Phi 270 F09 test 2
F09 test 2 topics
The following are the topics to be covered. The proportion of the test covering each will approximate the proportion of the classes so far that have been devoted to that topic. Your homework and the collection of old tests will provide specific examples of the kinds of questions I might ask.
Analysis. Be able to analyze the logical form of a sentence as fully as possible using conjunction, negation, and disjunction and present the form in both symbolic and English notation.
Synthesis. Be able to synthesize an English sentence that has a given logical form.
Derivations. Be able to construct derivations to show that entailments hold and to show that they fail. I may tell you in advance whether an entailment holds or leave it to you to check that using derivations. There may be a derivation where attachment rules (Adj and Wk) and detachment rules (MTP and MPT) may be used and where they will shorten the proof; but there will be other derivations where you must rely on the basic rules, either because detachment and attachment rules do not apply or because I tell you not to use them.
F09 test 2 questions
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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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Either the demand was greater than expected or the backup unit wasn’t ready. answer |
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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)
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| 5. |
¬ (A ∧ B) ⊨ B
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| 6. |
(A ∧ B) ∨ (B ∧ C) ⊨ B
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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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F09 test 2 answers
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| 7. | There are many possible answers; the following are only two samples: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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