Probabilistic Logic
A.Y. 2020/2021
Learning objectives
The course aims at developing the logico-mathematical background to assess critically the logic and episte-mology of inductive reasoning, or "reasoning with data". In addition to making students familiar with the rel-evant elementary logical, probabilistic and statistical notions, it focusses on how the formalisation of induc-tive inference sheds crucial methodological light on the "datacentric" revolution, which is currently dotting the development of the natural and social sciences.
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:
- know the central concepts and reasoning tools of discrete mathematics
- know the central concepts in elementary probability theory
- know how to apply elementary logic to formalize probabilistic concepts
- understand the epistemological questions related to inductive reasoning
- understand the relevance of a proper the epistemology of inductive inference in the wider methodological discussion on "big data"
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. In particular at the end of the course, students will be able to
- read and evaluate the scientific literature on inductive reasoning
- apply the tools learnt to solve scientific, philosophical and practical problems
- appreciate the relevance of inductive logic in the current debate on the datacentric revolution in the methodology of the social sciences
Students are expected to acquire a full understanding of the formal notions presented and master basic knowledge of the following topics:
- know the central concepts and reasoning tools of discrete mathematics
- know the central concepts in elementary probability theory
- know how to apply elementary logic to formalize probabilistic concepts
- understand the epistemological questions related to inductive reasoning
- understand the relevance of a proper the epistemology of inductive inference in the wider methodological discussion on "big data"
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. In particular at the end of the course, students will be able to
- read and evaluate the scientific literature on inductive reasoning
- apply the tools learnt to solve scientific, philosophical and practical problems
- appreciate the relevance of inductive logic in the current debate on the datacentric revolution in the methodology of the social sciences
Lesson period: Second 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
Second 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.
Online environments used:
Ariel: https://hhosnipl.ariel.ctu.unimi.it/
MSTeams: code available on Ariel.
Teaching methods:
Classes will be held according to the following risk scenarios:
- maximum severity (red zone): classes will be held only remotely in synchronous mode (using MSTeams)
- high severity (orange zone): lessons will be held in mixed mode, partly in person and partly online. the face-to-face lessons will allow the participation of students connected with MSTeams as well as students in the classroom. Online lessons will be held synchronously (using MSTeams)
- severity (yellow zone): classes will be held according with the orange zone guidelines and, if conditions allow, the number of lessons on campus will be increased.
The calendar of in person lessons and updates will be published on the online course platform.
Learning assessment procedures and evaluation criteria:
The exam is written and is held on exam.net in any emergency situation, whether yellow, orange or red zone, in compliance with the guidelines provided by the University.
Students wishing to participate in face-to-face lessons must refer to the following University provisions: https://www.unimi.it/it/studiare/frequentare-un-corso-di-laurea/seguire-il-percorso-di-studi/didattica-presenza
Students wishing to participate in MSTeams lessons must refer to the following technical guides: https://www.unimi.it/it/studiare/servizi-gli-studenti/servizi-tecnologici-e-online/microsoft-office-365-education
To participate in the exam sessions, students must refer to the following provisions: https://www.unimi.it/it/studiare/frequentare-un-corso-di-laurea/seguire-il-percorso-di-studi/esami/esami-distanza-faq-gli-student
Online environments used:
Ariel: https://hhosnipl.ariel.ctu.unimi.it/
MSTeams: code available on Ariel.
Teaching methods:
Classes will be held according to the following risk scenarios:
- maximum severity (red zone): classes will be held only remotely in synchronous mode (using MSTeams)
- high severity (orange zone): lessons will be held in mixed mode, partly in person and partly online. the face-to-face lessons will allow the participation of students connected with MSTeams as well as students in the classroom. Online lessons will be held synchronously (using MSTeams)
- severity (yellow zone): classes will be held according with the orange zone guidelines and, if conditions allow, the number of lessons on campus will be increased.
The calendar of in person lessons and updates will be published on the online course platform.
Learning assessment procedures and evaluation criteria:
The exam is written and is held on exam.net in any emergency situation, whether yellow, orange or red zone, in compliance with the guidelines provided by the University.
Students wishing to participate in face-to-face lessons must refer to the following University provisions: https://www.unimi.it/it/studiare/frequentare-un-corso-di-laurea/seguire-il-percorso-di-studi/didattica-presenza
Students wishing to participate in MSTeams lessons must refer to the following technical guides: https://www.unimi.it/it/studiare/servizi-gli-studenti/servizi-tecnologici-e-online/microsoft-office-365-education
To participate in the exam sessions, students must refer to the following provisions: https://www.unimi.it/it/studiare/frequentare-un-corso-di-laurea/seguire-il-percorso-di-studi/esami/esami-distanza-faq-gli-student
Course syllabus
1. Reasoning with data
- Data and its meaning
- Elementary descriptive statistics
- Elementary probability
2. The epistemology of reasoning with data: induction
- Hume's problem of induction
- Induction and knowledge
- More data vs better data
3. The logic of reasoning under uncertainty
- Introduction to Probability logic
- Coherence
- Conditional probability in a logical setting
- Data and its meaning
- Elementary descriptive statistics
- Elementary probability
2. The epistemology of reasoning with data: induction
- Hume's problem of induction
- Induction and knowledge
- More data vs better data
3. The logic of reasoning under uncertainty
- Introduction to Probability logic
- Coherence
- Conditional probability in a logical setting
Prerequisites for admission
Logical Methods (LM)
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.
Teaching Resources
Lecture notes and material will be made available by the instructor
Assessment methods and Criteria
Learning assessment will be through a written exam at the end of the course. Students attending the course can opt for a mid-term examinations at the end of each module.
The exam worth 6 CFU will be on the topics 1-4 (the first 40
hours). The exam worth 9 CFU will be on all the course topics (a
total of 60 hours).
The text of the partial and final exams includes open questions (30%), exercises (50%) and multiple choices tests (20%). These proportions broadly reflect their contribution to the composition of the final score. Multiple choice tests and open questions are aimed to broadly verify the understanding of concepts and definitions taught during the course whereas exercises are designed to evaluate problem solving skills.
The exam worth 6 CFU will be on the topics 1-4 (the first 40
hours). The exam worth 9 CFU will be on all the course topics (a
total of 60 hours).
The text of the partial and final exams includes open questions (30%), exercises (50%) and multiple choices tests (20%). These proportions broadly reflect their contribution to the composition of the final score. Multiple choice tests and open questions are aimed to broadly verify the understanding of concepts and definitions taught during the course 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.