
- Logics for vagueness and uncertainty
Skills acquisition and ability to apply knowledge:
Students are also expected to develop an ability to apply this basic knowledge to solve simple problems and to engage in further research within more advanced projects in specific applications of their interest. Notions and methods will be introduced in a problematic way so as to stimulate a critical, rather than passive, attitude towards knowledge. We also expect that training students in the use of formal languages and logical tools will improve their capability of communicating ideas, both at a theoretical and practical level, with the required precision and a sufficient amount of rigour.
Students are expected to acquire a full understanding of the formal notions presented and master basic knowledge of the following topics:
- Formal Methods and their applications:
- Basic mathematical notions (sets and their operations, relations, functions)
- Basic data structures (lists, trees, graphs)
- Regular Expressions
- Finite State Machines
- Classical logic and its applications:
- The semantics of classical logic
- Proof systems for classical logic
- Main applications of classical logic (automated theorem proving, logic programming)
- Non-classical logics and their applications:
- Modal and epistemic logics
- Many-valued logics
- Logics for vagueness and uncertainty
Skills acquisition and ability to apply knowledge:
Students are also expected to develop an ability to apply this basic knowledge to solve simple problems and to engage in further research within more advanced projects in specific applications of their interest. Notions and methods will be introduced in a problematic way so as to stimulate a critical, rather than passive, attitude towards knowledge. We also expect that training students in the use of formal languages and logical tools will improve their capability of communicating ideas, both at a theoretical and practical level, with the required precision and a sufficient amount of rigour.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
1. An introduction to mathematical reasoning
- sets, relations, functions
- mathematical proofs
2. Elementary classical logic
- Propositional logic
- Reasoning with quantifiers
- Logical methods for problem solving
3. Introduction to non-classical logics
- modal logics
- many valued logics
There is no difference between the syllabus for attending and non-attending students.
Part 1,2 and 3 make the 9CFU exam. The 6CFU exam includes parts 1 and 2 only
- sets, relations, functions
- mathematical proofs
2. Elementary classical logic
- Propositional logic
- Reasoning with quantifiers
- Logical methods for problem solving
3. Introduction to non-classical logics
- modal logics
- many valued logics
There is no difference between the syllabus for attending and non-attending students.
Part 1,2 and 3 make the 9CFU exam. The 6CFU exam includes parts 1 and 2 only
Prerequisites for admission
None
Teaching methods
Frontal and flipped lectures and assignments. The approach will be problem-oriented and students will be trained to learn by solving basic problems and exercises. As a consequence, attendance is highly recommended.
Teaching Resources
Available from https://myariel.unimi.it/user/view.php?id=42597&course=7340
Assessment methods and Criteria
The exam is written and marked as follows:
- Partial Examination (online on Moodle based on closed and open questions): 50% of the final grade.
- End of course test (online on Moodle based on closed and open questions): 50% of the final grade
- Partial Examination (online on Moodle based on closed and open questions): 50% of the final grade.
- End of course test (online on Moodle based on closed and open questions): 50% of the final grade
Modules or teaching units
Parte A e B
M-FIL/02 - LOGIC AND PHILOSOPHY OF SCIENCE - University credits: 6
Lessons: 40 hours
Parte C
M-FIL/02 - LOGIC AND PHILOSOPHY OF SCIENCE - University credits: 3
Lessons: 20 hours
Educational website(s)
Professor(s)
Reception:
Friday 8:30-11:30
Second Floor, Cortile Ghiacchiaia. Please email me to secure your slot.