Logic Code:  22.602    :  6
View general information   Description   The subject within the syllabus as a whole   Professional fields to which it applies   Prior knowledge   Information prior to enrolment   Learning objectives and results   Content   View the UOC learning resources used in the subject   Additional information on support tools and learning resources   Guidelines on assessment at the UOC   View the assessment model  
This is the course plan for the second semester of the academic year 2023/2024. To check whether the course is being run this semester, go to the Virtual Campus section More UOC / The University / Programmes of study section on Campus. Once teaching starts, you'll be able to find it in the classroom. The course plan may be subject to change.

Logic permeates the entire scientific world and contributes, directly or indirectly, with the rigor that characterizes it. It is a basic knowledge for all scientific disciplines, and especially for computer science, both in its theoretical aspect and in the most practical and applied aspect.

The logical foundations that this subject provides are projected towards other subjects of the computer science degrees. Given this fundamental nature, logic is located at the initial levels of these degrees, close to other fundamental subjects such as algebra and calculus, and also close to subjects in the areas of programming or computer architecture.


The Logic subject is related to the other subjects of a mathematical nature and provides students with the logical-mathematical foundations that will facilitate the study of subsequent subjects in different areas of knowledge.

It is fundamental for the entire area of programming languages because of its importance in providing algorithms with a good logical structure, and because of its relevance in the verification and formal derivation of algorithms.

It is also essential for the study of database subjects that follow the relational model as a data model, since the standard language is based on predicate logic, SQL, for its manipulation.

Finally, it provides the necessary knowledge for the study of subjects in the area of computer technology, since the correct operation of hardware requires a good logical design.


The Logic subject enhances skills that are useful and important when interpreting and analyzing problems, as a preliminary step to solving them mechanically. One of the objectives is to learn to formalize using logical language. In the professional activity of computer science, the task of proposing mechanized solutions to problems that are often poorly or poorly specified is common. The skills and aptitudes necessary to formalize and to validate or refute reasoning are, fundamentally, the same ones that allow detecting the problems of a poorly or not at all correct specification.

Day by day artificial intelligence and its methods gain importance in many professional fields related to computer science. In that case, logic would be an excellent introductory tool.


It does not require any specific prior knowledge, except those that are essential for access to technical degrees at the University.


It does not require having previously taken other subjects of the degree.


General objective:

  • To know the fundamentals of the logic of statements and predicates and know how to apply their basic methodologies.


  • Specific competence of the degree:
    • Ability to understand and use the scientific bases of software development to analyze each problem at the appropriate level of abstraction for each situation and to apply the acquired skills and knowledge to address and solve it.
  • Competences of the course:
    • To learn to formalize natural language expressions using predicate logic.
    • To acquire skills to validate reasonings in predicate logic using the natural deduction method.
    • To acquire skills to validate reasonings in predicate logic using the resolution method.
    • To understand semantics of logic and know how to apply it in the validation of reasonings.


The content of the course is divided into two didactic modules that have a remarkable interrelation between them.

Module 1: Logic of statement

  • Logic of statements and its language
  • Natural deduction
  • Truth and falsehood: alternative and complement of natural deduction
  • The algebra of statements
  • Resolution

Module 2: Predicate Logic

  • Predicate logic and its language
  • The natural deduction
  • Truth and falsehood in predicate logic
  • Normal forms
  • Resolution

As it can be seen in this table of contents, the topics of the first module are repeated in the second. The variation consists of the formalism used (more complex in the second part than in the first one).

In addition, there are two more modules that are not evaluable and that remain as annex and extension material. 

Module 3: Logic and Boolean Algebra

Module 4: Set Theory


Logic and Boolean algebra PDF
Predicate logic PDF
Basic set theory PDF
Logic of statements PDF
Logic: Weekly Study Guide PDF
Formalization in the propositional logic(1). Parenthetization and hierarchy of symbols in propositional logic Audiovisual
Natural deduction in the predicate logic. How to advance in a natural deduction in predicate logic? Audiovisual
Formalization in the predicate logic. Keys to the formalization with quantifiers in the predicate logic Audiovisual
Natural deduction in the propositional logic. Strategic approach to proves by natural deduction Audiovisual
Formalization in the propositional logic(2). Sufficient and necessary conditions in propositional logic Audiovisual


Textual modules.

Four textual modules published by the UOC. All the concepts that are exposed in the learning modules are illustrated with examples. In addition, each module contains a number of self-assessment exercises, all of them solved.


Educational software.

The UOC has developed educational software that facilitates and supports the learning of the most important topics of the course. It allows solving different exercises, guiding and informing about the correctness or not of the solutions. It is a tool that that is also used in self-assessment and continuous assessment.


The assessment process is based on students' own work and the assumption that this work is original and has been carried out by them.

In assessment activities, the following irregular behaviours, among others, may have serious academic and disciplinary consequences: someone else being involved in carrying out the student's assessment test or activity, or the work being not entirely original; copying another's work or committing plagiarism; attempting to cheat to obtain better academic results; collaborating in, covering up or encouraging copying; or using unauthorized material, software or devices during assessment.

If students are caught engaging in any of these irregular behaviours, they may receive a fail mark (D/0) for the assessable activities set out in the course plan (including the final tests) or in the final mark for the course. This could be because they have used unauthorized materials, software or devices (e.g. social networking sites or internet search engines) during the tests, because they have copied text fragments from an external source (internet, notes, books, articles, other student's projects or activities, etc.) without correctly citing the source, or because they have engaged in any other irregular conduct.

In accordance with the UOC's academic regulations , irregular conduct during assessment, besides leading to a failing mark for the course, may be grounds for disciplinary proceedings and, where appropriate, the corresponding punishment, as established in the UOC's coexistence regulations.

In its assessment process, the UOC reserves the right to:

  • Ask the student to provide proof of their identity, as established in the university's academic regulations.
  • Request that students provide evidence of the authorship of their work, throughout the assessment process, both in continuous and final assessment, by means of an oral test or by whatever other synchronous or asynchronous means the UOC specifies. These means will check students' knowledge and competencies to verify authorship of their work, and under no circumstances will they constitute a second assessment. If it is not possible to guarantee the student's authorship, they will receive a D grade in the case of continuous assessment or a Fail in the case of final assessment.

    For this purpose, the UOC may require that students use a microphone, webcam or other devices during the assessment process, in which case it will be the student's responsibility to check that such devices are working correctly.


There are two ways to pass the course:

  1. Through continuous assessment and a synthesis test:
    • If you pass the continuous assessment and get the minimum required mark in the synthesis test, your final mark will be based on the weightings specified in the course plan.
    • If you pass the continuous assessment and don't get the minimum required mark in the synthesis test, your final mark will be your numerical mark from the synthesis test.
    • If you pass the continuous assessment and don't sit the synthesis test, you'll receive a final mark of Absent.
    • If you fail the continuous assessment, you'll receive a final mark of Absent.
    • If you don't take part in the continuous assessment, you'll receive a final mark of Absent.

  2. Through an exam (if you take this route, you don't need to have passed the continuous assessment in order to sit the exam):
    • If you haven't taken part in the continuous assessment, your final mark will be your numerical mark from the exam.
    • If your continuous assessment mark is something other than Absent, your final mark will be the more favourable of: the numerical mark from the exam; or the calculation of your continuous assessment mark weighted with your exam mark, as specified in the course plan. In order to apply this calculation, you must get a minimum mark of 4 in the exam (if your mark is lower, your final mark for the course will be your exam mark).
    • If you don't sit the exam, you'll receive a final mark of Absent.