Logical Methods
A.Y. 2026/2027
Learning objectives
Students will acquire in-depth knowledge and skills on current research topics in logic.
Expected learning outcomes
Students will acquire the ability to:
- critically analyze the arguments and concepts underlying different logics and their applications;
- discuss and compare different philosophical positions that characterize the various logics;
- reflect on complex and articulated philosophical positions that either underpin or result from the definition of different logics and their applications;
- adopt their own stance in a philosophical debate on the foundations and consequences of the logics under study, and put forward arguments in support of it;
- effectively communicate the results of their research, including through multimedia techniques for presenting information, with possible applications in teaching;
- use relational, communicative, and organizational skills even in highly complex contexts and in managing group work;
- convey the acquired skills even in non-specialist contexts;
- reflect on their own abilities and on the evaluations received;
- independently search for the philosophical sources of a debate or school of thought underlying the logics studied;
- independently explore in depth a philosophical position or theoretical thesis underlying the logics studied.
- critically analyze the arguments and concepts underlying different logics and their applications;
- discuss and compare different philosophical positions that characterize the various logics;
- reflect on complex and articulated philosophical positions that either underpin or result from the definition of different logics and their applications;
- adopt their own stance in a philosophical debate on the foundations and consequences of the logics under study, and put forward arguments in support of it;
- effectively communicate the results of their research, including through multimedia techniques for presenting information, with possible applications in teaching;
- use relational, communicative, and organizational skills even in highly complex contexts and in managing group work;
- convey the acquired skills even in non-specialist contexts;
- reflect on their own abilities and on the evaluations received;
- independently search for the philosophical sources of a debate or school of thought underlying the logics studied;
- independently explore in depth a philosophical position or theoretical thesis underlying the logics studied.
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. Discrete mathematics
- Elementary notions (sets, relations and functions)
- Lists, trees and graphs
- Algorithms and complexity
2. Elementary classical logic
- Propositional logic
- Reasoning with quantifiers
- Logical methods for problem solving
3. Intuitionistic and modal Logic
- Intuitionistic logic and natural deduction
- Kripke semantics for Intuitionistic logic
- Kripke semantics for modal logics
6-CFU examinable material covers module 1-2 (20 lectures). 9-CFU examinable material includes all 3 modules (30 lectures)
- Elementary notions (sets, relations and functions)
- Lists, trees and graphs
- Algorithms and complexity
2. Elementary classical logic
- Propositional logic
- Reasoning with quantifiers
- Logical methods for problem solving
3. Intuitionistic and modal Logic
- Intuitionistic logic and natural deduction
- Kripke semantics for Intuitionistic logic
- Kripke semantics for modal logics
6-CFU examinable material covers module 1-2 (20 lectures). 9-CFU examinable material includes all 3 modules (30 lectures)
Prerequisites for admission
English, level B2. Certification required to take the exam.
Teaching methods
In-person 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 lecturer.
Further suggested readings (not required to take the exam):
M. D'Agostino, H. Hosni. Le vie della Logica. Einaudi 2024. (Not available in English.)
Esther Anna Corsi, Hykel Hosni. Logica pratica. Dai quesiti dei test di ammissione ai metodi della logica elementare. Milano University Press, Open Access https://libri.unimi.it/index.php/milanoup/catalog/view/291/1264/3180 (not available in English)
Further suggested readings (not required to take the exam):
M. D'Agostino, H. Hosni. Le vie della Logica. Einaudi 2024. (Not available in English.)
Esther Anna Corsi, Hykel Hosni. Logica pratica. Dai quesiti dei test di ammissione ai metodi della logica elementare. Milano University Press, Open Access https://libri.unimi.it/index.php/milanoup/catalog/view/291/1264/3180 (not available in English)
Assessment methods and Criteria
Learning evaluation will be through a written test at the end of each module. The final grade will be the average of the grades obtained in the single tests. Students who fail a partial test or prefer their grade to be discarded must take a final test covering the whole program.
Each 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.
Each 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.
Modules or teaching units
Parte A e B
PHIL-02/A - Logic and Philosophy of Science - University credits: 6
Lessons: 40 hours
Parte C
PHIL-02/A - Logic and Philosophy of Science - University credits: 3
Lessons: 20 hours
Professor(s)
Reception:
Wednesday 10:00-13:00 and via Teams upon request
Head of Department's Office, Cortile d’Onore