Course Policies
Table of contents
About
This course is an introduction to logical “metatheory”, that is, to logical reasoning about logic systems themselves. Topics include alternative alternative proof-theoretic presentations of logical systems as well as soundness and completeness theorems for propositional and first-order logic. Along the way, we will deepen our understanding of the elementary set-theoretic concepts underlying first order logic. Other topics may include basic results in the semantics of first order logic (such as the Craig interpolation theorem, the Beth definability theorem, or the Lowenhein-Skolem theorem).
Resources
Readings: The readings for this semester will be drawn from different textbooks. All readings will be available on ELMS. The main texts that we will use include:
- Barbara H. Partee, Alice ter Meulen, and Robert E. Wall. Mathematical Methods in Linguistics. Springer, 1990.
- Readings from the https://openlogicproject.org/
- Ian Chiswell and Wilfrid Hodges. Mathematical Logic. Oxford University Press, 2007.
Additional Reading: The following texts may be used (time-permitting) this semester. If there is enough interest, I may discuss last book in the list (Logic and Proof).
- Wilfrid Hodges. Elementary Predicate Logic. In D.M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 1, pages 1–131. D. Reidel, 1983.
- Herbert B. Enderton. A Mathematical Introduction to Logic. Harcourt Academic Press, 2001.
- Jouko Väänänen, Second-order and Higher-order Logic. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Fall 2019 edition, 2019.
- Logic and Proof by Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn.
Online Discussion: This term we will be using campuswire.com for class discussion. The system is highly catered to getting you help fast and efficiently from me and your classmates, and myself. Rather than emailing questions, I encourage you to post your questions on campuswire.com. Find our class page at: campuswire.com.
Gradescope: We will use Gradescope for your weekly problem sets. You should access gradescope through the ELMS website. You already are added to the Gradescope gradebook.
Weekly Schedule/Due Dates
Important note about the course: Typically, courses meet for 75 minutes twice a week. This semester, PHIL 370 was scheduled as a “hybrid course”. This means that there are two live sessions meeting for 50 minutes, and the reamining 50 minutes should be an online component. Since the course is entirely online becaue of Covid, this is not an ideal way to schedule the course (but we are stuck with this schedule). The 50 minute online component should be spent working on tutorials, watching any videos that I create, and interacting on campuswire.com. To make sure we get through all the material, discussion of some material may need to be entirely online. That is, you will be tested on all material discussed this semester whether online or in-class.
The tentative weekly schedule:
- Updates to the course, including updates to the course website, updates to the online notes, new videos to watch for the week, and/or updates to the weekly schedule will be announced Monday mornings (around 9:00am). The weekly announcement will be posted on ELMS as an announcement. Make sure that you receive email notifcations about this course on ELMS.
- Synchronous Zoom lectures on Mondays and Wednesdays 10:00am - 10:50pm.
- Throughout the week, use campuswire.com to ask questions about the problem sets, reading or lectures, or anything else you might want to discuss related to the course.
- Problem sets will be assigned roughly every week and will be due Fridays by 11:00 PM.
- Tutorials and participation questions (answered via PollEverywhere) should be answered during the live Zoom sessions and during the 50-minute online component of the course. All participation questions for the week are due Fridays by 11:00 PM.
Late Policy
The regular due-date for material assigned during the week will be Fridays at 11:00pm.
You will have as many chances as you need to answer the tutorial questions. The best way to succeed in this course is to work at the material each week, so you should make sure to finish the tutorial questions on time. Periodically throughout the semester, I will close past tutorials meaning that I will not accept any late tutorials assigned before that date.
Problem sets must be completed by the due-date. For some problem sets, I may give everyone a chance to redo their answers. You will lose points for late problem sets.
Exams must be submitted by the due date. Exams submitted after the due date will lose points and exams submitted after the late-due-date will not be accepted.
Contact me if you miss a graded poll question during lecture or will miss multiple lectures.
Please do not ask to complete all assignments that you missed at the end of the semester.
Course Requirements
The course requirements are:
Participation: There will be weekly “participation questions” (using PollEverywhere) and tutorials assigned via Gradescope. Many of the questions will be asked and answered during the live Zoom-sessions. The remainder of the quesitons should be answered during the 50-minute online portion of the course. You are encouraged to discuss these problems with your classmates and the instructor in class or on campuswire.
Problem Sets: There will be a number of problem sets assigned throughout the semester. Problem sets will be submitted through Gradescope (accessible through the course website). You can use your notes and the online textbook, but you should not discuss your answers with your classmates.
Exams: The exams will be take-home and submitted through Gradescope. Unlike the problem sets and tutorials, the exams will be timed: Once the exam is opened, you will have a fixed amount of time (e.g., 4 hours) to complete the exam. You can use your notes and the online textbook, but you should not discuss your answers with your classmates. There will be 3 exams given during the semester:
- Exam 1: Propositional Logic and Set Theory (tentatively scheduled for week 5 or 6)
- Exam 2: First Order Logic (tenatively scheduled for week 10 or 11)
- Final Exam: The final exam will be cummulative and assigned during exam week.
Grades
Grades will be assigned according to the following weights:
| Activity | Percent |
|---|---|
| Participation | 30% |
| Problem Sets | 30% |
| Exam 1 | 10% |
| Exam 2 | 10% |
| Final Exam | 20% |
You cannot pass the course if you do not submit a final exam.
See undergraduate catalogue for description of grades, e.g., A+, A, A-, etc.
Topics
Below is a list of topics that we will discuss during the semester. This is an ambitious list, which may change given the students’ background and interests. (Consult the overview page for the most up-to-date information about due dates for the problem sets and dates of the exams.)
- Elementary set theory
- Sets, relations, functions
- Properties of relations and functions
- Induction
- Possible topic: size of sets
- Propositional logic: syntax, basic proof theory
- Fitch-style natural deduction
- Hilbert-style axiomatic systems
- Tableaux systems
- Syntactic metatheorems (e.g., deduction theorem)
- Possible topic: Equivalence of formulations
- Propositional logic: Semantics, soundness, completeness
- Semantics for classical propositional logic
- Functional completeness
- Soundness and completeness for Hilbert systems
- Possible topic: Soundness and completeness for Tableaux systems
- First-order logic: Syntax and basic proof theory
- Syntax (terms and formulas)
- Hilbert-style axiom system
- Natural deduction system
- Possible topic: Tableaux system
- Syntactic metatheorems
- First-order logic: Semantics, soundness, completeness
- Semantics for first-order logic
- Soundness and completeness for Hilbert systems
- Adding identity
- Possible topic: Soundness and completeness for tableaux systems
- Possible topic: Compactness, Lowenheim-Skolem theorem
- Possible topic: Interpolation, Beth definability
- Some nonclassical logics (time permitting)
- Some modal logics
- Intuitionistic logic
- Many-valued logics
- Introduction to computability (time permitting)
- Models of computation
- Decidability of propositional logic
- Undecidability of first-order logic
Learning Outcomes
Students who successfully complete this course will be prepared to:
- Define the logical systems propositional logic and first order logic
- Be proficient with basic set-theoretic reasoning and mathematical induction
- Explain the similarities and differences between propositional logic and first order logic
- Reproduce the proofs of important meta-logical theorems (completeness and compactness)
Support
It’s expected that some aspects of the course will take time to master and people will master the material at different speeds. The best way to master this material is to be actively engaged in the course, work on the tutorials each week and ask questions in class and on campuswire.com. I will also hold virtual office hours for in-person discussions.
UMD has many resources available to help students. Below are links to some resources that you might find helpful.