Module page
Logica matematica
| academic year: | 2013/2014 |
| instructor: | Claudio Bernardi |
| degree course: | Mathematics - DM 270/04 (triennale), III year |
| type of training activity: | caratterizzante |
| credits: | 6 (48 class hours) |
| scientific sector: | MAT/01 Logica matematica |
| teaching language: | italiano |
| period: | I sem (30/09/2013 - 17/01/2014) |
Lecture meeting time and location
Presence: highly recommended
Module subject:
Natural language and formal language. Propositional calculus. Predicate calculus. Peano Arithmetic and Goedel Theorems. Introduction to the theory of recursive functions. Theories and models; properties of axiomatic theories.
Suggested reading: M. Borga, Elementi di logica matematica, La Goliardica E. Mendelson, Introduzione alla logica matematica, Boringhieri C. Toffalori, P. Cintioli, Logica matematica, McGraw Hill Notes are distributed about Goedel theorems, as well as exercises about all subjects.
Type of course: standard
Knowledge and understanding: Logical languages: connectives, quantifiers and their properties. An axiomatic system for propositional calculus. Tautologies and theorems. Deduction theorem and completeness theorem. An axiomatic system for predicate calculus. True formulas and valid formulas. Soundness and completeness theorem. Partial recursive functions; r.e. sets and recursive sets. First and second Goedel theorems.
Skills and attributes: Mathematical rigor and formalization. Recognizing: tautologies in propositional calculus, simple true formulas in predicate calculus, and so on. Application of inference rules. General rethinking of already studied mathematical subjects; translation of known concepts in an axiomatic theory with a suitable language. Proving classical logical theorems and solving exercises in mathematical logic.
Personal study: the percentage of personal study required by this course is the 65% of the total.