- Docente: Giovanna Corsi
- Credits: 12
- SSD: M-FIL/02
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Italian Studies, European Literary Cultures, Linguistics (cod. 0973)
Learning outcomes
In the first part of the course students are introduced to formal
reasoning, to propositional and first-order logic. These topics
constitute a pre-requisite to deal, in the second part of the
course, with problems related to the foundations of mathematics,
intensional semantics, theories of language, proof theory.
Course contents
I part First-order languages, in particular the language of
set theory. Naive set theory. Principles of comprehension and
extensionality. Operations on sets. Relations and functions. The
axiom of choice. Definitions by abstraction and definitions by
induction. Fixed points. Finite and infinite sets. The theorem of
diagonalization by Cantor. Transfinite numbers. On the paradoxes of
naive set theory. Discussion of the notion of existence in
mathematics: Poincare', Russell, Brouwer.
II parte for the students of Corso in
Italianistica, Culture Letterarie Europee, Scienze
Linguistiche [12cfu]. Grammars and automata. Automata accepting
formal languages. Automata and finite languages. Regular languages.
Context-free languages and context-sensitive languages. The Chomsky
hierarchy. Lambek's grammars.
II parte for the students of Corso Erasmus Mundus in
Culture Letterarie Europee. The program is the same as that of
the I part and the lectures will be in English.
Readings/Bibliography
Halmos P.R., Naive Set Theory, Springer, 1974.
Fraenkel A., Set Theory and Logic, Addison-Wesley,
1966.
Poincare' H., "La logique de l'infini' " in Gerhard Heinzmann (ed.)
Poincare', Russell, Zermelo et Peano : textes de la discussion
(1906-1912) Sur les fondements mathematiques : des antonomies a' la
predicativite', A. Blanchard, 1986.
Teaching methods
Lectures ex-cathedra with projections from "Le basi della
logica on-line".
Tutorials by dr Guido Gherardi will be arranged.
Assessment methods
A written test at the end of the first part and a brief essay
concerning 3 topics discussed during the second part of the
course.
Teaching tools
Standard tools: black-board and chalk, overhead projector, front
projector for slides.
Links to further information
http://www.moodle.unibo.it/course/category.php?id=23
Office hours
See the website of Giovanna Corsi