13135 - Logic (2)

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

LOGICA (12 cfu) = (A) + (B) For those students who haven't yet taken any exam in Logic.
LOGICA (10 cfu) = (A) + (B) For those students who haven't yet taken any exam in Logic.
LOGICA (10 cfu) = (C) + (B) For those students who have taken Istituzioni di Logica.
LOGICA(1) (5 cfu) = (C) or (B) at the student choice. For those students who have taken Istituzioni di Logica.
LOGICA(2) (5 cfu) = (C) or (B) to be agreed by the teacher. For those students who have taken Istituzioni di Logica.
LOGICA (3 cfu) = (A)
ISTITUZIONI DI LOGICA (5cfu) = (A)
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(A) basic notions of elementary logic.
1 Formalized languages, object language and metalanguage. Logical terms and extra-logical terms, logical form.
2 Sentential logic: truth functions, tautologies, logical consequence, consistency.
3 First-order languages: variables and quantifiers. Theory of syllogism.
4 Semantics for first-order languages.
5 Translation from natural language to first-order languages. The articles. Numerical quantifiers.
6 Semantic trees. Models and countermodels.
The first parte of the course will be online at the website http://www.moodle.unibo.it/course/category.php?id=23 "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.


(B) 1 Calculi for first-order logic. Elements of the theory of identity.
2 Deduction theorem (with proof). Soundness and completeness theorems (without proof).
3 First-order theories, in particular set theory and Peano arithmetic.
4 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.
5 First-order axiomatization of Peano arithmetic. Brief introduction to Goedel's incompleteness theorems.

(C) Propositional modal logics. Historical introduction to eletic modalities (it is necessary, it is possible), temporal (always, sometimes), deontic (it is obligatory, it is permitted). Formal approach to modalities: Charles Irving Lewis and the first modal calculi. The Kripkean turn, possible world semantics: frame, model, truth in a model. Main systems of modal logics. Canonical model and completeness theorem. Canonical and non canonical logics. Finite models and filtrations. Incomplete modal logics, a discussion.

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

(B) Handouts.
Dario Palladino, Logica e Teorie Formalizzate, Carocci 2004 (selected pages)

(C) Handouts.
Rob Goldblatt, Logics of time and computation, CSLI 1992 (pagine scelte)
G. E. Hughes, M. J. Cresswell: A new introduction to modal logic, Routledge, 1996 (pagine scelte)

Teaching methods

Lectures ex cathedra.

Assessment methods

Written examination for (A). Oral examination for (B) and (C).

Teaching tools

Standard tools: black-board and chalk, overhead projector, front projector for slides.

Office hours

See the website of Giovanna Corsi