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Analyze the sentences below in as much detail as possible using only connectives; that is, the unanalyzed components should all be sentences (rather than individual terms, predicates, or functors). Present the result in both symbolic and English notation. Be sure that the unanalyzed components of your answer are complete and independent sentences; also try to respect any grouping in the English. |
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| 1. |
There was an audience if there was food. answer |
| 2. |
Sam went unless he had to work, but he enjoyed the ride only if the weather was good. answer |
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Use derivations to check whether each of the entailments below holds. You may use detachment and attachment rules. If an entailment fails, present a counterexample that divides an open gap. |
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| 3. |
C → (B → A), C → B ⇒ C → A answer |
| 4. |
A → B, C → D ⇒ C → (E → ¬ B) answer |
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Analyze the sentence below in as much detail as possible, giving a key to your abbreviations of unanalyzed expressions. In this case you should identify components that are individual terms, predicates, or functors; however, you do not need to present the result in English notation (i.e., symbolic notation is enough). Your analysis should be in reduced form (i.e., you should not use abstracts and variables), so be sure that the unanalyzed components of your answer are independent—in particular, that none contains a pronoun whose antecedent is in another. (Also be sure also that the individual terms you identify really are individual terms and are not quantifier phrases or general terms, like simple common nouns.) |
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| 5. |
Nancy phoned Oliver and told him about his promotion. answer |
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Analyze the sentence using abstracts and variables to represent pronominal cross reference (instead of replacing pronouns by their antecedents). That is, each individual term in your analysis should appear only as often as it appears in the original sentence. In other respects, your analysis should be as described for 5. |
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| 6. |
Spot finished chewing his bone, and he buried it in a flowerbed. answer |
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Use a derivation to show that the entailment below holds. You may use detachment and attachment rules. Be sure to indicate the alias sets whenever an equation is added to the resources. |
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| 7. |
Ra(fb) ∧ ¬ Rc(fd), fb = fc ⇒ ¬ (a = c ∧ b = d) answer |
| 1. |
There was an audience if there was food there was an audience ← there was food
A ← F
A: there was an audience; F: there was food
F → A if F then A
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| 3. |
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| 5. |
Nancy phoned Oliver and told him about his promotion Nancy phoned Oliver ∧ Nancy told Oliver about his promotion Nancy phoned Oliver ∧ Nancy told Oliver about his promotion [ _ phoned _ ] Nancy Oliver ∧ [ _ told _ about _ ] Nancy Oliver Oliver’s promotion Pno ∧ Tno([ _’s promotion] Oliver)
Pno ∧ Tno(po)
P: [ _ phoned _ ]; T: [ _ told _ about _ ]; n: Nancy; o: Oliver; p: [ _’s promotion]
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| 6. |
Spot finished chewing his bone, and he buried it in a flowerbed Spot is such that (he finished chewing his bone, and he buried it in a flowerbed) [x finished chewing x’s bone, and x buried it in a flowerbed]x Spot [x’s bone is such that (x finished chewing it, and x buried it in a flowerbed)]xs [ [x finished chewing y, and x buried y in a flowerbed]y x’s bone]xs [ [x finished chewing y ∧ x buried y in a flowerbed]y([ _’s bone] x) ]xs
[[Cxy ∧ Bxy]y(bx)]xs
B: [ _ buried _ in a flowerbed]; C: [ _ finished chewing _ ]; b: [ _’s bone]; s: Spot
or: [[Cxy ∧ Bxy]xyz(bz)]zs (Note: a flowerbed is not an individual term so it must remain unanalyzed as part of a predicate) |
| 7. |
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