• Description

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 subject within the syllabus as a whole

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.

• Professional fields to which it applies

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.

• Prior knowledge

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

• Information prior to enrolment

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

• Learning objectives and results

General objective:

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

Competences:

• 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.

• Content

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

• View the UOC learning resources used in the subject

• Additional information on support tools and learning resources

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.

• Guidelines on assessment at the UOC

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.

• View the assessment model