Phi 270 F04 test 2
F04 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 negation and disjunction in addition to conjunction and confirm the form in both symbolic and English notation (that is, with the logical and symbol and by expressing forms using both … and …, etc.).
Synthesis. You may be given a symbolic form and an interpretation of its non-logical vocabulary and asked to express the sentence in English.
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 will be at least one derivation where detachment and attachment rules may be used and where they will shorten the proof. But there will be other derivations where you must rely on others rules, either because detachment and attachment rules do not apply or because I tell you not to use them.
I may also ask you to explain why a derivation rule is safe or sound with reference to the counterexamples that lurk in gaps before and after the rule is applied.
F04 test 2 questions
Analyze each sentence below in as much detail as possible, presenting the result using both in symbols and using English notation (i.e., both … and, etc.). 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. |
Dan found his wallet but not his keys
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| 2. |
Mike didn’t notice the problem, but either Nina or Oscar did
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| 3. |
Neither the house nor the apartment was both cheap and roomy
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| Use derivations to check whether each of the entailments below holds. If one fails, confirm 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 lurks in an open gap. | ||
| 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. | ||
| 4. |
A ∧ ¬ C ⊨ ¬ (B ∧ C)
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| 5. |
¬ (B ∧ C), A ∧ B ⊨ A ∧ ¬ C
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| 6. |
A ∨ B ⊨ A ∨ C
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| In 7 you may use attachment and detachment rules (and their use can simplify the derivation). | ||
| 7. |
¬ (A ∧ B), A ∨ ¬ C ⊨ ¬ (B ∧ C)
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F04 test 2 answers
| 6. |
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| 7. |
The first answer below uses detachment rules while the second shows how to construct a derivation in this case without them.
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