15-317 / 15-657 Constructive Logic

Fall 2022
Instructor: Karl Crary
Teaching Assistants: Joshua Clune, Isabel Gan, Shengchao Yang, Xinyi Lu
Mon & Wed, 11:50 am - 1:10 pm
Posner 152
9 units

This undergraduate course provides an introduction to constructive logics, such as intuitionistic and linear logic, with an emphasis on their application in computer science. This includes basic means for defining logics (for example, natural deduction and sequent calculus), establishing properties of logics (for example, cut elimination), and for investigating their computational interpretations (for example, via proof reduction or proof search).

Prerequisites: 15-317 is an introductory undergraduate course with a minimum grade of C in 15-150 as prerequisite. For the cross-listed graduate version, 15-657, some experience with functional programming is recommended.

Class Material

Schedule Lecture notes and additional readings
Assignments Homeworks assignments and due dates
Software Links to software and other resources

Course Information

Syllabus here
Recitations Section A, Tue, 9:05 am - 9:55 am, Isabel Gan
  Section B, Tue, 10:10 am - 11:00 am, Shengchao Yang
  Section C, Tue, 11:15 pm - 12:05 pm, Joshua Clune
  Section D, Tue, 5:45 pm - 6:35 pm, Xinyi Lu
Office hours Sundays, 4:00pm - 5:00pm, Remote (Zoom link) (Queue)
Mondays, 4:00 pm - 5:00 pm, GHC 9217
Tuesdays, 2:00 pm - 3:00 pm, GHC Commons
Wednesdays, 6:00 pm - 7:00 pm, GHC Commons
Thursdays, 1:00 pm - 2:00 pm, GHC Commons
Piazza page here
Grading 48% homework, 19% midterms, 29% final, 4% attendance
Notes Lecture notes are effectively the course textbook.
Homework Homework is assigned weekly and handed in via Gradescope.
See the syllabus for the late day policy.
Exams Open one-sheet-of-notes, closed internet.

Learning objectives: After taking this course, students should be able to

  • understand the distinction between classical and constructive logic, and the uses of constructive logic
  • define logical connectives and test these definitions for harmony
  • express and prove the relationships between different representations of a logic (e.g., natural deduction and sequent calculus), and explain what each representation is for
  • implement propositional theorem provers
  • use operational interpretations of logics via proof search (a.k.a. logic programming)
  • understand the applications of substructural logics

Accommodations for Students with Disabilities

If you have a disability and have an accommodations letter from the Disability Resources office, I encourage you to discuss your accommodations and needs with me as early in the semester as possible. I will work with you to ensure that accommodations are provided as appropriate. If you suspect that you may have a disability and would benefit from accommodations but are not yet registered with the Office of Disability Resources, I encourage you to contact them at access@andrew.cmu.edu.

Support for Students' Health and Well-Being

All of us benefit from support during times of struggle. There are many helpful resources available on campus and an important part of the college experience is learning how to ask for help. Asking for support sooner rather than later is almost always helpful. If you or anyone you know experiences any academic stress, difficult life events, or feelings like anxiety or depression, we strongly encourage you to seek support. Counseling and Psychological Services (CaPS) is here to help: call 412-268-2922 and visit their website at http://www.cmu.edu/counseling/. Consider reaching out to a friend, faculty or family member you trust for help getting connected to the support that can help.

The Scientific American article referenced in the syllabus.

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