CODE 84346 2024/2025 6 cfu anno 1 METODOLOGIE FILOSOFICHE 8465 (LM-78) - GENOVA 6 cfu anno 2 METODOLOGIE FILOSOFICHE 8465 (LM-78) - GENOVA M-FIL/02 Italian GENOVA 1° Semester AULAWEB

## OVERVIEW

The course expands a few topics in classical logic, introduces modal logics, and discusses 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 representation, 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 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 collaboratively or autonomously.
• Improve collaborative interaction, constructive communication, and dialogical skills.
• Approach the proposed problems with creativity.
• Show autonomy, capacity of confonting primary literature, argumentation skills, cooperative attitude, coordination and negotiation with others.

### 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, individually and in groups, to train individual and collective problem solving skills and rational interaction.

For the second part, the course consists of presentations of research topics and collaborative projects 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.

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.

September 2024

LOGIC (LM)

## EXAMS

### EXAM DESCRIPTION

The exam is divided into two parts.

1) Presentation or project or short essay, individually or in group, to be discussed in class on a topic selected among a list of proposals discussed in the second part of the course.

2) Oral exam about the topics of te first part of the course.

Attendance is strongly encouraged, due the the practical and interactive components of the course.

Non-attending students must contact me in time to decide the program.

The registration to the exam 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 logical and 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.

Attendance is strongly encouraged, due to the practice and interactive moments of this course. Non-attending students must contact me in due time to decide the program and select the topic for the presentation or short essay.

The assement depends on

• the correct use of the technical jargon of logic,
• the quality of exposition,
• the capacity of using logical methods,
• the capacity of approaching logical topics autonomously.
• the creative approach to problem solving.

### FURTHER INFORMATION

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