Linguistics 553 will cover those elements of logic that are fundamental to semantic theory. The course will treat basic set theory, propositional logic (formulas, truth-functional connectives, truth tables), predicate logic (quantification, interpretation relative to a model) and natural inference. Given these foundations, we will then cover intensional logic and type theory. The formal discussion will be highlighted with semantic treatments of some natural language phenomena (Montague's analysis of a fragment of English, definite descriptions, generalized quantifiers, reference in opaque contexts, perception verbs).

(Occasional) homework assignments

These may be done individually or collaboratively. If you collaborate, you must (a) write up the homework individually, because it's good practice, and (b) list your collaborators. (Some exercises may be marked as non-collaborative.)

Final exam

Anyone taking the "semantics foundation" series will necessarily take the four-hour exam covering this course and LING 548; the grade on that exam will be part of your grade in the course. Anyone not taking the series will...need to check with me later in the semester to see how the final exam will play out. (At worst, you'll probably just take half the exam.)

One term paper and presentation

Perhaps. I'll decide this in the next few weeks, taking into account the final exam. If there is a final paper, it will be squib-length; nothing too strenuous.

Attendance and class participation

No, I'm not doing a roll call each day, or writing down each time you miss class. But this is an interactive class, not in some buzzword sense of "interactive" but in the straightforward sense that there will be interaction, and not just me lecturing. Your observations, questions, proposals, etc. will drive the class, which is why participation matters enough to grade you on.

Textbook: Semantics in Generative Grammar, Irene Heim and Angelika Kratzer

Other texts: Various papers, which will be linked from the course website.

Here, roughly, is the table of contents from Heim & Kratzer:

1. Truth-conditional semantics; review of sets and functions.
2. Schönfinkelization, λ-notation; individuals and verbs.
3. Semantics and syntax: type-driven interpretation, θ-roles, etc.
4. Adjectives; the definite article
5. Relative clauses, variables, variable binding
6. Quantifiers: their semantic type; presuppositions
7. The syntax of quantifiers; movement vs. in situ
8. Constraints on the syntax of quantifiers
9. Bound pronouns, referential pronouns, ellipsis
10. Syntactic and semantic binding; crossover effects
11. E-type pronouns
12. Intensional semantics

That's not the syllabus; we may not do Chapter 11 at all, we'll probably do at least some things in a different order, we may discuss things not listed in the book (perhaps questions; perhaps tense). But it's a rough idea.

• First Handout: Mathematical Background (1-5)
• Second Handout: Lambda Calculus (6-11)
• Third set of notes: Verbs (12-15)
• Fourth set of notes: Transitive Verbs (16-18)
• Fifth set of notes: Transitive Verbs continued (19-22)
• Sixth set of notes: Beyond Verbs (23-26)
• Seventh set of notes: Adjectives (27-29)

• Homework 2
• Answers to Homework 2
• Lambda File for HW1. Lambda is available here. This is not required, but it's relatively strongly urged, in part because it provides good practice and in part because I can use the feedback on how it works as a tool.

• Some supplements to Handout Eight:
  • A handout by Lynsey Wolter that covers, as well as anything might, the basic facts about "bridging" as it applies to definites (i.e. getting uniqueness from things like "I went to a wedding. The bride wore white").
  • You can also go to the original discussion by H.H. Clark; it's neither long nor techncial.
  • Also, Greg Carlson et al. on "Weak Definite NPs" (where there's no uniqueness).
• Ninth Handout: Relative Clauses (31-36)
• Lambda File for Ninth Handout (and HW2). Again, this is not required, but it should once again provide good practice in working out the details of a derivation.

• Lambda File for 3/19. Note that (a) this file includes proper set-based definitions for "every" and "some" (as well as getting the argument order right for "respects"), and that (b) you'll need the super-secret update to Lambda to read them: this Windows .exe file or this Java .jar file.
• Homework 6