Semantics 1, SoSe 2016 (Sailer): Mock Exam

Mock exam file: File:SoSe16-mockexam.pdf

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 Shakespeare's The Tempest for the final exam this term.

Task 1: Ambiguity

Consider the following ambiguous sentences.

1. For each of these, determine the type of ambiguity.
2. Provide an unambiguous paraphrase for the possible readings.

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

Check your answer

1. Type of ambiguity: referential ambiguity
2. 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

1. Type of ambiguity: scope ambiguity
2. 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

1. Type of ambiguity: collective-distributive ambiguity
2. 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

1. Type of ambiguity: structural ambiguity
2. 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.

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 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.

Check your answer

thane₁(banquo)

2. Macbeth is king and Macbeth mistrusts Banquo.

Check your answer

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: Lexicon

Provide the lexical entries for the words in the sentence Banquo mistrusted Macbeth. Use the features PHON, HEAD, SUBJ, SPR, COMPS, DR, PARTS, and EX-CONT.

Check your answer

	Banquo	mistrusted	Macbeth
PHON	< Banquo >	< mistrusted >	< Macbeth >
HEAD	noun	verb	noun
SUBJ	< >	< NP[DR [a]] >	< >
SPR	< >	< >	< >
COMPS	< >	< NP[DR [b]] >	< >
DR	[a]banquo	[c]mistrust2	[b]macbeth
EX-C	??	[d]	??
PARTS	<banquo >	<mistrust2, mistrust2([a],[b]) >	<macbeth >

Task 8: Analysis: Syntactic structure and semantic combinatorics

Using the lexical entries from Task 7, provide the syntactic structure of the sentence Banquo mistrusted Macbeth. Indicate all the values for all features at each node in the tree.

Check your answer

Tree structure:

	Banquo	mistrusted	Macbeth
	[1]		[2]
PHON	< Banquo >	< mistrusted >	< Macbeth >
HEAD	noun	verb	noun
SUBJ	< >	< [1] NP[DR [a]] >	< >
SPR	< >	< >	< >
COMPS	< >	< [2] NP[DR [b]] >	< >
DR	[a]banquo	[c]mistrust2	[b]macbeth
EX-C	??	[d]	??
PARTS	<banquo >	<mistrust2, mistrust2([a],[b]) >	<macbeth >

	VP: mistrusted M.	S: B. mistrusted M.
PHON	< mistrusted, Macbeth>	< Banquo, mistrusted, Macbeth>
HEAD	verb	verb
SUBJ	< [1] NP>	< >
SPR	< >	< >
COMPS	< >	< >
DR	[c]	[c]
EX-C	[d]	[d]
PARTS	<mistrust2, mistrust2([a],[b]) ,	<mistrust2, mistrust2([a],[b]),
	macbeth >	macbeth, banquo >

Task 9: General mechanisms of LRS

1. Enumerate all possible logical forms that would be compatible with the parts list of the sentence from Task 8.

Check your answer

Logical form 1: mistrust₂(banquo,macbeth) Logical form 2: mistrust₂(macbeth,banquo)

2. Use the parts values 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 precate. Therefore, macbeth cannot function as predicate, not can mistrust₂ function as its argument.

3. How do we manage to prevent some of the hypothetically possible logical forms that you listed in subtask 1 from occurring?

Check your answer

The subject, Banquo, should be linked to the first semantic argument slot of the predicate mistrust₂ - analogously for the complement and the second argument slot of the predicate. This is specified in the lexical entry of the verb, where the DR values of the subject ([a]) and the complement ([b]) are identified with the first and the second argument slots of mistrust₂ respectively.

Task 10: Local semantic phenomena

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

A sortal restriction is violated:

1. The verb start takes an eventuality as its semantic argument. The NP Lady Macbeth's madness is such an eventuality, but the crazy queen is not (it refers to an indivdiual).
2. The deviant sentence is an instance of a violated sortal restriction because the resulting sentence cannot be interpreted.

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

Check your answer

A weaker, further semantic selection restriction is violated.

1. Usually the verb kill takes a living being as its syntactic complement and its patient argument. In the second version, the complement NP refers to an abstract entity.
2. Even though the usual semantic selection restriction of the verb kill is violated in the seconde sentence, this violation does not lead to uninterpretability. Rather the sentence is interpreted in a figurative way, i.e., killing one's honorability is seen as causing one's own good reputation to disappear.

Task 11: Local semantics phenomena

Consider the following data on the verb build. Provide a lexical entry that includes all features from figure 1 and encodes explicitly the linking information, the sortal restriction, and (some of) the further semantic selection restrictions. Describe how your lexical entry will be allow you to account for the data.

(2) a. Macbeth built a wall.

b. The Scots built a wall.

c. #Macbeth built a war.

d. ??Macbeth built Lady Macbeth.

e. ??The wall built a war.

f. #The war built a wall.

Check your answer

Lexical entry:

PHON < build >

HEAD verb

SUBJ < NP [DR [a]] >

SPR < >

COMPS < NR [DR [b]] >

DR [c] build_2-obj,obj

EX-C ??

PARTS < [c], [c]([a],[b]) >

PRESUP < Gen x Geny (build_2-obj,obj(x,y) : (have-will₁(x) ∧ non-living-entity₁(y)))

Description:

• Linking: The DR-values of the subject and the direct object of the verb build, [a] and [b], are linked to the first respectively the second argument slot of the predicate build₂.
• Sortal restriction: The arguments of build_2-obj,obj cannot be events but must be concrete objects, i.e., they must be of sort obj. This is shown by the uninterpretability of (2c) and (2f). It is formally modelled via the sortal restrictions encoded in the name of the predicate.
• Further semantic selection restriction: The "builder" is typically an entity with a will of its own. The "built" is typically not a living entity. This is expressed by a prototypicality presupposition in the lexical entry of the verb.