02607 - Logic

Learning outcomes

Students will get to know about extensions of propositional and first order logic: in the first part, modal logics viewed as extensions of the propositional classical logic and in the second part some first order theories together with some of their metatheoretical properties.

Course contents

(A) (6 cfu) Basic notions of formal logic.
1 Formalized languages, object language and metalanguage. Logical terms and extra-logical terms, logical form.
2 Definitions by mathematical induction
3. Sentential logic: truth functions, tautologies, logical consequence, consistency.
4. Hilbert's style calculus for proposiitonal logic.
5. Proofs by mathematical induction
6. Deduction theorem (with its proof)
7. Gentzen's style calculus for propositional logic
8.  First-order languages: variables and quantifiers. Theory of syllogism.
9. Translation from natural language to first-order languages. The articles. Numerical quantifiers.

The first parte of the course will be online at the website http://www.moodle.unibo.it/course/category.php?id=129 "Le basi della logica on-line", so that students will be able to solve exercises in an interactive form with the assistance of suitable software.

(A + B) (12 cfu) 
(B) Firts-order logic
1 Semantics for first-order languages
2. Hilbert's style calculi for first-order logic. Elements of the theory of identity.
3. Deduction theorem (with proof).
4. Soundness and completeness theorems.
5. Gentzen's style calculus for first-order logic
6. Construction of models and countermodels
7. First-order theories, in particular set theory and Peano arithmetic.
8. As to set theory, the principles of extensionality and comprehension will be discussed as well as Russell's paradox. A brief introduction to Zermelo-Fraenkel set theory.
9 First-order axiomatization of Peano arithmetic. Brief introduction to Goedel's incompleteness theorems.

Readings/Bibliography

(A)
Dario Palladino, Corso di Logica, Carocci 2002 (except the last chapter).
Le basi della logica on-line at http://www.moodle.unibo.it/course/category.php?id=23
Lectures notes by the teacher

(B)
Dario Palladino, Logica e Teorie Formalizzate, Carocci 2004 (selected pages)
Lectures notes by the teacher

Teaching methods

Lectures ex cathedra and tutorials

Assessment methods

Written examination for (A). Written and oral examination for (B).

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=129

Office hours

See the website of Giovanna Corsi