Mathematical Proof Methods for Logic

Course manual 2019/2020

Course content

We survey landmark results in the meta-theory of first-order languages, after warming up with purely propositional languages. In particular, we provide a sound and complete axiomatization of first-order logic, and draw classic consequences: compactness and the upward and downward Skolem-Löwenheim theorems. We focus on a rigorous presentation of the material and development of technical prowess in working with formal logics. We intermittently consider some philosophical ramifications. 

Study materials

Literature

• Lecture notes, problem sets and solution sets will be provided via Canvas, as the course proceeds.

• Required: Dirk van Dalen, Logic and Structure, 5th Edition, Springer

• Recommended: Daniel Velleman, How to Prove it, 2nd Edition, Cambridge University Press

Objectives

• Learn the statements and proofs of the basic results of mathematical logic.
• Master the basic proof-theoretic and model-theoretic techniques used in mathematical logic.
• Develop ability to prove theorems through the study of these techniques.

Teaching methods

• Lecture
• Self-study
• Problem sets/feedback

• There will be six mandatory weekly homework assignments.
• Two assignments are take-home exams counting towards final grades.
• The remainder won’t count towards final grades; they exist to provide feedback.
• The final sit-down exam will be closed book and test a student's ability to reproduce the proofs for major results.

Learning activities

Attendance

The programme does not have requirements concerning attendance (OER-B).

Additional requirements for this course:

• Participation. Students are expected to actively participate in the tutorial sessions, to do the relevant work for the lectures, and to complete the given assignments. Students are also expected to keep informed about the course by regularly accessing Canvas. 
• Self-study. The course is not suitable for self-study, and it is assumed that students will take part in all classes. The lecturer cannot answer questions during lectures resulting from lack of attendance on a student’s part. 
• Late arrival. Arriving late to a session is highly disruptive to the other students and to the lecturer. Therefore, the following rule is applied: a student who arrives more than five minutes late shall wait until the break taking place during each session after the first 45 minutes. 

Assessment

• Passing criteria. To pass the course, the student’s final grade must be at least 6. Moreover, in order to be admitted to the in class examination, the student must have completed at least 75% of the non-examinable assignments. 
• Availability of exams. Take-home exams will be made available on Canvas. The first take-home exam will be made available on Monday 23 September and must be handed in by Monday 30 September before 5pm. The second take-home exam will be made available on Friday 11 October and must be handed in on Friday 18 October by 5pm. 
• Late hand-ins. Take-home exams that are handed in late count as insufficient. 
• Collaboration. For take-home exams, discussion of the exam problems in a group of up to three students is permitted. The names of the other students in one’s group must be recorded on one’s completed exam. Further, each student must independently write up their completed exam. For the in-class exam, collaboration and discussion is not permitted. No one else, and no text beside the course materials, may be consulted while you complete any of the exams. 
• In-class exam. The in-class examination will take place on Wed 23 October 2019 at 9am at SP F1.02. It will concern material covered throughout the course. Further details about the content of the in-class examination will be made available to students during class. 
• Score report. The score obtained for each take-home exam and for the in-class examination will be recorded on Canvas. 
• Resits. In January, resits are held. The resit is an in class examination, the exact date of which will be communicated to the students concerned. 
• Options for appeal. If you wish to object to the assessment of an exam, please contact the Examinations Board. More information is available at: http://www.illc.uva.nl/MScLogic/current- students/regulations/oer.html 

Inspection of assessed work

The manner of inspection will be communicated via the digitial learning environment.

• The weekly assignments are marked by the teaching assistant and handed out to the students in a tutorial. Further feedback may be obtained during office hours.
• Office hours: Thursdays 10am-noon @ SP107 F2.02, or by appointment.

Assignments

Assignments 1, 2, 4, 5

• Graded with feedback, doesn't count towards final grade

Assignments 3 and 6: Take-home exams

• Graded with feedback, counts towards final grade

• Homework release: The first assignment will be released, via Canvas, on Mon 9 September at 9pm. Thereafter, with the exception of the take-home exams, an assignment will be released every Monday at 9pm, and is due the Friday after its release at 5pm.

• Homework submission: Completed assignments are to be submitted via Canvas. We accept both hand-written and typed homework, but strongly encourage and prefer typed homework. Hand-written assignments must be exceptionally neat: we cannot grade what we cannot read (hence, hand-written assignments must be legibly scanned for submission).

• Homework collaboration: It is acceptable to work on homework problems - including for the take-home exams - in groups of a maximum size of three students. If so, you must note the students you worked with on your assignment. Further, individual homework assignments must be written up individually: if two assignments are too close in presentation, we may construe this as plagiarism.

• Late homework: Of the non-examinable homework assignments, you may make one late submission without penalty: more precisely, you may turn in one non-examinable problem set up to one working day late (i.e. up till 5pm the following Monday) without penalty. Otherwise, without special permission, late homework will not be accepted. Take-home exams may not be submitted late.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• dr. P.M. Hawke

Staff

• L. Bussière
• Frederik Lauridsen