Phi 270 F04 test 3
F04 test 3 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. Two sorts of questions are possible here corresponding to the sorts of analyses you have done in chs. 5 and 6: (i) analysis by truth-functional connnectives only with atomic sentences as the ultimate components (the focus would, of course, be on conditionals—i.e., on the symbolic representation of if, only if, and unless) and (ii) analysis using truth-functional connnectives and the ideas of predicates, individual terms, and functors.
Synthesis. You may be given a symbolic form and an interpretation of its non-logical vocabulary and asked to express the sentence in English. This form might be either a truth-functional compound of unanalyzed component sentences or a form built using predicates, individual terms, and functors as well as connectives.
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. In particular be ready to use the rule RC (Rejecting a Conditional) from ch. 5.
Remember that, if a derivation includes forms involving predicates and functors, presenting a counterexample will require the description of a structure and not merely an assignment of truth values. You will be allowed to use either tables or diagrams to describe structures.
F04 test 3 questions
| Analyze the sentences below in as much detail as possible using only connectives; that is, the unanalyzed components should all be sentences (rather than individual terms, predicates, or functors). Present the result in both symbolic and English notation. Be sure that the unanalyzed components of your answer are complete and independent sentences; also try to respect any grouping in the English. | |
| 1. |
Dan wasn’t home unless it was a holiday.
answer |
| 2. |
If ten days had passed, then the return was accepted only if the item was damaged.
answer |
| Use derivations to check whether each of the entailments below holds. You may use detachment and attachment rules. If an entailment fails, present a counterexample that divides an open gap. | |
| 3. |
A → (B → ¬ C) ⊨ C → (B → ¬ A)
answer |
| 4. |
A → B ⊨ B → C
answer |
| Analyze the sentence below in as much detail as possible, giving a key to your abbreviations of unanalyzed expressions. In this case you shouldidentify components that are individual terms, predicates, or functors; however, you do not need to present the result in English notation (i.e., symbolic notation is enough). (Be sure that the unanalyzed components of your answer are independent—in particular, that none contains a pronoun whose antecedent is in another—and be sure also that the individual terms you identify really are individual terms rather than general terms or quantifier phrases.) | |
| 5. |
Ann called Bill and he picked her up at the garage.
answer |
| 6. |
If Carol’s father is Dave’s boss, then she has either met Dave or heard her father speak of him.
answer |
| Use a derivation to show that the entailment below holds. You may use detachment and attachment rules. (Be sure to indicate the alias sets at each stage when they change.) | |
| 7. |
a = fc, b = fd, Rac ⊨ c = d → Rbd
answer |
F04 test 3 answers
| 1. |
Dan wasn’t home unless it was a holiday Dan wasn’t home ← ¬ it was a holiday ¬ Dan was home ← ¬ it was a holiday
¬ H ← ¬ D
H: Dan was home; D: it was a holiday |
| 3. |
|
| 5. |
Ann called Bill and he picked her up at the garage Ann called Bill ∧ Bill picked Ann up at the garage [ _ called _ ] Ann Bill ∧ [ _ picked _ up at _ ] Bill Ann the garage Cab ∧ Pbag C: [ _ called _ ]; P: [ _ picked _ up at _ ]; a: Ann; b: Bill; g: the garage |
| 6. |
If Carol’s father is Dave’s boss, then she has either met Dave or heard her father speak of him Carol’s father is Dave’s boss → Carol has either met Dave or heard her father speak of him Carol’s father = Dave’s boss → (Carol has met Dave ∨ Carol has heard her father speak of Dave) [ _’s father] Carol = [ _’s boss] Dave → (Carol has met Dave ∨ Carol has heard Carol’s father speak of Dave) fc = bd → ([ _ has met _ ] Carol Dave ∨ [ _ has heard _ speak of _ ] Carol Carol’s father Dave) fc = bd → (Mcd ∨ Hc(fc)d) M: [ _ has met _ ]; H: [ _ has heard _ speak of _ ]; f: [ _’s father]; b: [ _’s boss]; c: Carol; d: Dave |
| 7. |
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