09674 - Logic and Epistemology

Learning outcomes

The course aims to provide students with the fundamental conceptual tools to address some central epistemological notions such as belief, truth, epistemic justification. Their mutual relations, as well as the relationships holding between them and other core epistemological notions, will be investigated in depth. Students will acquire the capability to orientate themselves in the contemporary debate on the nature and role of scientific theories and on the relationship between observation and theory, to critically analyze original texts, and to discuss the main theoretical perspectives dealt with in the course.

Course contents

II MODULE (Francesco Bianchini) From philosophy of science to artificial intelligence

The first module of the course consists of two parts. In the first part I deal with typical issues of the philosophy of science, starting from their historical development and evolution, and with regard to present-day debates. Main topics are: inductivism, verificationism and falsificationism, the underdetermination of scientific theories, reductionism, scientific realism, the models of scientific explanation and the use of models in science. In the second part, starting from the crisis of foundations in mathematics, I deal with some issues of philosophy of science related to artificial intelligence, its birth, its development and some of its main subjects, pointing out and discussing the most important epistemological issues of artificial intelligence.

This is a basic course and does not require previous knowledge of the fields related to its main topics.

 

I MODULE (Guido Gherardi) Propositional Modal Logics

The second set of lectures (30 hours) will deal with 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 that precise state of things, but also on others. The truth or the falsehood today of “tomorrow the course will start” does not only depend on what is happening now, but also on what it will happen tomorrow. This basic example suffices to understand how the possible world semantics can provide suitable models for all cases in which semantical values depend on a variety of interrelated states of things. In particular, the notions of necessity and possibility find a satisfying treatment in the Kripkean possible world semantics.

This part of the course will start with an historical overview about the philosophical investigation of the aletic modalities “to be necessary” and “to be possible”. It will then treat the following subjects: syntax of propositional modal logics; Kripkean possible worlds semantics; expressible and non-expressible properties in modal propositional logic language; main systems of normal modal logics; labelled sequent calculi for modal logics; Completeness Thorems.

Readings/Bibliography

II MODULE

J. Ladyman, Filosofia della scienza. Un’introduzione, Carocci, Roma, 2007.

D. Gillies, Intelligenza artificiale e metodo scientifico, Raffaello Cortina, Milano, 1998.

K. Warwick, Intelligenza artificiale. Le basi, Flaccovio Editore, 2015.

 

During the course passages are read and discussed from:

V. Somenzi, R. Cordeschi, La filosofia degli automi, Bollati Boringhieri, Torino, 1994.

G. Boniolo, M.L. Dalla Chiara, G. Giorello, C. Sinigaglia, S. Tagliagambe, Filosofia della scienza, Raffaello Cortina, Milano, 2002.

 

I MODULE

The handout provided by the teacher during the course will constitute the most important didactical support for the student.

The following volumes are recommended as side material:

M. Mugnai: Possibile/Necessario. il Mulino. 2013.

Chagrov, M. Zakharyaschev: Modal Logic. Claredon Press. 1997

S. Negri, J. von Plato: Proof Analysis: a contribution to Hilbert’s last problem. Cambridge University Press. 2011

Possible further bibliographic references may be provided by the teacher during the course.

 

 

Teaching methods

Lectures. Personal or group presentations on a subject agreed with teachers will be possible.

Assessment methods

A distinct oral examination will have to be taken for each module of the course. The examinations aim at assessing the attainment of the expected learning outcomes. The final grade is the simple mean of the grades received in the two examinations.

 

II MODULE

Student will be tested through an oral examination in which s/he will face general subjects of philosophy of science and artificial intelligence. The knowledge of the topics of the course and the capability of using them autonomously will be taken into consideration, together with the ability in producing personal remarks on the contents developed during the lessons. If it will be possible, student might be required to apply the main concepts in simple exercises.

 

 

More specifically, the achievement of the following targets will have a growing weight:

 

1) the completeness of the basic knowledge strictly connected to the program;

2) the appropriateness of the specific language;

3) the capability of personally re-using concepts learned during the course;

4) the capability to manage interdisciplinary reflections and argumentations;

5) the capability to apply the subjects to specific research cases and to produce autonomous and original remarks.

 

1) and 2) are the lowest targets for the pass mark. 3) could give a fair evaluation, the more being so the less the learned knowledge will be mnemonic. 4) is for a good outcome, 5) for an excellent one.

 

I MODULE

During the oral exam the level of the student's comprehension concerning the basic notions and the poof techniques for the treatment of Propositional (Normal) Modal Logics introduced in the course will be tested. The student is supposed to be able to present the definitions of the basic concepts of the theory correctly and to reconstruct the proofs discussed in the lectures, by showing a suitable use of the formal language and a correct comprehension of the conceptual structure involved.

 

 

Teaching tools

II MODULE

Slides and online contents will be used during lectures.

 

I MODULE

Blackboard and handouts will be used by the teacher.

Office hours

See the website of Guido Gherardi

See the website of Francesco Bianchini