85001 - Logical Methods for Philosophy

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education

Academic Year 2021/2022

Learning outcomes

At end of course, the student has a critical and updated knowledge of the development of the logic of research and issues related to epistemology, the theory of computability, the development of theoretical computer science.

Course contents

Aim of the course is to provide the fundamental tools for the basic knowledge of modal and non-classical  logics conceived asa tool for philosophical analysis.

The topic of the course will be the propositional modal logics through the so-called possible world semantics. According to such semantics the truth of a statement in a state of things (“world”) does not depend only on this precise state of things, but also on others. This holds in particular for those statements that refer to what is necessary, possible, or impossible. For their treatment the ordinary truth-table semantics is useless. The notions of necessity and possibility find instead a satisfying treatment in the Kripkean possible world semantics. The intuitive idea is that of classifying as "necessary" in our world a statement that is true in all worlds that we can conceive, and as "possible" a statement that is true in at least one of such worlds.

Topics dealt with in the course:

- Historical overview about the philosophical investigation of the aletic modalities “to be necessary” and “to be possible”.

- Syntax of propositional modal logics.

- Kripkean possible worlds semantics.

-Expressible properties in modal propositional logic language and the theory of correspondences.

- Non-expressible properties in modal propositional logic language.

- Main systems of normal modal logic.

- Labelled sequent calculi for modal logics.

- Soundness and completeness.

-Admissibility of the structural rules of inference.


The treatment of the topics will be homogeneously distributed during the course.

Non-attending students are referred to the instructions given in the section "Readings/Bibliography".


  • Textbook:

Corso di logica modale proposizionale, Eugenio Orlandelli e Giovanna Corsi, Carocci 2019. Chapters 1, 2, 3, 9.

  • Optional books:

Logica modale quantificata e designatori non rigidi, Eugenio Orlandelli, CLUEB 2019.

Introduzione alle logiche modali, M.Frixione, S.Iaquinto, M.Vignolo, Editori Laterza 2016.

A Short Introduction to Intuitionistic Logic. Grigori Mints. Springer 2000.


Non-attending students must study two of these books (the choice has to be agreed together)

Teaching methods

Lessons in classroom with electronic blackboards also available in streaming. If possible, short presentations by the students.

Assessment methods

Oral  exam  based on the lessons and  the volumes cited the Bibliography section. Among other things, it will be asked to write down some definitions/proofs presented in the course.

Assessment criteria and thresholds of evaluation:

30 cum laude: Excellent performance as to knowledge, terminology and critical expression, essentially containing no mistakes.

30: Excellent performance, knowledge is complete, well articulated and correctly expressed, although with some slight faults.

27-29: Good performance, knowledge comprehensive and satisfactory, essentially correct expression, with some big mistake or gaps.

24-26: Fairly good, knowledge present in significant points, but not complete and not always expressed with correctness, presence of many mistakes and gaps.

21-23: Sufficient, knowledge is sometimes superficial, but the guiding general thread is included. Expression and articulation incomplete and often not appropriate, presence of many mistakes or gaps.

18-21: Almost sufficient, knowledge present only on the surface. The guiding principle is not included with continuity, presence of many big mistakes or gaps.

<18: Not sufficient, knowledge absent or very incomplete, lack of guidance in discipline, expression seriously deficient. Exam failed.

Teaching tools

- On line streaming

- Electronic blackboard

- Handouts of the teacher.

Office hours

See the website of Eugenio Orlandelli