Elements of Logic

Cod: 22216

Department: DCET

Department: DCET

ECTS: 5

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 130

Total contact time: 20

Total contact time: 20

In this curricular unit, some advanced aspects of the systematic formalization of mathematical reasoning carried out by Mathematical Logic are developed, including results of decidability, undecidability, completeness and incompleteness of mathematical theories.

Logic;

Mathematical reasoning;

Proof Theory;

Axiomatic Theories.

Mathematical reasoning;

Proof Theory;

Axiomatic Theories.

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

• Recognize the usefulness of Logic in the formalization of mathematical reasoning;

• Work with a set of methods and concepts of first order logic, proof theory and model theory;

• Understand and apply results of decidability, undecidability, completeness and incompleteness of mathematical theories.

• Recognize the usefulness of Logic in the formalization of mathematical reasoning;

• Work with a set of methods and concepts of first order logic, proof theory and model theory;

• Understand and apply results of decidability, undecidability, completeness and incompleteness of mathematical theories.

- Propositional Calculus
- Normal forms
- Predicate Calculus
- Formal proof systems
- Peano arithmetic and other axiomatic theories

• M. Edmundo, Introdução à Lógica, author notes, 2013.

• R. Cori, D. Lascar, Mathematical Logic, Part I, Oxford University Press, 2000.

• E. Mendelson, Introduction to Mathematical Logic, Fourth Edition Champman & Hall/CRC 2001.

• Hanbook of Mathematical Logic, volume 90, edited by Jon Barwise, 1977.

• R. Cori, D. Lascar, Mathematical Logic, Part I, Oxford University Press, 2000.

• E. Mendelson, Introduction to Mathematical Logic, Fourth Edition Champman & Hall/CRC 2001.

• Hanbook of Mathematical Logic, volume 90, edited by Jon Barwise, 1977.

Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and
final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.