Master in Logic, 120 credits
The purpose of the Master's Programme in Logic is to provide a new generation of students with thorough theoretical knowledge, and the ability to apply it, within a central intellectual field, which gets its theoretical interest and practical value from a unique combination of humanities, mathematics and information science. For the Faculty of Arts this is a commitment to promote and further develop the field of mathematical humanities.
The main goal is that students, after successful completion of the programme, will have a coherent training and thorough understanding of the theoretical fundamentals of the subject of logic itself, its general role in the sciences and humanities, as well as its applications in fields like philosophy, linguistics, mathematics and computer science. Students will be well prepared for a career of research and development in logic and its applications, both in academia and industry.
The programme starts with a number of core courses, common for all students, which provide a solid foundation in the fundamentals of theoretical logic and its applications, and then follow elective courses, tailored to the background, interests and career plans for individual students.
The structure of the programme changed slightly in 2021. If you started the programme in 2021 or earlier please see the old information available here.
Obligatory courses are listed below. You will find links to the course syllabi and to the latest Canvas activity for each course:
- Logical Theory, 15 cr, LOG111. Canvas activity for fall 2023.
- Set Theory, 7.5 cr, LOG121. Canvas activity for fall 2023.
- Modal Logic, 7.5 cr LOG131. Canvas activity for fall 2023.
- Proof Theory, 7.5 cr, LOG221. Canvas activity for spring 2023.
- Philosophy of Logic, 7.5 cr, LOG250. Canvas activity for spring 2023.
- Model theory, 7.5 cr, LOG211. Canvas activity for fall 2023.
- Colloquium course: History, methodology and applications of logic, 7.5 cr, LOG310
See below for elective courses.
The Research Seminar in Logic
- Every second Friday at 10:15 - 12:00.
- All are welcome.
- Please subscribe to the mailing list: https://listserv.gu.se/sympa/subscribe/logic
The Colloquium in Logic
- Some Fridays at 10:15 - 12:00.
- The focus of these talks is to give an overview of logic areas for master students.
- All are welcome.
- Talks around 45 minutes and then discussions/social chat.
- Announcements here on Canvas and schedule available here.
Elective courses are chosen by the student after counseling with the teacher who is assigned as her study tutor; this is to ensure that the student builds a sensible and competitive profile, with respect to her individual background, interests, potential and plans for future professional life.
There are three sets of elective courses to choose among: 1) the five recommended elective logic courses, 2) courses in other subject areas that you apply for through universityadmissions.se and 3) one of the five Specialization in Logic courses that can be tailored toward your special interests and needs.
1) The five recommended elective logic courses
- Models of Computation, LOG260: A model for computability describes how, and if, a function or operation can be computed. The course covers the many such models and how these models are related to one another. The course content includes: Finite automata, regular and context-free languages, Turing computability and recursive functions, the recursion theorem and relative Turing computability, basic results in complexity theory.
- Advanced Set Theory, LOG270: The course covers results of relative consistency in the axiomatic set theory Zermelo-Fraenkel (ZF). By using internal models for set theory, the relative consistency of Foundation, Choice and the Continuum hypothesis (CH) are shown. The method of forcing is used to prove the independence of CH, as well as other cardinal axioms.
- Logic, Games and Automata, LOG290: The course covers the mathematical theory that underlies reactive systems, typically finite state-based systems equipped with a system for interaction with the environment. The theory is studied through three theoretical perspectives: logic, games and automata. Automata theory is a powerful model of computing for state-based systems, logic provides a formal language for the specification of correctness properties, and by using ideas from game theory mathematical models of the system-environment interaction can be built.
- Category Theory, LOG350: The course starts with general category theory and defines the concept of a category. Examples of categories, constructed in set theory, are presented. Then, a number of central concepts in category theory defined by using abstract limits and universal properties are presented. The course also provides an introduction to topos theory, and its connection to logic and set theory. Finally, two central concepts in general category theory are defined and exemplified: functors and natural transformations.
- History of Logic, LOG280: History of Logic aims to visit the history of Western logical thought at 5 crucial moments; i) Aristotle’s syllogistic; ii) Leibniz’ universal calculus; iii) Kant’s logic of pure reason; iv) Bolzano’s logic as theory of science; and v) Frege’s logic as a foundation for arithmetics. The course aims to unveil the historical details of the shift from Aristotelian logic - which dominated Western logical thought until Frege’s time - to post-Fregean logic, which, triggered by mathematical enterprises, departs in fundamental ways from the Aristotelian tradition.
2) Courses in other subject areas
Such courses will need to be applied for (in time) through universityadmissions.se and observe that to include such a course in your exam you will need to get the course confirmed by your study tutor. Also note that you will need to fulfill the prerequisites. Below you will find a list of some of the courses at GU that we think may interest you:
- Computational semantics (LT2813)
- Artificial Intelligence: Cognitive Systems (LT2318)
- Topology (MMA100)
- Algebraiska strukturer (MMG500)
- Functional Programming (DIT143)
- Types for Programs and Proofs (DIT235)
3) One of the five Specialization in Logic courses
Specialization in Logic 1-5, 7.5 credits: LOG230, LOG240, LOG320, LOG330, and LOG340 can be filled with different content and are usually offered as reading courses. They can be used for preparing you for the thesis work and it is recommended to take at least one during the third semester of the programme. Below you will find some possible specializations:
- Formal theories of truth
- Computability and complexity theory
- Game theory and logic
- Philosophy of Mathematics
- Knowledge representation and logic for the web
- Models of Arithmetic
- Advanced philosophical logic
- Provability logic
But also other specializations, determined in consultation with your study tutor, are possible.
The syllabus page shows a table-oriented view of course schedule and basics of course grading. You can add any other comments, notes or thoughts you have about the course structure, course policies or anything else.
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