Course syllabus
Welcome to Logic and Completeness
This course is part of the Master in Logic and available as a free standing course. The course is typically taken in parallel with LOG121 Set Theory.
In previous years this course went under the name Logical Theory (LOG111). This course corresponds to the first half of Logical Theory.
Course content
Formal logic is the study of reasoning and meaning from a rigourous and mathematically precise standpoint. This course provides an introduction to formal logic central to the fields of mathematics, philosophy and theoretical computer science. The course covers two formal logics in detail, propositional logic and first order predicate logic, giving a comprehensive overview of their syntax, semantics and proof systems. Detailed proofs of the soundness and completeness theorems for both propositional and predicate logic are included. Elementary results on the semantics of predicate logic, such as the compactness theorem and (downwards) Löwenheim–Skolem–Tarski theorem, are presented with applications.
This course will follow the lecture notes Logical Theory.
Teachers & Examiners
The course is taught and examined by Graham Leigh graham.leigh@gu.se
Introduction
Monday 31 August at 11:15 - 12:15 in room J406.
Finding the room: All lectures/classes will be held in the Humanisten building at the Renströmsgatan 6 on Lorensberg Campus. J4xx indicates that the room is in the new part of the building (around the open staircase) on floor 4 (one floor above the main entrance). The rest of the number identifies the room according to some hitherto undisclosed total order.
Registration
You will be able to register on the course one week before it starts. When you have registered for the course you will get access to more course information.
You can find information regarding registration here.
Schedule
Below are links to the schedule in TimeEdit. There are two links - one which require login (your GU account) and one that does not. The link requiring login shows some additional information.
Schedule for LOG112 without login and with login
The schedule is preliminary until two weeks before the course starts. Please also note that the schedule is a "living document" and could be subject to changes throughout the semester. Make a habit of checking it every once in a while!
Course Syllabus and literature list
You can search for the course code (and other courses) on https://www.gu.se/en/study-gothenburg/study-options/find-syllabus-and-reading-list?hits=25 to find the course syllabi and literature list.
Weekly lecture plans
Weekly lecture plans with short comments and reading instructions will be made available through the Modules page. Please see the module for more information.
Examination
The examination (Swedish: tentamen) will take place on Thursday, 29 October 2026 at 8:00–12:00 in the central university examination halls. See the TimeEdit entry for location details. A resit examination is scheduled on Friday, 11 December 2026, 08:00–12:00.
Learning outcomes
On successful completion of the course the student will be able to:
Knowledge and understanding
- demonstrate knowledge of the syntax and semantics of propositional and predicate logic,
- demonstrate an understanding of the central results from the course, including soundness and completeness for propositional and predicate logic,
- present formal derivations for propositional and predicate logic in a proof system such as natural deduction,
Competence and skills
- relate syntactic concepts, such as substitution and derivability, to semantic phenomena and vice versa,
- formulate and present proofs of the central results in the course and their dependent lemmas,
- apply methods and results from the course in independent problem-solving,
Judgement and approach
- critically assess the applicability of formal logic in modelling phenomena.
Course evaluations
The course will be evaluated through a course questionnaire.
Special pedagogical support
If you have a disability and are in need of special pedagogical support please see the information available at the student portal.
Contact information
- Course coordinator Graham Leigh graham.leigh@gu.se
- answers questions about the course content, literature and schedule.
- Education administrator Sandra Schriefer, sandra.schriefer@gu.se answers questions about registration, study interruptions, study breaks, certificates, etc.
- Education administrator Annika Herrström, annika.herrstrom@gu.se answers questions about examination administration.
- Program Coordinator Ivan Di Liberti, ivan.di.liberti@gu.se is responsible for programme issues and study guidance for students of the programme.
Plagiarism and academic integrity
Please take the time to go through the module Academic Integrity 1 to make sure that you understand what plagiarism is, why one should not plagiarise, and what happens if one does plagiarise.
Student information
Welcome to the department of Philosophy, Linguistics and Theory of Science