Objectives and competences

The master's degree in Pure and Applied Logic joins the forces of the University of Barcelona (UB) and the Polytechnic University of Catalonia (UPC), with the expertise of the Artificial Intelligence Research Institute (IIIA) of the Spanish National Research Council (CSIC), thus creating Spain's largest cluster of internationally recognized experts and passionate teachers in the field. Because of this, our master's degree was awarded the international recognition of excellence by the University of Barcelona.

While the master includes fundamental courses in the main areas of logic, our programme encourages students to design their individual journey through the topic by choosing between a variety of advanced courses on algebraic logic, computability theory, computational complexity, history of logic, model theory, non-classical logic, proof theory, and set theory.

Consult the Digital Repository to browse some of the master's theses completed as part of this programme

Basic information

TypeMaster's degree
Faculty or schoolFaculty of Philosophy
Branch of knowledge
  • Mathematics and statistics
  • History, archaeology, geography, philosophy and humanities
  • Computer and systems engineering
Mode of delivery
  • Face-to-face
Number of places available25
Length of course2 academic years
Language(s) of instructionEnglish
Approximate price per credit27.67 euros per credit (82 euros for students who are not EU nationals and do not currently reside in Spain). Fees for the academic year 2023-2024
Course detailsIndicators
Open pre-enrolmentNo
Open enrolmentNo
Lead to doctoral studiesYes
Admission for applicants not holding a degree qualificationNo
Main universityUniversitat Barcelona
  • Universitat Barcelona
  • Universitat Politècnica de Catalunya
Bridging coursesYes

Objectives and competences


The master's degree in Pure and Applied Logic provides advanced training in the main areas of logic. Graduates will be in a perfect position to start a research career in logic and related areas. The course also serves as excellent preparation for employment opportunities requiring a high level of analytical and problem-solving skills.


Generaal competences

  • Capacity to carry out original research in logic and to apply the knowledge and skills acquired to new multidisciplinary environments.
  • Capacity to present the solutions to exercises and problems in a clear, concise, and coherent manner.
  • Capacity to argue correctly and justify assertions with evidence, in line with the current standards of the research community.
  • Capacity to write and present a master's degree thesis.
  • Capacity to work properly and efficiently in order to resolve the problems posed in the different subjects from the master's degree.
  • Capacity to plan adequately the public exhibition of a research project according to time and facilities available.
  • Capacity to make efficient use of IT and audiovisual technologies to communicate the results of a research project.


Specific competences 

  • Capacity to resolve problems in logic in an understandable and elegant manner.
  • Command the fundamental concepts of mathematical logic.
  • Capacity to resolve problems related to the master's degree courses.
  • Capacity to apply the concepts of contemporary logic to the study of the history of logic.
  • Capacity to understand the technical concepts to study the arguments used in the philosophy of mathematics and philosophy of logic.
  • Capacity to design algorithms dealt with during the master's degree.
  • Capacity to understand articles from the scientific literature.
  • Capacity to formulate original and meaningful conjectures in various areas of logic.
  • Capacity to plan and conduct a piece of original research in one of the topics covered by the master's degree.
  • Command of the mathematical tools used in specialized branches of mathematical logic.
  • Capacity to demonstrate a broad knowledge of non-classical logics.
  • Capacity to integrate semantic, syntactic and algebraic tools to study different kinds of logic.
  • Capacity to relate the topics in logic covered by the modules with their corresponding philosophical implications.
  • Capacity to explain current trends of research in mathematical logic in a clear and comprehensible manner.


Access and admission

Applicant profile and access requirements

Recommended applicant profile

Students applying to the master's degree must have:

- An interest in the field of logic.
- An analytical mind and the capacity for rigorous, abstract reasoning (for instance, having successfully completed modules in mathematics or formal logic at undergraduate or postgraduate level).
- A good level of spoken and written English.

Access requirements and conditions

General requirements
In accordance with Article 16 of Royal Decree 1393/2007, of 29 October, students wishing to be admitted to a university master's degree must hold one of the following qualifications:

  • Official Spanish university degree.

  • A degree issued by a higher education institution within the European Higher Education Area framework that authorizes the holder to access university master's degree courses in the country of issue.

  • A qualification issued by an institution outside the framework of the European Higher Education Area. In this case, applicants must request homologation of the degree to its equivalent official Spanish university qualification or obtain express approval from the University of Barcelona, which will conduct a study of equivalence to ensure that the degree is of a comparable level to an official Spanish university qualification and that it grants access to university master's degree study in the country of issue. Admission shall not, in any case, imply that prior qualifications have been recognized as equivalent to a Spanish master's degree and does not confer recognition for any purposes other than that of admission to the master's degree course.

Specific requirements
The bachelor's degrees that grant direct access to this master's degree are Mathematics, Computer Science, Philosophy and Physics, as well as degrees in related disciplines.

In principle, graduates of any of the official degrees that grant access may apply. Candidates who do not hold any of these degrees may also be considered for admission, if they show that they fit the recommended profile and that, in the opinion of the Coordination Committee, they have sufficient knowledge of logic.

At the discretion of the Coordination Committee, philosophy graduates may be required to take the bridging subjects Mathematical Language and Reasoning, Arithmetic, and Linear Algebra from the UB bachelor's degree in Mathematics.

Candidates should have a level of English equivalent to B1 in the Common European Framework of Reference for Languages. They will be required to understand lectures and complete written exercises and assignments in English.



2 February - 16 July 2024.


  • Pre-enrolment fee: A pre-enrolment fee of 30,21 euros is charged. Students who apply to more than one master's degree must pay the fee for each pre-enrolment request. Pre-enrolment requests cannot be processed until this fee has been paid.Fees will only be refunded if the master's degree in question is suspended.
  • Reserved places: A maximum of 5% of the new places of the master's degree are reserved for students who meet the general and specific access requirements and accredit the recognition of a degree of disability equal to or greater than 33%.

Required documentation

Selection criteria

Applications are considered by the Coordination Committee on the basis of the following criteria:

  1. Grade average in bachelor's or postgraduate degrees.

  2. Prior training in logic, which should at least include a good knowledge of first-order logic.

  3. Reference letters.

  4. Candidate's motivation for studying the master's degree.

The Coordination Committee scores each of the criteria as follows: a maximum of 70 points from criteria 1 and 2; a maximum of 20 points for criterion 3; and a maximum of 10 points for criterion 4. Knowledge of English is required.


All applicants will be informed of the outcome of their application by email. Successful applicants will also receive a formal letter of admission.


As a general rule, at the UB you will be required to enrol online. Remember that you can lose your place if you do not enrol on the day you have been assigned

Course curriculum

Subjects and course plans

Distribution of credits

Compulsory 30
Optional 40
Compulsory placements 0
Compulsory final project 20

List of subjects

Subject Type Language Credits
Specialization: Pure and Applied Logic
Algebraic Logic Optional 2nd semester 5
Algorithms for VLSI Optional 1st semester 6
Basic Model Theory Compulsory 2nd semester 6
Basic Set Theory Compulsory 1st semester 6
Combinatorial Problem Solving Optional 2nd semester 6
Combinatory Set Theory Optional 2nd semester 5
Computability Theory Compulsory 1st semester 6
Computational Complexity Optional 2nd semester 6
Final Project Compulsory 2nd semester 20
Introduction to Mathematical Logic Optional 1st semester 5
Mathematical Logic Compulsory 2nd semester 6
Modal Logic Optional 2nd semester 5
Non-Classical Logics Compulsory 1st semester 6
Orders, Reticles and Boolean Algebra Optional 1st semester 5
Universal Algebra Optional 1st semester 5

Previous years


Placements in a company or another type of organization are an integral part of university studies, providing first-hand experience of working methodologies in students' chosen professional fields. They offer invaluable practical experience for the transition into work after graduation.

Placements are supervised by tutors and subject to assessment. They are therefore included in the academic record.  There is also an option to complete non-curricular placements of up to 500 hours, which can be extended to 900 hours. For both curricular and non-curricular placements, an educational cooperation agreement is signed between the UB and the company, institution or other organization at which the placement will be carried out.

Institutional information

Career opportunities

What can you work on ?

This master's degree is specifically focused on research. Career opportunities include academic positions or posts at research institutes, and the typical opportunities available to graduates in mathematics, computer science and other disciplines that provide rigorous training in analysis and problem-solving, such as jobs in science and technology companies and in finance.

Access to the labour market

Data from the university system in Catalonia

Contact us

Faculty of Philosoy
Montalegre, 6 - 08001 Barcelona

Secretary: 934 037 722 - 934 037 719

Coordinator: 93 403 75 16

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