Phi 270 F05 test 2
F05 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.
Definitions of basic concepts. Be able to state (in terms of possible worlds and truth values) the conditions under which sentences are mutually exclusive, jointly exhaustive, or contradictory and also the conditions under which the relation of relative exhuastiveness holds between sets.
Analysis. Be able to analyze the logical form of a sentence as fully as possible using negation and disjunction in addition to conjunction and present the form in both symbolic and English notation (that is, with the logical and symbol and by expressing forms using both ... and …, etc.).
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.
F05 test 2 questions
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Complete the following to give a definition in terms of truth values and possible worlds. |
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| 1. |
φ and ψ are mutually exclusive (i.e., φ, ψ ⊨ ⊥) if and only if …
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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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| 2. |
The job didn’t have both good pay and flexible hours, and Sam didn’t apply for it.
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| 3. |
Although neither Luke nor Mary saw the movie, either Nancy or Oscar did.
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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. |
¬ B ⊨ ¬ (A ∧ (B ∧ C))
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| 5. |
¬ (A ∧ B) ⊨ ¬ A
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| 6. |
(A ∧ B) ∨ C ⊨ C ∨ B
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In 7 you may use attachment and detachment rules (and their use can simplify the derivation). |
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| 7. |
A ∨ B, ¬ (B ∧ C), C ⊨ A
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F05 test 2 answers
| 1. |
φ and ψ are mutually exclusive if and only if there is no possible world in which both are true (or: … if and only if, in every possible world, at least one is false) |
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| 6. |
It is also possible to begin with PE; if that’s done, IP and Nc will be needed to close one of the gaps. |
| 7. |
The first answer below uses detachment rules while the second shows one way to construct a derivation without them.
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