General information

Course description

Semantics is the study of the (literal) meaning of words and sentences. The meaning of a sentence is usually predictable from the words in the sentence and its syntactic structure. Yet, this relationship between form and meaning is not a simple one-to-one mapping. Instead, it is rich in ambiguities, pleonastic marking and elements without any identifiable meaning contribution. We will work on an account that is founded on classical tools of semantic research but still directly addresses these empirical challenges. After the class, the participants will be able to identify - and partly analyze - interesting semantic phenomena in naturally occurring texts. They will have acquired a basic working knowledge in formal logic, which they will be able to apply in the description of meaning

Time and place

Tuesday 08:15-9.45
Starting: 10.4.2018
Room: IG 0.251 (IG-Farben-Haus)

Olat course

Direct link: https://olat-ce.server.uni-frankfurt.de/olat/auth/RepositoryEntry/5912854558

Password: Please send an e-mail to the lecturer (sailer@em.uni-frankfurt.de)

Modules

Lehramt Englisch (L2/5, L3): FW2
BA English Studies: 3.4(1)
BA Empirische Sprachwissenschaft: K 6.1, En 4.1, DH 6.1

Contact

Manfred Sailer
e-mail: sailer@em.uni-frankfurt.de
office: IG 3.214
office hours: contact via e-mail!
www: http://user.uni-frankfurt.de/~sailer/index.htm

Course requirements

L2 and L5

regular attendance
pass all assignment sheets
Modulprüfung (optional): 90 min written exam (2 CP): 17.7.2018

L3

regular attendance
pass all assignment sheets
Modulprüfung (optional):
- 20 min. oral exam
- not possible: kleine Hausabeit

MSc Wirtschaftspädagogik

regular attendance
pass all assignment sheets
Modulprüfung (optional): 90 min written exam (2 CP): 17.7.2018

BA English Studies

regular attendance
pass all assignment sheets
literary scenario:

Part 1: Extract 15 ambiguous sentences from the text such that all types of ambiguity covered in class are represented provide unambiguous paraphrases of the readings determine the type of ambiguity

Part 2:

Define a formal model consisting of 3 characters from your text, which contains 2 properties, 1 2-place relation

Formulate 2 atomic formulae and compute their truth value.

Formulate 4 complex formulae with at least 1 logical connective in each and compute their truth value.

Formulate 1 complex formula with at least 2 logical connectives in

it and compute its truth value.

BA Empirische Sprachwissenschaft

K 6.1

regular attendance
Modulprüfung (obligatory): 90min. written exam: 17.7.2018

En 4.1

not possible: You have done this course as part of K6.1, so you can directly do constraint-based Semantics 2.

DH 6.1

not possible: You have done this course as part of K6.1, so you can directly do constraint-based Semantics 2.

Erasmus 6 CP

regular attendance
pass the assignment sheets
90min. written exam: 17.7.2018
small literary scenario:

Part 1: Extract 4 ambiguous sentences from the text such that different types of ambiguity covered in class are represented provide unambiguous paraphrases of the readings determine the type of ambiguity

Part 2:

Define a formal model consisting of 3 characters from your text, which contains 2 properties, 1 2-place relation

Formulate 2 atomic formulae and compute their truth value.

Formulate 2 complex formulae with at least 1 logical connective in each and compute their truth value.

Formulate 1 complex formula with at least 2 logical connectives in it and compute its truth value.

The grade will be determined by the result of the written exam.

Mock exam

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 show The Fresh Prince of Bel-Air 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

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

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

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

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

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
	[1]		[2]
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	??	??	??
PARTS	< [a]banquo >	< [b]mistrust₂, [b]([a],[c]) >	<[c]macbeth >

Task 8: Analysis

Provide the full HPSG and LRS analysis of the sentence Banquo mistrusted Macbeth. Use the features PHON, HEAD, SUBJ, SPR, COMPS, DR, PARTS, and EX-CONT. You only need to mention the EX-CONT value at the highest node in the tree.

Check your answer

Tree structure:

	Banquo	mistrusted	Macbeth
	[1]		[2]
PHON	< [4] Banquo >	< [5] mistrusted >	< [6] Macbeth >
HEAD	noun	[3] 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],[c]) >	<macbeth >

	VP: mistrusted M.	S: B. mistrusted M.
PHON	< [5], [6] >	< [4], [5], [6] >
HEAD	[3]	[3]
SUBJ	< [1] NP>	< >
SPR	< >	< >
COMPS	< >	< >
DR	[c]	[c]
EX-C	[d]	[d]
PARTS	<mistrust₂, mistrust₂([a],[c]) ,	<mistrust₂, mistrust₂([a],[c]),
	macbeth >	macbeth, banquo >

Task 8': Principles of syntax

1. How is the COMPS value of the VP determined by the lexical entries of the words and the principles of grammar?

Check your answer

The VP is licenced as a head-complement structure. The constraint on head-complement structures requires that the head daughter have a non-empty COMPS list and the mother have an empty COMPS list.
(It is also required that the non-head daughters are identical to the elements on the head daughter's COMPS list, but this is not relevant for the question at hand.)

2. How is it guaranteed that the PHON values of the words all appear in the PHON value of the sentence?

Check your answer

The Phonology Principle specifies that the PHON value of a mother is the concatenation of the PHON values of its daughter(s). Therefore, a element of the PHON value of a word in a sentence will always be part of the PHON values of every phrase that dominates this word. Since the overall sentence dominates all its component words, its PHON value comprises the PHON values of all words of this sentence.

3. How is it achieved that the HEAD value of the sentence is verb?

Check your answer

The HEAD value of the lexical verb, mistrust, is verb. In the VP, the lexical verb is the syntactic head of the phrase. According to the Head Feature Priniciple, the HEAD value of the mother node is the same as that of its head daughter, i.e., verb. Since this VP is the headdaughter of the sentence, the sentence's HEAD value should also be the same, i.e., verb again.

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

Under the assumption that the linking information was missing in your answer to Task 8, there are two possible logical forms (EX-CONT values):

mistrust₂(macbeth,banquo)
mistrust₂(banquo,macbeth)

2) Explain how the following formulae are excluded from occurring as EX-CONT values of the sentence from Task 7.

(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.

Meeting 13

Possible EX-CONT values

Given the following PARTS lists, what are possible EX-CONT values (if we do not assume other restrictions)

1. PARTS < pat, alex,like, like(__,__) >

Check your answer

like(pat,alex)
like(alex,pat)

2. PARTS < alex,snore, snore(__), ¬(__) >

Check your answer

¬(snore(alex))

3. PARTS < alex,alex,snore >

Check your answer

There is no possible EX-CONT value because the three elements on the PARTS list cannot be combined.

3. PARTS < alex,alex,snore, snore(__) >

Check your answer

snore(alex)

4. PARTS < alex,alex,snore, snore(__), __ ∧ __ >

Check your answer

snore(alex) ∧ snore(alex)

Analysis of simple sentences

Alex snored.

syntactic structure:

Words: Phrase:

Alex snored S: Alex snored.

HEAD [4]noun HEAD [5]verb HEAD

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Fido chased a mouse.

syntactic structure:

Words:

Fido chased a mouse

HEAD [8]noun HEAD [9]verb HEAD [10] det HEAD [11] noun

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Phrases:

NP: a mouse VP: chased a mouse S: Fido chased a mouse.

HEAD

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Pat gave Alex a ride.

syntactic structure:

Words:

Pat gave Alex a ride

HEAD [9]noun HEAD [10]verb HEAD [11] noun HEAD [12] det HEAD [13] noun

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Phrases:

NP: a ride VP: gave Alex a ride S: Pat gave Alex a ride.

HEAD

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Feel free to send feedback on this exercise to Manfred Sailer.

Basic combinatorics: Canonical examples

(the following exercises are adapted from the textbook material to [Chapter 5].

Possible EX-CONT values

Given the following PARTS lists, what are possible EX-CONT values (if we do not assume other restrictions)

1. PARTS < pat, alex,like, like(__,__) >

Check your answer

like(pat,alex)
like(alex,pat)

2. PARTS < alex,snore, snore(__), ¬(__) >

Check your answer

¬(snore(alex))

3. PARTS < alex,alex,snore >

Check your answer

There is no possible EX-CONT value because the three elements on the PARTS list cannot be combined.

3. PARTS < alex,alex,snore, snore(__) >

Check your answer

snore(alex)

4. PARTS < alex,alex,snore, snore(__), __ ∧ __ >

Check your answer

snore(alex) ∧ snore(alex)

Meeting 12

Basic syntactic notions

Parts of speech

a. Alex/

talked/

to/

my/

best/

friend/

.

b. You/

might/

suspect/

that/

Pat/

is/

a/

genius/

.

c. The/

title/

of/

a/

book/

largely/

determines/

whether/

it/

will/

be/

successful/

or/

a/

flop/

.

Feel free to send feedback on this exercise to Manfred Sailer.

Syntactic categories

Feel free to send feedback on this exercise to Manfred Sailer.

Lexical entries as Attribute-Value Matrix

Provide the required information on the lexical properties of the underlined words in the following sentences.
Note:

Put a minus ("-") if a slot should not receive any filling
Use det, noun, prep or verb for the HEAD values.

PHON <

>

HEAD

SUBJ <

>

SPR <

>

COMPS <

>

PHON <

>

HEAD

SUBJ <

>

SPR <

>

COMPS <

>

PHON <

>

HEAD

SUBJ <

>

SPR <

>

COMPS <

>

PHON <

>

HEAD

SUBJ <

>

SPR <

>

COMPS <

>

Feel free to send feedback on this exercise to Manfred Sailer.

Analysis of simple sentences

Alex snored.

syntactic structure:

Words: Phrase:

Alex snored S: Alex snored.

HEAD [4]noun HEAD [5]verb HEAD

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Fido chased a mouse.

syntactic structure:

Words:

Fido chased a mouse

HEAD [8]noun HEAD [9]verb HEAD [10] det HEAD [11] noun

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Phrases:

NP: a mouse VP: chased a mouse S: Fido chased a mouse.

HEAD

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Pat gave Alex a ride.

syntactic structure:

Words:

Pat gave Alex a ride

HEAD [9]noun HEAD [10]verb HEAD [11] noun HEAD [12] det HEAD [13] noun

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Phrases:

NP: a ride VP: gave Alex a ride S: Pat gave Alex a ride.

HEAD

SUBJ <

> SUBJ <

>

SPR <

> SPR <

>

COMPS <

> COMPS <

>

Feel free to send feedback on this exercise to Manfred Sailer.

Meeting 8

Video

Watch the following video on logical determiners:

Exercises

After having watched the video, work on the following tasks.

Task 1 Identify the determiners in the following sentence.

(a) Juliet talked to some stranger at the party.

(b) Every Capulet is an enemy to some Montague.

(c) Many people in Verona are not happy about the Capulet-Montague feud.

Check your solutions here:

(a) some

(b) every, some

(c) many

Task 2 Identify the formula that corresponds to the translation of the sentence.

Task 3 The sentence: Some Tybalt loved some Montague. is translated into the formula
∃ y (montague₁(y) : love₂(tybalt,y).

Given this table, is the overall formula true or false? (Give a reason for your answer.)

Check your solutions here:

The formula is false, because there is no individual in our model for which both the restrictor and the scope are true.

Task 4 Variable assignment function
Start with the following variable assigment function g: g(u) = Romeo, g(v) = Juliet, g(w) = Romeo, g(x) = Laurence, g(y) = Mercutio, g(z) = Juliet

Provide the changed variable assignment function g[v/Paris].

Check your solutions here:

g[v/Paris](u) = g(u) = Romeo
g[v/Paris](v) = Paris
g[v/Paris](w) = g(w) = Romeo
g[v/Paris](x) = g(x) = Laurence
g[v/Paris](y) = g(y) = Mercutio
g[v/Paris](z) = g(z) = Juliet

More exercises on quantifiers

The following material is an adapted form of material created by student participants of the project e-Learning Resources for Semantics (e-LRS).
Involved participants: AnKa, Katharina, Lara

Restricted Quantifiers

Find the right formula for the sentence below.

Different types of Quantifiers

Which type(s) of quantifiers does the sentence below have?

2. Write down the logical formula(e) that correspond to the sentence Ramon signs every sculpture he makes.

Check your solutions here

Sentence: Ramon signs every sculpture he makes.

Universal Quantifier

∀x ((sculpture(x) ∧ make(ramon, x)) ⊃ sign(ramon, x))

Paraphrse: "For every thing x, if x is a sculpture and x is made by Ramon then x is signed by Ramon."

We use the name constant ramon for both the name (Ramon) and the personal pronoun he that referes to Ramon.

In restricted quantifier notation

∀x ((sculpture(x) ∧ make(ramon, x)) : sign(ramon, x))

Here, the N' is "sculpture he makes" and therefore its translation appears in the part before the colon.

Scopal Ambiguity

1. In which way is the following sentence ambiguous?

Everyone loves someone.

The following pictures may help you:

One Reading
Another Reading

Check your solutions here:

In this sentence, the scopal ambiguity is created by the two quantifiers everyone and someone.

When looking at the two pictures that try to help you, you can see two possible readings:

1. For every person there is, there is at least one other person who loves him / her.

2. There is one person that is loved by everyone else.

2. Write down the two possible logical forms.

Check your solutions here:

1. For every person there is at least one person who loves him / her:

∀x (person(x) ⊃ ∃y (person(y) ∧ love(x,y)

Or, in restricted-quantifier notation: ∀x (person(x) : ∃y (person(y) : love(x,y)

2. There is one person that is loved by everyone:

∃y (person(y) ⊃ ∀x (person(x) ∧ love(x,y)

Or, in restricted-quantifier notation: ∀x (person(x) : ∃y (person(y) : love(x,y)

Meeting 6

Video

The next video shows how the truth value of a more complex formula can be computed. The example contains two connectives:

kill(malcom,lady-macbeth) ∨ ¬thane(macbeth)

The video shows two different methods: top down and bottom up.

Meeting 5

Video

Connectives

The following video presents the step-by-step computation of the truth value of two formulae with connectives. The example uses a model based on Shakespeare's play Macbeth. The two formulae are:

¬ king(lady-macbeth)
king(duncan) ∨ king(lady-macbeth)

The next video shows how the truth value of a more complex formula can be computed. The example contains two connectives:

kill(malcom,lady-macbeth) ∨ ¬thane(macbeth)

The video shows two different methods: top down and bottom up.

Truth tables

Truth tables are also useful to compute the truth value of complex formulae. This is shown in the following podcast, created by Lisa Günthner.

Meeting 3

Computing the truth value of atomic formulae

The following video presents the step-by-step computation of the truth value of two atomic formulae. The example uses a model based on Shakespeare's play Macbeth. The two formulae are:

kill(macbeth,duncan)
kill(lady-macbeth,macbeth)

Meeting 2

Our literary scenario

Literary scenario: TV series How I met your mother
Wikipedia entry: https://en.wikipedia.org/wiki/How_I_Met_Your_Mother

Why it is too difficult to go directly from language to the world

The following architecture is extremely useful when talking about semantics:

A natural language expressions: Daenerys loves Drogo.
... is mapped to some expression from a formal language (here: predicate logic): love2(daenerys,drogo)
This logical expression is then interpreted with respect to our scenario/world: The formula love2(daenerys,drogo) is true, because, in our scenario, Daenerys loves Drogo.

The following properties of natural language make it useful to use the intermediate step of a logical language:

The same expression can have different meanings (ambiguity).
Different expressions can have the same meaning (synonyms, paraphrases)

Find examples for the above-mentioned properties (ambiguity, synonymy, paraphrases).

Check your answers

1. one form, two meaingns: Ambiguity: (see earlier in this meeting and the slides of last week's meeting)

1.a Ambiguous words: date (fruit or point in time); bank (financial institute or bank of a river)

1.b. Ambiguous sentences: Sycorax and Prospero were stranded on the island with their children.

2. two forms, one meaning:

2.a Synonymous words: couch - sofa; instant - moment

2.b Paraphrases:

active-passive pairs: Prospero set Ariel free. - Ariel was set free by Prospero.
cleft sentences: Prospero set Ariel free. - It was Prospero who set Ariel free.
different ways to express a possessor: Sycorax was the first inhabitant of the island. and Sycorax was the island's first inhabitant.

Towards a formal model

First steps

The following material is an adapted form of material created by student participants of the project e-Learning Resources for Semantics (e-LRS). Involved participants: Lisa, Marthe, Elisabeth, Isabelle.

You can think of building a formal model like being the producer of a film who has to collect everything that should be included in the film.

Here is a very simple story from which we can derive an example model.

The universe and name symbols

Task: Assume three individuals from our Game of Thrones-scenario.

Formally we collect the individuals of our model in a so-called universe (U). For the fairy-tale story, we can define the universe as follows:

U = {Redridinghood, Grandmother, Wolf}

Do a similar definition for your own scenario.

We can introduce name symbols for some of our individuals. For example: redridinghood, grandmother, wolf.

We link the name symbols to the individuals in our modal. To do this, we introduce the interpretation function. We will written the interpretation function as as I.
This function can be defined in the following way:

I(grandmother) = Grandmother
I(redridinghood) = Red Riding Hood
I(wolf) = Wolf

Relations and predicate symbols

In the fairy-tale scenario we express a relation between Little Red Riding Hood and the Wolf, namely that Little Red Riding Hood is the Wolf's afternoon snack. To formalize this, we collect all pairs of individuals which are such that the first element in the pair is the afternoon snack of the second. Note: A pair is written in between pointy brackets.

Formally we can write this down as follows:
{< x, y > | x is y 's afternoon snack} = { < Redridinghood, Wolf >, < Grandmother, Redriding hood >.}

We can also assume empty relations:

{< x, y > | x is y 's father } = { }

Note, if a relation works both ways, two pairs must be added:

{< x, y > | x talks with y} = { <Redridinghood, Wolf >, < Wolf, Redridinghood >}

Just like with names, we want to have symbols that we can use in the logical language. For our example, let's take the predicate symbols afternoon-snack-of_2 and father-of_2, and talks-with_2. (The number 2 indicates that the interpretation consists of pairs, not just of single individual) There interpretation is defined as follows:

I(afternoon-snack-of_2) = { < x, y > | x is y 's afternoon snack } = { <Redridinghood, Wolf >, <Grandmother, Wolf > }.

Task: For each of your properties, invent an appropriate predicate symbol. Define its interpretation.

Properties and predicate symbols

A property is a specification that either holds of an individual or not. In the little story, having a big mouth is a property of the Wolf, but of noone else in the story. Being female holds of both Little Red Riding Hood and the Grandmother.

We can think of a property as the set of individuals that have this property. Under this view, the property of being female would be the set {Redridinghood, Grandmother}.

Alternatively it is convenient to think of properties as 1-place relations. Under this view, the property of being female would be a set of lists of length 1. This is what the property of being female then looks like: { <Redridinghood>, <Grandmother> }

Task: Using your Game of Thrones universe, define two properties in the format of 1-place relations.

Just like before, we want to have symbols that we can use in the logical language. For our example, let's take the predicate symbols female_1 and has-big-mouth_1. There interpretation is defined as follows:

I(female_1) = { < x > | x is female } = { <Redridinghood>, <Grandmother> }.

Task: For each of your properties, invent an appropriate predicate symbol. Define its interpretation.

Meeting 1

Literary scenario: TV series How I met your mother
Wikipedia entry: https://en.wikipedia.org/wiki/How_I_Met_Your_Mother

pat ¦	snore ¦	snore(pat)
			Pat
			snored

pat ¦	chris ¦	like ¦	like(pat,chris)
				Pat
				likes
				Chris

	∃x (montague₁(x) : (at-party₁(x) ∧ fall-in-love-with₂(x,juliet)))
	∃x ((montague₁(x) ∧ at-party₁(x)) : fall-in-love-with₂(x,juliet))
	∃x (montague₁(x) : (at-party₁(x) ∧ fall-in-love-with₂(x,juliet))
	∃x ((montague₁(x) ∧ fall-in-love-with₂(x,juliet)) : at-party₁(x))

	∃x (student(x) : (hear(x,concert) ∧ interview(holmes,x)))
	∃x ((student(x) ∧ hear(x,concert)) : interview(holmes,x))
	∃x (student(x) ∧ hear(x,concert) ∧ interview(holmes,x))
	∃x ((student(x) ∧ interview(holmes,x)) : hear(x,concert))

	existential
	universal

	existential
	universal

	existential
	universal

	existential
	universal

Semantics 1, SoSe 2018 (Sailer)

General information

Course description

Time and place

Olat course

Modules

Contact

Course requirements

L2 and L5

L3

MSc Wirtschaftspädagogik

BA English Studies

BA Empirische Sprachwissenschaft

K 6.1

En 4.1

DH 6.1

Erasmus 6 CP

Mock exam

Task 1: Ambiguity

Task 2: Model and Interpretation

Task 3: Formulae

Task 4: Interpreting formulae

Task 5: Variables

Task 6: Quantifiers

Task 7: Analysis

Task 8: Analysis

Task 8': Principles of syntax

Task 9: General mechanisms of LRS

Meeting 13

Possible EX-CONT values

Analysis of simple sentences

Basic combinatorics: Canonical examples

Possible EX-CONT values

Meeting 12

Basic syntactic notions

Parts of speech

Syntactic categories

Lexical entries as Attribute-Value Matrix

Analysis of simple sentences

Meeting 8

Video

Exercises

More exercises on quantifiers

Restricted Quantifiers

Different types of Quantifiers

Scopal Ambiguity

Meeting 6

Video

Meeting 5

Video

Connectives

Truth tables

Meeting 3

Computing the truth value of atomic formulae

Meeting 2

Our literary scenario

Why it is too difficult to go directly from language to the world

Towards a formal model

First steps

The universe and name symbols

Relations and predicate symbols

Properties and predicate symbols

Meeting 1

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