| Phi 270 Fall 2013 |
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Phi 270 F03 test 2
F03 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.
Basic concepts of deductive logic. In addition to the concepts that were topics for the first test--entailment (or validity), equivalence, tautologousness, absurdity, and inconsistency--you will be responsible for the concepts of a mutually exclusive, jointly exhaustive, or contradictory pair of sentences. You should be able to define each in terms of possible worlds and truth values, and you should be prepared to answer questions about them, justifying your answer by reference to the definitions.
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 with the way of 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 some derivations where detachment and attachment rules may be used and where they will shorten the proof. But there will be others 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 by comparing the counterexamples that lurk in gaps before and after the rule is applied.
F03 test 2 questions
| 1. |
Define contradictoriness by completing the following:
φ and ψ are contradictory if and only if …
(Your answer should define contradictoriness in terms of truth values and possible worlds.)
answer |
| Analyze each sentence below in as much detail as possible, presenting the result using both symbolic and English notation for the connectives. Besure that the unanalyzed components of your answer are complete and independent sentences; also try to respect any grouping in the English. | ||
| 2. |
Ann found the note but didn’t recognize the signature
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| 3. |
Either the manufacturer and the distributor weren’t both available or neither of them changed its offer
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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) which lurks in an open gap. | ||
| Do not use attachment or detachment rules in 4 and 5. That is, do not use Adj or the new rules of 4.3; instead use only the basic rules for exploiting resources, planning for goals, and closing gaps. | ||
| 4. |
¬ B ⊨ ¬ (A ∧ B)
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| 5. |
¬ (¬ A ∧ ¬ B), C ∧ ¬ B ⊨ A
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| In 6 and 7 you may use attachment and detachment rules if you have an opportunity to do so. | ||
| 6. |
A ∨ B ⊨ C ∨ D
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| 7. |
¬ (A ∧ C), A ∨ B, ¬ (B ∧ ¬ D) ⊨ ¬ (C ∧ ¬ D)
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F03 test 2 answers
| 1. | φ and ψ are contradictory if and only if there is no possible world where they have the same truth value. |
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