OVERVIEW

The course provides the main elements of propositional and first-order logic, introduces modal logics, and presents some topics in non-classical logics. The objective of the course is to approach a number of research problems at the intersection of mathematical logic and philosophical logic, knowledge represetnation, formal semantics, formal ontology, or artificial intelligence.

AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the course is to introduce a number of research topics in mathematical logic that are of interest for philosophers working in areas such as philosophical logic, knowledge represetnation, formal semantics, formal ontology, or artificial intelligence. 

AIMS AND LEARNING OUTCOMES

Objectives of the course are:

• Expand the comprehension of propositional and first-order logic, by approaching the technical aspects and by training the skills required to prove statements about logical systems. 
• Introduce logical calculi (e.g. Hilbert Systems).
• Enrich the comprehension of the semantics of first-order logic, focussing on the notions of first-order theory and model.
• Introduce the metatheorems (soundness and completeness) for the calculi.
• Introduce the main concepts of propositional modal logics  (Kripke semantics, correspondence theory, limits of Kripke semantics)
• Introduce a number of aspects of non-classical logics. 
• Approach research topics at the intersection of mathematical logic and philosophical logic, knowledge representation, formal semantics, formal ontology, or artificial intelligenge 

At the end of the course, students are expected to 

• Understand the technical aspects of propositional and predicate logic and of the logical calculi introduced. 
• Know how to prove simple properties about logical systems.
• Understand and apply logical calculi. 
• Understand the metatheorems.
• Understand and apply the main concepts of modal logic.
• Understand the differences between classical and a number of non-classical logics.
• Begin approaching research topics in logic by understanding logical texts. 

PREREQUISITES

Students must have already attended an introductory course of Logic.

TEACHING METHODS

Lectures are hopefully held in presence, with the possibility of distance learning on Teams (access codes will be provided). 

For the first part, the course consists of frontal lecture and exercise sessions.

For the second part, the course consists of presentations of research topics and discussion. During the course, compatibly with the available resources, external experts could be invited to hold seminars on specific topics.

Students are required to register at Aulaweb, where teaching materials will be uploaded.

SYLLABUS/CONTENT

The course is divided into two parts:

1) An overview of propositional and first-order logic, an introduction to modal logics, an introduction to topics in non-classcial logics. 

2) A number of presentations of research topics at the intersection of mathematical logic and philosophical logic, formal semantics, formal ontology, knowledge representation or artificial intelliegence. 

First part:

• Propositional logic, its syntax and semantics, logical calculi. 
• Hilbert systems, soundness and completeness. 
• First-order logic, syntax and semantics. 
• First-order theories and models. 
• Hilbert systems for first-order logic, soundness and completeness. 
• Introduction to modal logics, Kripke semantics, correspondence theory, 
• Overview of systems of modal logics: alethic, deontic, epistemic, agentive, temporal. 
• Limits of Kripke semantics 
• Topics in non-classical logics. 

Second part:

• Presentations of selected research topics. 

RECOMMENDED READING/BIBLIOGRAPHY

All the required materials (slides, lecture notes, articles, chapters) will be provided in AulaWeb.

Alternatively,

For the part on propositional and first-order logic and Hilbert systems:

• E. Mendelson. Introduzione alla logica matematica. Bollati Boringhieri. (chapter 1 to 2.6).

Or

• D. Palladino. Logica e teorie formalizzate, Carocci. (chapters 1  and 2).

For the part on modal logics:

• B. Chellas, Modal Logic: An Introduction, Cambridge: Cambridge University Press.

or

• Frixione M., Iaquinto S., Vignolo M., Introduzione alle logiche modali, Laterza.

For the second part of the course:

An article or chapters among those suggested and included in Aulaweb.

For NON-attending students: besides the texts reported above, please contact me to decide the program. 

TEACHERS AND EXAM BOARD

Exam Board

DANIELE PORELLO (President)

MARCELLO FRIXIONE

MARIA CRISTINA AMORETTI (Substitute)

LESSONS

LESSONS START

29 September 2021

Wednesday 11.00 -- 13.00

Thursday  11.00 -- 13.00 

Class schedule

LOGIC (LM)

EXAMS

EXAM DESCRIPTION

The exam is divided into two parts.

1) Presentation or project or short essay (15 points over 30) on a topic selected among a list of proposals discussed in the second part of the course. 

2) Oral exam (15 points over 30) about the topics of te first part of the course. 

NON-attending students: the exam is simlar, only please contact me to decide the topics for point 1).

The registration for the examination is mandatory and must be done at least one week before the exam.

ASSESSMENT METHODS

Attending students

- The presentation or project or short essay (15 points out of 30) assesses the student’s ability to understand, synthesize and expose a text of philosophical logic,  or a problem, and to apply the tools of logical reasoning in the discussion of philosophical problems;

-The oral exam (15 points out of 30) assesses the student’s ability to understand, retain, explain and apply the logical concepts introduced in the fist part of the course. 

Exam schedule

FURTHER INFORMATION

Students that do not attend classes are required to get in touch with the professor.