Mock exam, WiSe 2019/20 (Sailer): Difference between revisions

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referential ambiguity
referential ambiguity<br />
Reading 1: ''he'' refers to ''Macbeth''. Paraphrase: ''Duncan trusted Macbeth because Macbeth was a thane.''<br />Reading 2: ''he'' refers to ''Duncan''. Paraphrase: ''Duncan trusted Macbeth because Duncan was a thane.''
Reading 1: ''he'' refers to ''Macbeth''. Paraphrase: ''Duncan trusted Macbeth because Macbeth was a thane.''<br />Reading 2: ''he'' refers to ''Duncan''. Paraphrase: ''Duncan trusted Macbeth because Duncan was a thane.''
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scope ambiguity
scope ambiguity<br />
Reading 1: ''every'' takes scope over ''a''. Paraphrase: ''For every king there is at least one thane such that the king trusts that thane.''<br />Reading 2: ''a'' takes scope over ''every''. Paraphrase: ''There is one particular thane such that each king trusts this thane.''
Reading 1: ''every'' takes scope over ''a''. Paraphrase: ''For every king there is at least one thane such that the king trusts that thane.''<br />Reading 2: ''a'' takes scope over ''every''. Paraphrase: ''There is one particular thane such that each king trusts this thane.''
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collective-distributive ambiguity
collective-distributive ambiguity<br />
Reading 1: collective reading. Paraphrase: ''Macbeth and Macduff are married to each other''<br />Reading 2: distributive reading. Paraphrase: ''Macbeth and Macduff are both married, but not to each other.''
Reading 1: collective reading. Paraphrase: ''Macbeth and Macduff are married to each other''<br />Reading 2: distributive reading. Paraphrase: ''Macbeth and Macduff are both married, but not to each other.''
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structural ambiguity
structural ambiguity<br />
Reading 1: the PP ''with a dagger'' is a modifier of the verb ''kill'' Paraphrase: ''Macbeth used a dagger to kill a king.''<br />Reading 2: the PP ''with a dagger'' is a modifier of the noun ''king''. Paraphrase: ''Macbeth killed a king who had a dagger.''
Reading 1: the PP ''with a dagger'' is a modifier of the verb ''kill'' Paraphrase: ''Macbeth used a dagger to kill a king.''<br />Reading 2: the PP ''with a dagger'' is a modifier of the noun ''king''. Paraphrase: ''Macbeth killed a king who had a dagger.''
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Latest revision as of 15:46, 5 March 2020

The examples in the text are based on Shakespeare's play Macbeth. The full text of the play is available on Projekt Gutenberg.

We will use the TV series Friends for the final exam this term.


Task 1: Ambiguity

Consider the following ambiguous sentences. For each of them, provide an unambiguous paraphrase for the possible readings.

(1) a. Duncan trusted Macbeth because he was a thane.

Check your answer

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

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

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.

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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

1. Define a universe that consists of Macbeth and Banquo.

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U = { Macbeth, Banquo }

2. Define the interpretation of the names macbeth and banquo in an intuitively plausible way.

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I(macbeth) = Macbeth,
I(banquo) = Banquo

3. Define the interpretation of the properties thane1, king1, and witch1 is such a way that Macbeth is a king, both are thanes and neither is a witch.

Check your answer

I(thane1) = {<Macbeth>, <Banquo>},
I(king1) = {<Macbeth>},
I(witch1) = {}

4. Define the interpretation of the 2-place relations mistrust2 and kill2 in such a way that Macbeth and Banquo mistrust each other and Macbeth kills Banquo.

Check your answer

I(mistrust2) = {<Macbeth, Banquo>, <Banquo, Mactbeth>},
I(kill2) = {<Macbeth,Banquo>}

Task 3: Formulae

Write down logical formulae that express the meaning of the following sentences.

1. Banquo is a thane.

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thane1(banquo)

2. Macbeth is king and Macbeth mistrusts Banquo.

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king1(macbeth) ∧ mistrust2(macbeth,banquo)

3. If Banquo is king then Macbeth does not kill Banquo.

Check your answer

king1(banquo) ⊃ ¬ kill2(macbeth,banquo)

Task 4: Interpreting formulae

Compute the interpretation of the following formulæ step by step.

1. mistrust2(macbeth,macbeth)

Check your answer

[[mistrust2(macbeth,macbeth)]] = 1
iff < [[macbeth]], [[macbeth]] > is in [[mistrust2]]
iff < I(macbeth), I(macbeth) > in I(mistrust2)
iff < Macbeth, Macbeth > in { <x,y> | x mistrusts y } = { <Macbeth, Banquo>, <Banquo, Macbeth> }

Since this is not the case, [[mistrust2(macbeth,macbeth)]] = 0.


2. ¬king(banquo)

Check your answer

[[¬ king1(banquo)]] = 1
iff [[king(banquo)]] = 0
iff < [[banquo]]> is not in [[king1]]
iff < I(banquo> is not in I(king1)
iff < Banquo > is not in { <x> | x is king } = { <Macbeth>}

Since this is the case, [[¬ king1(banquo)]] = 1


3. witch1(banquo) ⊃ king1(macbeth)

Check your answer

[[witch1(banquo) ⊃ king1(macbeth))]] = 1
iff [[witch1(banquo)]] = 0 or [[king1(macbeth) = 1
iff < [[banquo]] > is not in [[witch1]] or < [[macbeth]] > is in [[king1]]
iff < I(banquo) > is not in I(witch1) or < I(macbeth) > is in I(king1)
iff < Banquo > is not in { <x> | x is a witch} = { } or < Macbeth > is in { <x> | x is king} = { <Macbeth>}.

Since both are the case, [[witch1(banquo) ⊃ king1(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) kill2(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:

[[kill2(z,x)]]g = 1
iff < [[z]]g, [[x]]g > is in [[kill2]]g
iff < g(z), g(x) > is in I(kill2)
iff < Banquo, Macbeth > is in { <x,y> | x killed y} = { <Macbeth, Banquo> }.

Since this is not the case, [[kill2(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))

The formula is true in my model, because there is only one king, Macbeth, and Macbeth killed Banquo.
(Note: The English sentence is in passive, but this has no effect on the logical form.)

2. Macbeth mistrusts every witch.

Check your answer

x (witch(x) : mistrust(macbeth, x))

The formula is true in my model, because there are no witches in my model. Therefore, the formula with the universal quantifier is trivially true.

Task 7: Analysis: Syntactic structure and semantic combinatorics (15 points)

Provide the syntactic structure of the sentence Banquo mistrusted Macbeth. Indicate all the values for all features at each node in the tree.
Note: There is no linking information in this task!!!

Use the features PHON, HEAD, SUBJ, SPR, COMPS, and PARTS.


Check your answer

Tree structure:

Tree-BanquoMistrustedMacbeth.jpg


Banquo mistrusted Macbeth
[1] [2]
PHON  < [4] Banquo >  < [5] mistrusted > < [6] Macbeth >
HEAD  noun  [3] verb noun
SUBJ  < >  < [1] NP > < >
SPR  < >  < > < >
COMPS  < >  < [2] NP > < >
PARTS  <banquo  <mistrust2, _(_,_) >   <macbeth >


VP: mistrusted M. S: B. mistrusted M.
PHON  < [5], [6] >  < [4], [5], [6] >
HEAD   [3]   [3]
SUBJ  < [1] NP>  < >
SPR  < >  < >
COMPS  < >  < >
PARTS  <mistrust2, _(_,_) ,    <mistrust2, _(_,_),
  macbeth >   macbeth, banquo >


Task 8: General mechanisms of LRS

1. Enumerate all possible logical forms that would be compatible with the PARTS lists of the sentence form Task 8.

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There are two possible logical forms: mistrust2(banquo,macbeth) and mistrust2(macbeth,banquo)

2. Use the PARTS value from Task 8 to show that the following expressions are excluded as possible logical forms of the sentence.

(a) mistrust2(macbeth,banquo,banquo)

(b) mistrust2(banquo,banquo)

(c) macbeth(mistrust2,banquo)

Check your answer

(a) The expression cannot be a possible logical form, because it is not a well-formed formula: the predicate mistrust can only combine with two arguments, not with three. (This is indicated with the element mistrust2(...,...).

(b) The formula does not use all expressions from the PARTS list: the expression macbeth is missing.

(c) macbeth denotes an individual , mistrust2 is a predicate. Therefore, macbeth cannot function as predicate, not can mistrust2 function as its argument.



Task 10: Linking

Provide the full lexical entry of the verb from the sentence in Task 7 in such a way that it includes the linking information. Show that this will leave us only with the intended reading of the sentence.

Check your answer

PHON < mistrusted >
HEAD verb
SUBJ < NP[DR [a] ] >
SPR < >
COMPS < NP[DR [b] ] >
DR [c]
PARTS < [c]mistrust2, [c]([a],[b]) >


  • The verb specifies that (i) DR value of the element on its COMPS list must occur as the second argument of the predicate mistrust2, and (ii) that the DR value of the element on its SUBJ list must occur as the first argument of this predicate.
  • The constraint on head-complement combinations ensures that the non-head daughter is identical with the element on the head daughter's COMPS list. In our case, this means that the NP Macbeth is on the verb's COMPS list. Consequently, this NP's DR value, the name symbol macbeth needs to occur as the second argument of the predicate mistrust2.
  • Analoguously, constraint on head-subject combinations ensures that the non-head daughter is identical with the element on the head daughter's SUBJ list. In our case, this means that the NP Banquo is on the VP's SUBJ list. As the SUBJ list of a VP and its head daughter, the verb mistrusted are identical, the noun Banquo is on the verb's SUBJ list.
    Consequently, this NP's DR value, the name symbol banquo needs to occur as the first argument of the predicate mistrust2.
  • Only the formula mistrust2(banquo,macbeth) satisfies the linking constraint.

The reading mistrust2(macbeth,banquo) is excluded because the syntactic arguments are not associated with the required semantic argumets as described above.


Task 11: Local semantic phenomena (3 points)

What kind of semantic restriction is violated in the deviating forms of the following sentences? Give a reason for your decision

1. [Lady Macbeth’s madness]/#[The crazy queen] started after Duncan’s death.

Check your answer

The verb start requires that its subject argument be an event or a state, i.e. something that has temporal boundaries. An object or person, such as the Queen, cannot start. This version of the sentence is not interpretable. We find a violation of a sortal restriction in the second version of the example.

2. Macbeth killed [the king]/?[his honourableness].

Check your answer

The verb kill typically requires that its direct object be a living entity, i.e. you can only kill people, animals, etc. This restriction is satisfied in the first version of the sentence. But one cannot really kill abstract properties such as one's honorableness. However, we can make sense out of the sentence: At the beginning of the play, Macbeth is a very honorable man. In the course of the play, however, he becomes more and more vicious and obsessed by power and fear that he loses all his honorableness by his own acts. In this sense, we can say that he "kills" his honorability. As we can interpret the



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