| Phi 270 Fall 2013 |
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Phi 270 F08 test 2
F08 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 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 the basic rules, either because detachment and attachment rules do not apply or because I tell you not to use them.
I might also ask you to answer a question about derivations, either one you have given or derivations in general. For example, you might be asked about a particular point in a derivation to list the active resources and goal or to indicate all the basic rules that could be applied. I might also ask, though this is less likely, that you explain why a given derivation rule is legitimate. (You’ve seen questions of the first sort in your homework; for an example of the second sort, see question 7 of test 1 for 2000.)
F08 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 (i.e., using ∧, etc. and also both ... and, etc.). Be sure that the unanalyzed components of your answer are complete and independent sentences, and try to respect any grouping in the English. |
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| 1. |
Neither Ann nor Bill got the joke, but Carol did. answer |
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| 2. |
Either Ann didn’t reach Bill, or he wasn’t both free and able to help her. answer |
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Synthesize an English sentence (the more idiomatic the better) that has the following analysis: |
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| 3. |
¬ (B ∨ M) (B: Sam had heard of the book; M: Sam had heard of the movie) answer |
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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. |
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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. |
A ∧ ¬ B ⊨ ¬ (C ∧ B) ∧ A
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| 5. |
¬ (A ∧ B), A ⊨ ¬ B
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| 6. |
B ∨ A ⊨ C ∨ B
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For 7 you should show the first stage of each of the possible ways of beginning the derivation with the basic rules (i.e., the rules allowed in 4-6); and you should complete one of these derivations. In completing it, you may use attachment and detachment rules (and their use can simplify the derivation). |
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| 7. |
B ∨ A ⊨ A ∨ B
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F08 test 2 answers
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