homework eleven

1. Complete this Monday's class exercise and hand it in. The exercise consisted in completing all the quantifier definitions on pages 1, 2, and 5 of the first handout on constraints for quantifier denotations.

2. Step by step, translate the tree structure (18) on p. 201 of Heim & Kratzer into ETL. Add non-logical constants as needed. Assume (in line with our current assumptions) that the binder index "1" in (18) is actually represented as a suitable lambda-operator.

homework ten

Due on Monday, November 26.

homework nine

This week's homework assignments are sprinkled throughout the combined handout for Wednesday and Friday. There are four translation exercises in all. They are due on November 14. November 12 is a holiday. This time round, pay particular attention to the presentation of your computations. Leave out unnecessary details. Imagine you had to present the computations in a journal article to show that the proposed analyses work. In a journal article, you don't want to use up too much space for obvious computations, since space is expensive. You do want to present computations that are easy to read and understand, though. Please present each computation with the relevant tree and type your work, using the correct logical symbols. If you don't have logical symbols, it's time to get them.

homework eight

Due on Monday, November 5. Group work continues to be encouraged. Tutorials continue to be offered three times a week.

1. Submit all of the lambda-exercises.

2. Construct elementary examples of alpha, beta, and eta conversion, and prove the equivalence of the original and the converted formulas, using the semantic rules of TL in Partee et al.. Check Potts' Logic for Linguists if you forgot what the different types of conversion are.

3. Complete the translation exercise in last week's handout.

homework seven

Due on Monday, October 29. A group discussion on this topic is highly encouraged.

The central issue that is addressed in Breheny, Katsos, & Williams (2006) is the impact of contextual pressures on the perceived presence or absence of scalar implicatures. After reading the whole article and reviewing last week's handout, pick one relevant issue or passage in Breheney et al.'s paper that relates to one relevant issue or passage in last week's handout and comment on it in the light of what you learned about exhaustive interpretations during the last weeks. You want to end up with a short "squib" or "snippet" that is (a) well-written and conclusively argued, (b) self-contained, that is, understandable to trained linguists who have neither read the article nor seen my lecture notes, (c) informed by what we talked about in class, (d) has concrete examples and stays away from issues that are too big to be discussed in a short essay in a satisfactory manner. This is not an easy essay to write. For it to be self-contained, you have to assess what the current common ground with respect to the issue you picked is and you have to summarize the relevant points in Breheny et al.'s paper and the lecture notes. Since the essay needs to be short and should stay away from generalities, you have to pick a small, yet interesting and relevant, issue that relates to concrete linguistic examples that you can come up with on your own. The Editorial Statement of the online journal Snippet explains nicely what such short essays in linguistics look like.

homework six

Due on Friday, October 19. Groupwork is highly recommended.

Look at the sentences below after reviewing the corrected and combined handout for Wednesday's and Friday's lectures. For each sentence state (a) how the extension of book and the extension of disappeared (taken to be sets of individuals) have to be related in order for the sentence to be true in a model and (b) under what conditions the sentence would be true in a minimal model with respect to disappeared. What do those results mean for the proposal to account for exhaustive interpretations via minimal models? Carefully word your answer and add suitable illustrations by picking particular domains, for example. You want to end up with a pretty piece of prose. I should add that the difficulties for the minimal model approach that are illustrated by examples (2) to (6) below are genuine challenges for any approach to exhaustification. The different approaches will eventually be judged by their responses to those challenges.

1. A book disappeared.

2. No book disappeared.

3. More than one book disappeared.

4. At least one book disappeared.

5. At most two books disappeared.

6. Between three and seven books disappeared.

homework five

Due on Friday, October 12 in class. Please type your homework. Groupwork is highly encouraged, in particular for question 1.

1. We saw on Wednesday that the exclusive interpretation of or in the sentences we looked at seemed to disappear in certain linguistic environments like the scope of negation or the antecedent of conditionals. These are also environments that license negative polarity items like ever in English: I haven't ever been in Florida contrasts with the ungrammatical I have ever been in Florida. As far as you can tell, does the exclusive interpretation of or generally disappear in precisely those environments where negative polarity items are licensed (see Chierchia 2004 for a more general discussion of this connection)? You won't be able to fully explore this issue, of course, but concoct some relevant examples and explain what they show. Do they confirm or disconfirm Chierchia's hypothesis?

2. Pick three exercises of your choice from Potts' package. The package has answers to the exercises, just like the Partee et al. textbook. Proceed as in the earlier logic exercises. First try to find an answer on your own after reviewing the relevant handout. Write down your answer, paying particular attention to your wording. Then check Potts' answer. Correct yours if necessary and write down any question you may have, again paying attention to your wording and use of technical terms, symbols and formulas. Submit the final product in a form that will make it easy for me to give you feedback.

homework four

novice

Partee et al., chapter 13, exercises 6 and 7, pages 369 to 371.

From now on, use some consistent standard notation for lambda-expressions whenever possible.

advanced

Derive the reading of Schein's sentence (1) that we have been interested in compositionally via a step by step translation of a plausible phrase structure tree into an expression of a typed lambda-calculus. Do what you can. It doesn't matter if you get stuck.

(1) Three video games taught every quarterback two new plays. (Schein 1993)

homework three

novice

Partee et al., chapter 7, exercises 1 to 4, pages 175 to 178.

advanced

1. Explain to a novice what donkey sentences are and why they are such an important construction in natural language semantics. What exactly is the challenge they present?

2. Explain to a novice why (1) is a good illustration for a quantifier scope ambiguity, but (2) is not.

(1) Some virus infected every file.

(2) Every file was infected by some virus.

homework two

novice

Partee et al. chapter 6: exercises 4, 5, 6, 7. I suggest you do the exercises first, write down the answers in your own way on a piece of scratch paper, then look up the answers in the back of the book. If you think you made a mistake and understand what the mistake was, correct your answer for the homework you submit. If there is something you still don't understand, write down what it is so that I can help you understand the problem.

Heim & Kratzer chapter 2: exercises 1, 2, and 4 on pages 39 & 40.

intermediate

Look again at Heim & Kratzer, chapter 2. Rewrite all function expressions in exercises 1, 2, and 4 on pages 39 & 40 in standard lambda-notation if this is possible. Why is it not always possible? Do the exercises as specified, but use standard notation whenever you can. The standard lambda notation is introduced in Partee et al., for example, or in Gamut. You can use the Penn lambda-calculator for practice.

advanced

For those with some experience in model-theoretic semantics: write down some thoughts that explain the use of models in natural language semantics. Heim and Kratzer deliberately do not relativize their denotations to models. Models also do not play a role in Larson and Segal's Knowledge of Meaning: An Introduction to Semantics (free access from campus via the CogNet library). David Lewis does not use models in his seminal paper "General Semantics" (big PDF file, access with your UMail password). What are models meant to capture in formal semantics? What is their job? When trying to find an answer to this important foundational question, imagine yourself in the shoes of a semantics teacher who has to explain to her students why it is that many textbooks and articles in natural language semantics relativize semantic denotations to a model. In fact, formal semantics is often literally equated with model-theoretic semantics, rather than just truth-theoretic semantics, for example. Why?

The use of models in natural language semantics is not uncontroversial. To see what the potentially problematic issues are, take a look at John Etchemendy's book on logical consequence, which is featured on the book shelf page. There is an earlier article by Etchemendy on model-theoretic semantics, which appeared in Linguistics and Philosophy, and there is also an unpublished article that clarifies certain issues in his book. You can access both articles with your UMail user name and password. Another highly recommended article on model-theoretic semantics is Thomas Ede Zimmermann's "Meaning Postulates and the Model-Theoretic Approach to Natural Language Semantics", which also appeared in Linguistics and Philosophy.

homework one

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