The aim of the course is to introduce you to the kinds of questions logicians ask about logics, the meta-theory of logic. To illustrate these questions, we will use natural logic (NL), propositional logic (PL), modal logic (ML) and first-order logic (FOL). All of these logical systems are important in philosophy, computer science, AI, linguistics and mathematics. We will discuss syntax & semantics for these logics, logical consequence, axiomatic systems, compactness, definability issues, completeness and the relationship between these different logical systems.

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Related Courses. For more information about the topics which may be discussed during the semester, you can consult the webpages of the following related courses that I have taught:

• PHIL 151, Symbolic Logic , Similar course on meta-theory taught at Stanford University
• Modal Logic, Graduate seminar on modal logic

We will not follow a single book for this course. The reading material will be provided by the instructor and will be made available in class (and possibly on the website) during the course. The primary sources of the reading material will come from the following texts:

• H. Enderton, A Mathematical Introduction to Logic, Academic Press, 2nd Edition, 2001
• Lecture notes on modal logic prepared by the instructor.
• Lecture notes on ``Logical Systems" by Larry Moss.
• Background on sets and relations.

The following texts are recommended for further reading:

Please consult this schedule regularly throughout the semester as meeting times and readings may change.

Date	Lecture	Notes/Readings
8/30	No class
9/4	Introdcutory remarks, Natural Logic I: The Logic of All and Some	Moss notes, pgs. 5 - 10
9/6	Natural Logic II Soundness and Completeness	Moss notes, sections 1.1 - 1.3
9/11	Natural Logic III Completeness	Moss notes, sections 1.4 - 1.5 PS 1
9/13	Natural Logic IV: Completeness (All and Some fragment)
9/18	Discussion Class	PS 1 due
9/20	Natural Logic V: Completeness (All and Some fragment with names)
9/25	Introduction to Propositional Logic: Axiom systems, Deduction Theorem	M. Fitting, Notes on Propositional Calculus
9/27	Soundness and the Deduction Theorem	Fitting notes, Sections 1-7 Homework 2
10/2	Completeness of Propositional Logic, I	Fitting notes, Sections 8 - 13
10/4	Completeness of Propositional Logic, II	Fitting notes, Sections 8 - 13
10/9	Completeness of Propositional Logic, III	HW 2 (Exercises 7.1, 11.1 and 13.1) in Fitting notes
10/11	Lecture canceled
10/16	Functional Completeness of Propositional Logic	HW 2 Due
10/18	Introduction to Modal Logic	Modal Logic Notes
10/23	Definability and Modal Deductions	Modal Logic Notes
10/25	Definability in Modal Logic	Midterm (take-home)
10/30	University Closed
11/1	Deductions in Modal Logic
11/6	Completeness in Modal Logic, I	Midterm due
11/8	Discussion Class: Answers to the Midterm, I
11/13	Discussion Class: Answers to the Midterm, II	Notes on Natural Logic (answer to question 1 from the midterm)
11/15	Completeness in Modal Logic, II
11/20	Syntax and Semantics of First-Order Logic (FOL)	Notes on First Order Logic
11/22	Thanksgiving break
11/27	Deductions in FOL	HW 3
11/29	Soundness and completeness of FOL
12/4	Completeness of FOL	HW 3 Due, HW 4 Notes on First Order Logic
12/6	Completeness of FOL
12/11	Completeness of FOL	HW 4 Due
12/17	Final Exam, 10:30am - 12:30pm, MMH 1304

Homework assignments count for 50%, midterm 20% and final exam 30%. The midterm will be a take-home exam while the final will be an in-class exam. Solutions to the problem sets will be made available after the assignment is due.

For the midterm and final exam, you may NOT collaborate with others in any way. For the homework assignments, you are encouraged to work in small groups. You may discuss the problems with one another or with me as much as you want. But you must always do the final write-up completely on you own. A good strategy when working together is to use a blackboard and erase it completely before writing up your (separate) answers. Please write the name of your discussion partner(s) on the front page of your assignments.