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.

Propositional calculus:
• 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 Bibliography:

M. J. Edmundo, G. Ferreira and J. Gaspar, Introdução à Lógica Matemática: Cálculo de Proposições e Cálculo de Predicados (Introduction to Mathematical Logic: Propositional Calculus and Predicate Calculus). E-book, Series: eUAb | University Collection No. 36, Universidade Aberta. It can be purchased at  https://resellers.euebooks.com/uab/catalog/all

Supplementary Bibliography (purchase not required):

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.

Other materials, namely notes on Set Theory, will be provided online.

E-learning.

Continuous assessment is privileged: 2 digital written documents (e-folios) during the semester (40%) and a final digital test, Global e-folio (e-folio G) at the end of the semester (60%). In due time, students can alternatively choose to perform one final exam (100%).