Logics

Recommended Prerequisites

Knowledge of group theory obtained in a first undergraduate course of Algebra.

Teaching Methods

The teaching/learning process follows an approach based on online collaborative learning, in virtual class, that involves the realization of assignments, both individual and in group.

The evaluation of this LU is based on the following factors: quality of the student participation in discussions in the virtual class; the results of  assignments. The weighting factors and the criteria of evaluation of the learning outcomes will be subject of negotiation between students and teacher.   

Learning Outcomes

The aim of the unit is to equip students with the necessary techniques, competences and knowledge in the area of Logics so that these can be used in automatic theorem proving.

After completing this unit, the students should

• appreciate the importance of Logics and of its applications to decidability in Mathematics ;
• Identify, classify and absorb the principles, concepts and techniques of Logics and their applications to automatic theorem proving.

Work Placement(s)

No

Syllabus

1. Propositional Logic
2. Normal forms
3. First Order Logic - Semantics
4. First Order Logic - Calculus
5. Arithmetic
6. (Un)Decidability and Complexity
7. Algorithms for Theorem Proving.  

Assessment Methods

Assessment
Exam: 30.0%
Research work: 35.0%
Resolution Problems: 35.0%

Bibliography

- “Mathematical logic”, R. Cori & D. Lascar, Oxford University Press, 2000.

- “Automated reasoning with Otter”, J. A. kalman, Rinton Press, 2001.

- “Automated deduction in equational logic and cubic curves”, W. McCune and R. Padmanabhan, Lecture Notes in Computer Science, Springer-Verlag, 1996.