Logical Methods
A.Y. 2021/2022
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 cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
During the ongoing covid emergency, the course syllabus will be maintained with the following changes made to enhance the effectiveness of the online version of the course, which was originally designed for face-to-face teaching.
The lessons will be held in dual mode. The face-to-face lessons will allow the participation of students connected with MSTeams as well as students in the classroom.
The recordings of the lessons will remain available at least until the end of the semester
Teams: keys 3pwwwf
Students wishing to participate in face-to-face lessons must refer to the following University provisions: https://www.unimi.it/en/study/bachelor-and-master-study/following-your-programme-study/teaching-activities-campus
Students wishing to participate in MSTeams lessons must refer to the following technical guides: https://www.unimi.it/en/study/student-services/technology-and-online-services/microsoft-office-365-education
To participate in the exam sessions, students must refer to the following provisions:
https://www.unimi.it/en/study/bachelor-and-master-study/following-your-programme-study/sitting-exams
The lessons will be held in dual mode. The face-to-face lessons will allow the participation of students connected with MSTeams as well as students in the classroom.
The recordings of the lessons will remain available at least until the end of the semester
Teams: keys 3pwwwf
Students wishing to participate in face-to-face lessons must refer to the following University provisions: https://www.unimi.it/en/study/bachelor-and-master-study/following-your-programme-study/teaching-activities-campus
Students wishing to participate in MSTeams lessons must refer to the following technical guides: https://www.unimi.it/en/study/student-services/technology-and-online-services/microsoft-office-365-education
To participate in the exam sessions, students must refer to the following provisions:
https://www.unimi.it/en/study/bachelor-and-master-study/following-your-programme-study/sitting-exams
Course syllabus
1. Discrete mathematics discreta
- Elementary notions (sets, relations and functions)
- Graphs, state transition systems, algorithms
2. Classical propositional logic
- rules of inference
- logical consequence
3. First order logic
- rules of inference and semantics
- elementary first order theories
4. Modal Logic
- relational structures
- normal modal logic
6CFU examinable material convers parts 1-3 (20 lectures). 9 CFU examinable material includes all 30 lectures
- Elementary notions (sets, relations and functions)
- Graphs, state transition systems, algorithms
2. Classical propositional logic
- rules of inference
- logical consequence
3. First order logic
- rules of inference and semantics
- elementary first order theories
4. Modal Logic
- relational structures
- normal modal logic
6CFU examinable material convers parts 1-3 (20 lectures). 9 CFU examinable material includes all 30 lectures
Prerequisites for admission
None
Teaching methods
Frontal lectures. The approach will be problem-oriented and students will be trained to solve basic logical problems through exercises.
Teaching Resources
One handout for each main topic provided by the lecturers.
Assessment methods and Criteria
Learning assessment will be through a written test at the end of the course.
The test includes open questions (30%), multiple-choice questions (20%), and exercises (50%), all weighted depending on their degree of difficulty. Open and multiple-choice questions are aimed at broadly verifying the understanding of concepts and definitions, whereas exercises are designed to evaluate problem solving skills.
The test includes open questions (30%), multiple-choice questions (20%), and exercises (50%), all weighted depending on their degree of difficulty. Open and multiple-choice questions are aimed at broadly verifying the understanding of concepts and definitions, whereas exercises are designed to evaluate problem solving skills.
Unita' didattica A
M-FIL/02 - LOGIC AND PHILOSOPHY OF SCIENCE - University credits: 3
Lessons: 20 hours
Unita' didattica B
M-FIL/02 - LOGIC AND PHILOSOPHY OF SCIENCE - University credits: 3
Lessons: 20 hours
Unita' didattica C
M-FIL/02 - LOGIC AND PHILOSOPHY OF SCIENCE - University credits: 3
Lessons: 20 hours
Professor(s)
Reception:
Friday 8:30-11:30
Second Floor, Cortile Ghiacchiaia. Please email me to secure your slot.