| 4-4. |
Identify individual terms and quantifier phrases in the following sentence and indicate links between pronouns and their antecedents. (You can do this by marking up an English sentence; you are not being asked to provide a symbolic analysis.)
Everyone who Carol lent the book to spoke to her at length about it.
[answer] |
| Analyze the following generalizations in as much detail as possible. Provide a key to the non-logical vocabulary (upper and lower case letters) appearing in your answer and restate the result using an unrestricted quantifier. | |
| 4-5. |
Bob called no one.
[answer] |
| 4-6. |
Among contestants, only professionals were finalists.
[answer] |
| Analyze the following sentences in as much detail as possible, providing a key to the non-logical vocabulary (upper and lower case letters) appearing in your answer. | |
| 5-1. |
Bob doesn't own any map showing Dafter.
[answer] |
| 5-2. |
Nothing anyone said bothered Dave.
[answer] |
| Use derivations to establish the validity of the following arguments. You may use attachment rules. | |||
| 5-3. |
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| 5-4. |
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| 5-5. |
Use a derivation to show that the following argument is not valid and describe a structure dividing one of the derivation's open gaps. (You will not need the rules UG+, RUG+, and ST of §7.8 that were designed to avoid unending derivations.)
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| You will receive credit for one of the following (but you may attempt both): | ||||
| 5-6a. | Synthesize an English sentence whose analysis would yield the following form. | |||
| 5-6b. |
Use derivations to establish the validity of the following argument. You may use attachment rules.
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| 4-4. |
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| 4-5. |
Bob called no one no one is such that (Bob called him or her) (∀x: x is an person) ¬ Bob called x
(∀x: Px) ¬ Cbx
[C: λxy (x called y); P: λx (x is person); b: Bob]
∀x (Px → ¬ Cbx) |
| 5-3. |
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| 5-5. |
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The structure below divides both gaps; it will continue to divide the first gap when the arrow from 1 to itself is dropped.
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| 5-6a. |
(∀x: x is a door) (the key opens x → (∀y: y is a door) the key opens y) (∀x: x is a door) (the key opens x → every door is such that (the key opens it)) (∀x: x is a door) (the key opens x → the key opens every door ) (∀x: x is a door) if the key opens x, then it opens every door every door is such that (if the key opens it, then it opens every door) If the key opens any door, then it opens every door |
| 5-6b. |
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