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.