| Phi 270 Fall 2013 |
|
(Site navigation is not working.) |
Phi 270 F11 test 2
F11 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 attachment rules (Adj and Wk) and detachment rules (MTP and MPT) 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.
F11 test 2 questions
|
Analyze each sentence below in as much detail as possible, presenting the result in symbols and in 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. |
||
| 1. |
The club’s president wasn’t available, but either its first or its second vice president was. answer |
|
| 2. |
Ann and Bill weren’t both happy with the resort, and neither visited it again. answer |
|
|
Synthesize an English sentence (the more idiomatic the better) that has the following analysis: |
||
| 3. |
(M ∧ N) ∨ ¬ (M ∨ N) M: Mike finished the game; N: Nick finished the game |
|
|
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. Your table should indicate the value of any compound component by writing this value under the main connective of the component, and you should be sure to mark the final values you have calculated for the premises and the conclusion (e.g., by circling them). Do not use attachment or detachment rules in these derivations. 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. |
¬ S ⊨ ¬ (S ∧ ¬ T)
answer |
| 5. |
B ∧ ¬ (A ∧ B) ⊨ ¬ A ∧ B
answer |
| 6. |
A ∨ B ⊨ A ∧ B
answer |
| 7. |
C ∧ D ⊨ D ∨ E
answer |
F11 test 2 answers
| 4. |
|
| 6. |
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
It is OK to end your derivation when you have reached a dead-end gap, so, in this case, stages 5-7 were not needed |
| 7. |
The following are two possible answers, but there are others: |
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||