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Analyze each sentence below in as much detail as possible, presenting the result in both symbols and English notation. Provide a key to your abbreviations of unanalyzed components, and be sure that they are complete and independent sentences. Try to respect any grouping in the English. |
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| 1. |
Either the demand was greater than expected or the backup unit wasn’t ready. answer |
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| 2. |
Ann and Bill were not both notified, but neither needed a reminder. answer |
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Synthesize an English sentence (the more idiomatic the better) that has the following analysis: |
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| 3. |
¬ S ∧ T (S: Sam heard the siren; T: Tom heard the siren) answer |
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Use derivations to check whether each of the claims of entailment below holds. If one fails, present a counterexample by providing a table in which you calculate the truth values of the premises and conclusion on an extensional interpretation (i.e., an assignment of truth values) that divides an open gap. |
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Do not use attachment or detachment rules in 4-6. That is, do not use Adj or the rules MTP, MPT, and Wk of §4.3; instead use only the basic rules for exploiting resources, planning for goals, and closing gaps. |
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| 4. |
¬ B ⊨ ¬ (A ∧ B)
answer |
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| 5. |
¬ (A ∧ B) ⊨ B
answer |
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| 6. |
(A ∧ B) ∨ (B ∧ C) ⊨ B
answer |
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You may use attachment and detachment rules in 7. They can be used to shorten the derivation somewhat; but, of course, it can also be completed without using them. |
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| 7. |
B, ¬ (B ∧ C) ⊨ ¬ C ∨ A
answer |
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| 4. |
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| 6. |
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| 7. | There are many possible answers; the following are only two samples: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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