| 1. |
Define contradictoriness by completing the following:
φ and ψ are contradictory if and only if …
(Your answer should define contradictoriness in terms of truth values and possible worlds.)
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| Analyze each sentence below in as much detail as possible, presenting the result using both symbolic and English notation for the connectives. Besure that the unanalyzed components of your answer are complete and independent sentences; also try to respect any grouping in the English. | ||
| 2. |
Ann found the note but didn’t recognize the signature
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| 3. |
Either the manufacturer and the distributor weren’t both available or neither of them changed its offer
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| Use derivations to check whether each of the entailments 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) which divides an open gap. | ||
| Do not use attachment or detachment rules in 4 and 5. That is, do not use Adj or the new rules of 4.3; instead use only the basic rules for exploiting resources, planning for goals, and closing gaps. | ||
| 4. |
¬ B ⊨ ¬ (A ∧ B)
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| 5. |
¬ (¬ A ∧ ¬ B), C ∧ ¬ B ⊨ A
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| In 6 and 7 you may use attachment and detachment rules if you have an opportunity to do so. | ||
| 6. |
A ∨ B ⊨ C ∨ D
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| 7. |
¬ (A ∧ C), A ∨ B, ¬ (B ∧ ¬ D) ⊨ ¬ (C ∧ ¬ D)
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| 1. | φ and ψ are contradictory if and only if there is no possible world where they have the same truth value. |
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| 5. |
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| 7. |
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