Semantics 1, SoSe 2014: Mock exam: Difference between revisions
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=== Task 6: Quantifiers === | |||
Provide logical formulae that expresse the meaning of the following sentences. Are the formulae true in | |||
your model (not in the entire play)? Give a short reason (you don’t need to compute the truth value). | |||
1. Banquo was killed by a king. | |||
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Check your answer | |||
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∃ ''x'' ('''king'''(''x'') : '''kill'''(''x'', '''banquo''')) | |||
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2. Macbeth mistrusts every witch. | |||
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Back to the material for [[Semantics_1,_SoSe_2014|Semantics 1, SoSe 2014]]. | Back to the material for [[Semantics_1,_SoSe_2014|Semantics 1, SoSe 2014]]. |
Revision as of 21:29, 4 July 2014
Mock exam file: File:Mock-exam-sose14.pdf
The examples in the text are based on Shakespeare's play Macbeth. The full text of the play is available on Projekt Gutenberg.
Task 1: Ambiguity
Consider the following ambiguous sentences.
- For each of these, determine the type of ambiguity.
- Provide an unambiguous paraphrase for the possible readings.
(1) a. Duncan trusted Macbeth because he was a thane.
Check your answer
- Type of ambiguity: referential ambiguity
- Reading 1: he refers to Macbeth. Paraphrase: Duncan trusted Macbeth because Macbeth was a thane.
Reading 2: he refers to Duncan. Paraphrase: Duncan trusted Macbeth because Duncan was a thane.
b. Every king trusts a thane.
Check your answer
- Type of ambiguity: scope ambiguity
- Reading 1: every takes scope over a. Paraphrase: For every king there is at least one thane such that the king trusts that thane.
Reading 2: a takes scope over every. Paraphrase: There is one particular thane such that each king trusts this thane.
b. Macbeth and Macduff are married.
Check your answer
- Type of ambiguity: collective-distributive ambiguity
- Reading 1: collective reading. Paraphrase: Macbeth and Macduff are married to each other
Reading 2: distributive reading. Paraphrase: Macbeth and Macduff are both married, but not to each other.
b. Macbeth killed a king with a dagger.
Check your answer
- Type of ambiguity: structural ambiguity
- Reading 1: the PP with a dagger is a modifier of the verb kill Paraphrase: Macbeth used a dagger to kill a king.
Reading 2: the PP with a dagger is a modifier of the noun king. Paraphrase: Macbeth killed a king who had a dagger.
Task 2: Model and Interpretation
(Note: For this task you do not need to use the functional notation and the types)
1. Define a universe that consists of Macbeth and Banquo.
Check your answer
U = { Macbeth, Banquo }
2. Define the interpretation of the names macbeth and banquo in an intuitively plausible way.
Check your answer
I(macbeth) = Macbeth,
I(banquo) = Banquo
3. Define the interpretation of the properties thane, king, and witch is such a way that Macbeth is a king, both are thanes and neither is a witch.
Check your answer
I(thane) = {Macbeth, Banquo},
I(king) = {Macbeth},
I(witch) = {}
4. Define the interpretation of the 2-place relations mistrust and kill in such a way that Macbeth and Banquo mistrust each other and Macbeth kills Banquo.
Check your answer
I(mistrust) = {<Macbeth, Banquo>, <Banquo, Mactbeth>},
I(kill) = {<Macbeth,Banquo>}
Task 3: Formulae
Write down logical formulae that express the meaning of the following sentences.
1. Banquo is a thane.
Check your answer
thane(banquo)
2. Macbeth is king and Macbeth mistrusts Banquo.
Check your answer
king(macbeth) ∧ mistrust(macbeth,banquo)
3. If Banquo is king then Macbeth does not kill Banquo.
Check your answer
king(banquo) ⊃ ¬ kill(macbeth,banquo)
Task 4: Interpreting formulae
Compute the interpretation of the following formulæ step by step.
1. mistrust(macbeth,macbeth)
Check your answer
[[mistrust(macbeth,macbeth)]] = 1
iff < [[macbeth]], [[macbeth]] > is in [[mistrust]]
iff < I(macbeth), I(macbeth) > in I(mistrust)
iff < Macbeth, Macbeth > in { <x,y> | x mistrusts y } = { <Macbeth, Banquo>, <Banquo, Macbeth> }
Since this is not the case, [[mistrust(macbeth,macbeth)]] = 0.
2. ¬king(banquo)
Check your answer
[[¬ king(banquo)]] = 1
iff [[king(banquo)]] = 0
iff < [[banquo]]> is not in [[king]]
iff < I(banquo> is not in I(king)
iff < Banquo > is not in { <x> | x is king } = { <Macbeth>}
Since this is the case, [[¬ king(banquo)]] = 1
3. witch(banquo) ⊃ king(macbeth))
Check your answer
[[witch(banquo) ⊃ king(macbeth))]] = 1
iff [[witch(banquo)]] = 0 or [[king(macbeth) = 1
iff < [[banquo]] > is not in [[witch]] or < [[macbeth]] > is in [[king]]
iff < I(banquo) > is not in I(witch) or < I(macbeth) > is in I(king)
iff < Banquo > is not in { <x> | x is a witch} = { } or < Macbeth > is in { <x> | x is king} = { <Macbeth>}.
Since both are the case, [[witch(banquo) ⊃ king(macbeth))]] = 1.
Task 5: Variables
Provide a g-function that maps the variables x, y, and z to individuals from the universe and compute the interpretation of the following formula with respect to the model and your g.
(i) kill(z,x)
Check your answer
Example solution (other values for g are equally possible).
g(x) = Macbeth,
g(y) = Banquo,
g(z) = Banquo.
With this variable assignment we can compute the truth value of the formula:
[[kill(z,x)]]g = 1
iff < [[z]]g, [[x]]g > is in [[kill]]g
iff < g(z), g(x) > is in I(kill)
iff < Banquo, Macbeth > is in { <x,y> | x killed y} = { <Macbeth, Banquo> }.
Since this is not the case, [[kill(z,x)]]g = 0.
Task 6: Quantifiers
Provide logical formulae that expresse the meaning of the following sentences. Are the formulae true in your model (not in the entire play)? Give a short reason (you don’t need to compute the truth value).
1. Banquo was killed by a king.
Check your answer
∃ x (king(x) : kill(x, banquo))
2. Macbeth mistrusts every witch.
Back to the material for Semantics 1, SoSe 2014.