| Phi 270 Fall 2013 |
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Phi 270 F13 test 2
F13 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 although, while the majority of the test will be devoted to derivations, the proportion won’t be as large as the proportion of the classes devoted to them in this section of the course. 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 (they are never required) and where they will shorten the proof; but there will be other derivations where you must rely on the other rules, either because detachment and attachment rules do not apply or because I tell you not to use them.
You should also be ready to give the proximate argument of a gap at any stage and to indicate all the rules that might be applied (as you did in the homework for §3.5).
F13 test 2 questions
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Analyze each sentence below in as much detail as possible, presenting the result using symbolic notation and also using English notation. Provide a key to your abbreviations of unanalyzed components, and be sure that these components are complete and independent sentences. Try to respect any grouping in the English. |
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| 1. |
Ed didn’t get to both London and Berlin last summer, and he didn’t try to get to Rome. answer |
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| 2. |
Fred had tried to call either Bill or Carol, but neither of them had received a call from him. answer |
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Synthesize an English sentence that has the analysis below. Choose a simple and natural sentence whose organization reflects the grouping of the logical form: |
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| 3. |
(¬ A ∧ B) ∧ ¬ (C ∨ D) A: Ann liked the movie; B: Bill liked the movie; C: Carol went to the movie; D: Dave went to the movie |
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Use derivations to check whether each of the claims of entailment below holds. If a derivation 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. You should display intermediate steps in your calculation by writing the value of any compound component under the main connective of the component, and you should be sure to mark the final values you have calculated for each of the premises and for the conclusion (e.g., by circling these values). 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. |
K ∧ L ⊨ ¬ (K ∧ ¬ L)
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| 5. |
¬ (¬ B ∧ A), A ⊨ B
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| 6. |
D ∧ (E ∨ F) ⊨ D ∧ E
answer |
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You may use attachment and detachment rules in 7. While those rules can be used to shorten the derivation somewhat, it can also be completed without using them. |
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| 7. |
(A ∧ B) ∨ C ⊨ A ∨ C
answer |
F13 test 2 answers
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| 7. |
The following are three possible answers, but there are others: |
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