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 representation, formal semantics, formal ontology, or artificial intelligence. 

AIMS AND LEARNING OUTCOMES

Objectives of the course are:

• Expand the comprehension of classical propositional and first-order logic.
• Introduce logical calculi (e.g. Hilbert Systems, Natural Deduction, or Sequent Calculi).
• 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 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 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 logics.
• Understand the main elements of  number of selected non-classical logics.
• Familiarise with research topics in logic by approaching logical texts autonomously. 

PREREQUISITES

The course is designed to expand the course of logic for the bachelor in philosophy.

Knowledge of classical propositional and first-order logic is then a prerequisite for this course. 

TEACHING METHODS

Lectures are hopefully held in presence. Non-attending students are rerquired to contact me to decide the content of the exam and to access to further teaching materials. 

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, logical calculi, 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:

• Hilbert systems, soundness and completeness. 
• First-order theories and models. 
• Natural Deduction and Sequent Calculi.
• 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.