Logic and Set Theory

Cod: 21079

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

Total contact time: 26

1. Proposicional calculus

2. Predicate calculus

3. Set theory

It is intended that at the end of this Course, students should be able to:

• Recognize the usefulness of the formal reasoning, especially of mathematical reasoning.

• Apply the key techniques of propositional calculus, predicate calculus and set theory.

• The language of propositional calculus.

• The semantics of propositional calculus.

• The proofs in propositional calculus.

Predicate Calculus:

• The first-order languages.

• The semantics of predicate calculus.

• The proofs in predicate calculus.

Set theory:

• The nature of definitions.

• A subsystem of axioms to set theory.

• Operations on sets.

• Relations and functions.

Main

M. J. Edmundo, G. Ferreira e J. Gaspar, Introdução à Lógica Matemática (available online).

Complementary readings:

- M. S. Lourenço, Teoria Clássica da Dedução, Assirio & Alvim 1991.

- Richard T. W. Arthur, Natural Deduction: An Introduction to Logic with Real Arguments, a Little History, and Some Humour, Broadview Press, 2011.

E-learning.