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### Lectures 8-9

Ling 442

Exercises (1)

- Reconstruct the original English sentence for each:
- |⟦birds⟧⟦fly⟧| > ½ |⟦birds⟧|
- ⟦dog⟧ ⟦bite⟧ {}
- ⟦student⟧ ⟦study_hard⟧
- ⟦politician ⟧⟦honest⟧ = {}
- |⟦girl⟧ ⟦is_talking⟧| = 3

Exercises (2)

- Some extra stuff:
- ⟦bark⟧ ⟦dog⟧
- |⟦person⟧| < ½ |⟦cow⟧|
- |⟦king_of_France⟧| = 1 and ⟦king_of_France⟧⟦bald⟧
- Represent the truth conditions in terms of the set-theoretic notation.
- More than three phonologists gathered.
- The three phonologists gathered.

Exercises (3)

- Downward entailingness
- Negative polarity items
Everyone who has even been to A will want to go back.

Similarly for someone and no one

Which positions accept negative polarity items like ever?

Exercises (4)

- What determiners are strong/weak?
- every, no, some, most, three, several
Kearns asks us to check whether you can switch the two sets (the denotations of CN and VP) to obtain the same truth conditions.

Exercises (5)

What is the difference between (1) and (2)?

- He got on his horse and rode into the sunset.
(2) He rode into the sunset and got on his horse.

How do you represent the following in Predicate Logic?

(3) Bill and Mary met in Seattle.

(4) Bill and Mary are a nice couple.

Exercises (6)

- Let’s talk about exercise (17) on p. 43-44
- Translate each sentence into Predicate Logic.
- Clive gave every child a biscuit or a Batman comic.
- There’s no business like show business.
- Translate into PL with modal operators.
(3) If wishes were horses beggars would ride.

Exercise (7)

- Represent each sentence using set-theoretic symbols.
- None of the ten bombs exploded.
- All the three candidates showed up.
- What’s wrong with the following?
(3) [every x: student (x) & [a y: paper (y)]] submitted (x, y)

A language w/ restricted Q

- Most birds fly.
- Most x [bird(x) fly (x)] (does not work)
- From now on, we will use a language that allows us to write:
[most x: bird (x)] fly(x)

Its truth conditions are exactly the same as the original English sentence. This notation allows us to represent scope interactions of quantifiers too.

Scope ambiguity

- Every boy likes some rock star.
- [every x: boy(x)][some y: rock star (y)][likes (x, y)]
- [some y: rock star (y)][every x: boy(x)][likes (x, y)]

“Strong” vs. “Weak” Determiners

- This distinction is due to G. Milsark
- The existential construction (There be …) can be used as a test.
OK: There is/are Det CN weak Det

weak DPs: cardinal and non-presuppositional

No good: There is/are Det CN strong Det

srong DPs: proportional and presuppositional

Ambiguity

Many and few are ambiguous between strong and weak interpretations.

- No flies and few fleas survived. (strong)
- Lee found (very) few fleas. (weak)
- Many students preferred assignments to tests. (strong?)
- Many people are out there. (weak)

Different types of there BE constructions

- Basic existential
- Indicating location
- Presentational there BE
- Task there BE
- List there BE

Russell’s the

- Russell’s contention: the is not presuppositional.
⟦The CN VP⟧ = true iff

|⟦CN⟧| = 1 and ⟦CN⟧ ⟦VP⟧

IF the CN is in the plural form, then the truth conditions are

|⟦CN⟧| > 1 and ⟦CN⟧ ⟦VP⟧

Frege’s the

⟦The CN VP⟧ has a true value only if

|⟦CN⟧| = 1

If this condition is met, then ⟦The CN VP⟧ = true iff ⟦CN⟧ ⟦VP⟧

Caveats

- (69) and (70) are not semantically. You need to modify them as follows:
[several x: car (x)][the y: garage (y) & for (y, x)] ~ leave (x, y)

[the y: garage (y)][several x: car (x) & in (x, y)[ ~ leave (x, y)

- Ignore 6.10

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