Course syllabus
Welcome to Logical Theory, LOG111, 15 credits - Fall 2021
This course is both part of the Master in Logic as well as available as a free standing course. The first part of the course runs in parallell with the course on Set theory and the the second part with the course on Modal logic.
Course content
The course starts with a comprehensive presentation of syntax, semantics and proof systems for propositional logic; and continues with classical first-order predicate logic.
Detailed proofs of the completeness theorems for both propositional and predicate logic are included. Basic results, such as the compactness theorem and Löwenheim-Skolem's theorem, together with more advanced results and concepts, for example, model completeness, form the model theoretical part of the course.
As examples of other logics, second-order and intuitionistic logic are presented together with completeness results. Basic proof theory is introduced and lead up to a proof of normalisation for natural deduction, both for classical and intuitionistic logic. Gödel's incompleteness theorems and basic recursion theory are also included.
Teachers
The course is taught by Fredrik Engström, Graham Leigh and Rasmus Blanck.
Introduction
The introduction to the course, as well as the master's programme in logic, took place on Tuesday August 31 9:45 - 11:30 in room J444 and over Zoom.
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
A preliminary schedule for the first half of course is available through TimeEdit. All lectures will be given at campus and streamed over zoom. Use the following Zoom links:
- For Fredrik's lectures: https://gu-se.zoom.us/j/68979883181?pwd=MDRHK2FBNlptWlJhUWxtQytoWHUydz09
- For Rasmus' exercise sessions: https://gu-se.zoom.us/j/61095074028?pwd=YkR6WDJKbmUwOTBLVWd4ODFjUWRSZz09
Literature
The course uses the Open Logic Textbook (OLT). A separate remix for the course is available here and will be updated whenever needed. Please check back regularly for updates and if you find typos, errors or have suggestions for improvement please contact the course instructor.
You can always find the very latest version of the text at GitHub.
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 part 1 and part 2 for the plans.
Examination
Please be aware that due to the special covid-19 situation the form of the examination has been altered and we will make sure that you can take the two examinations online from your home.
There will be two sit down written examinations, one for each part of the course. You will be able to take the exams from your home using Zoom. These are individual exams and you are not allowed to collaborate or communicate with anyone during the exam. However, you are allowed to read the book, your notes and use the internet (but not to communicate or ask questions). You will need to be able to identify yourself by showing a valid id-card or passport over zoom which means that you need a computer with a camera. More information about the exams will be available later.
The hand-in problems and assignments are not obligatory to pass the course, but we strongly recommend students to take the opportunity to get feedback on your solutions.
Example of exam questions can be found here: exam_2020_oct_LOG111.pdf and here: exam_2019_oct_LOG110.pdf (note that the exam from 2019 is a closed book exam). See also exam_2021_jan_LOG111_II.pdf for an exam for the second half of the course and exam_2020_jan_LOG110_II.pdf for another one (note that the exam from 2020 is a closed book exam and also included material on cut elimination that is not included this year).
Learning outcomes
On successful completion of the course the student will be able to:
Knowledge and understanding
- describe and demonstrate an understanding of basic model theory and proof theory including completeness theorems, for propositional logic, first-order logic, intuitionistic logic, and second-order logic.
- describe the relationship between intuitionistic and classical logic from both a model theoretic and proof theoretic perspective.
- describe the relationship between second-order logic, first-order logic, and propositional logic.
- describe and discuss Gödel's first and second incompleteness results as well as Gödel-Rosser's theorem.
Competence and skills
- formulate and present proofs of the most important results in the course including completeness, incompleteness and normalisation theorems, as well as of lemmas used in the proofs.
- apply methods and results of the course in independent problem-solving.
Judgement and approach
- critically discuss, analyse and evaluate the results in the course as well as their applications.
See the course syllabus for more information.
Course evaluations
The course will be evaluated through a course questionnaire. A short summary of the course evaluation from last year is available here.
The report from the course is now available: Course report LOG111 2021 with evaluation.pdf
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 Fredrik Engström, fredrik.engstrom@gu.se answers questions about the course content, literature and schedule.
- Education administrator
- Program Coordinator Fredrik Engström, fredrik.engstrom@gu.se is responsible for programme issues and study guidance for students of the programme.
- Student counselor Peter Johnsen, peter.johnsen@gu.se, is responsible for study guidance of the free-standing course.
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
Course summary:
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