SoSe25: Semantics 1

General 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.

Meeting 5 (21.5.2025)

Computing the truth value of complex formulae

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)

Interpretation of formulae with logical connectives

Consider these two natural language sentences. While keeping in mind the scenario given in a previous exercise, create complex formulae with logical connectives and compute the interpretation, respectively.

a.) Alice is a dog and Lisa and Tom enjoy watching football together.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px" Check your answers

Sentence: Alice is a dog and Lisa and Tom enjoy watching football together.

Here the interpretation in predicate logic notation:

[[dog (Alice) Ʌ enjoy-watching-football-together (Lisa,Tom)]] = false

because [[dog (Alice)]]= false

because I(Alice)= <Alice> and <Alice> is NOT an element of I(dog)

and [[enjoy-watching-soccer-together (Lisa,Tom)]] = true

Meeting 4 (14.5.2025)

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:

• kill2(macbeth,duncan)
• kill2(lady-macbeth,macbeth)

Syntax of atomic formulae

Exercise 1

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, and Isabelle.

This exercise is based on the following scenario:

At the time Alice, Paul, Tom and Lisa live in Berlin, but they rather want to live in Munich. Alice is married to Paul. They are Tom and Lisa's parents. Both Lisa and her father are tall, while Alice and Tom are rather small. Lisa and her mom share the same hair color, which is blonde. The family enjoys watching American football games together. But while the girls also like watching soccer, the boys get bored of it. Walter, the family's dog, doesn't care about sports at all, he likes to eat the familiy members´ shoes.

Which of the following expressions of predicate logic are formulae? Give an explanation for your decision. If the expression is not a formula try to change it into one.
(Click on the box if the expressionis a formula. When you press the submit button, you will see a suggestion for the second part of the question.)

1

family-dog

2

blonde(alice,paul)

3

father-of(alice,lisa)

4

tall(alice)

5

enjoy-watching-football-together

For a general explanation of formulae Click here

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Exercise 2

For the following exercises we use names and properties from the The Lord of the Rings novels.

Names: frodo, sam, gandalf, aragorn
1-place predicates: hobbit, wizard
2-place predicates: know, help

1 Click on the items that are well-formed expressions of the semantic representation language.

	gandalf
	hobbit
	sauron
	frodo ∧ gandalf
	know(gandalf)
	help(aragorn,frodo)

2 Click on the expressions that are well-formed formulae.

	hobbit
	frodo
	hobbit(aragorn)
	hobbit(frodo) ∧ wizard(gandalf)
	hobbit(frodo) ¬ wizard(sam)

Interpretation of atomic formulae

Interpret the following formulae as true or false. If you have not defined these relations or properties in your model use the ones given in a previous exercise.

• father-of-someone(paul,lisa)

Check your answers

[[father-of-someone(paul,lisa)]] = true iff
< [[paul]], [[lisa]] > ∈ [[father-of-someone]] iff
< I(paul), I(lisa) > ∈ I(father-of-someone) iff
< Paul, Lisa> ∈ {<Paul, Tom>,<Paul, Lisa>}.

Since this is the case, the formula is true.

• blonde(walter)

Check your answers

[[blonde(walter)]] = true iff
< I(walter) > ∈ I(blonde) iff
< Walter > ∈ {< Alice >,< Lisa >}.

Since this is not the case, the overall formula is false.

• enjoy-watching-football-together(alice,tom)

Check your answers

[[enjoy-watching-football-togehter(alice,tom)]] = true iff
< I(alice), I(tom) > ∈ I(enjoy-watching-football-together) iff
< Alice, Tom > ∈ {<Alice, Paul>,<Paul, Alice>,<Alice, Lisa>,<Lisa, Alice>,<Alice, Tom>,<Tom, Alice>,<Paul, Lisa>,<Lisa, Paul>,<Paul, Tom>,<Tom, Paul>,<Tom, Lisa>,<Lisa, Tom>}

Since this is the case, the formula is true.

Meeting 3 (7.5.2025)

Models

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.

Watch a short podcast what first-order models look like.

Based on this podcast, we can define a scenario as follows:

• Universe: U = {LittleRedRidingHood, Grandmother, Wolf}
  
• Properties:

RedHood = { < x> | x wears a read hood } = { <LittleRedRidingHood> }

Female = { <x> | x is female } = { <LittleRedRidingHood>, <Grandmother> }

BigMouth = { <x> | x has a big mouth } = { <Wolf> }

LiveInForest = { < x> | x lives in the forest } = { <Grandmother>, <Wolf>}

• Relations:

GrandChildOf = { <x,y> | x is y 's grandchild } = { <LittleRedRidingHood,Grandmother > }

AfternoonSnackOf = { <x,y> | x is y 's afternoon snack } = { <LittleRedRidingHood,Wolf > }

From this scenario, we can build a model M = < U, I >

• Universe: U = {LittleRedRidingHood, Grandmother, Wolf}
• Name symbols: NAME = {little-red-riding-hood}
  Note: In our model, only one individual has a name.
• Predicate symbols: PREDICATE = {red-hood1, female1, big-mouth, live-in-forest1, grand-child-of2, afternoon-snack-of2}
• Interpretation function I:

• for name symbols: I(little-red-riding-hood) = LittleRedRidingHood
• for predicate symbols:
  

I(red-hood1) = RedHood = { < x> | x wears a read hood } = { <LittleRedRidingHood> }

I(female) = Female = { <x> | x is female } = { <LittleRedRidingHood>, <Grandmother> }

I(big-mouth1) = BigMouth = { <x> | x has a big mouth } = { <Wolf> }

I(live-in-forest1) = LiveInForest = { < x> | x lives in the forest } = { <Grandmother>, <Wolf>}

I(grand-child-of2) = GrandChildOf = { <x,y> | x is y 's grandchild } = { <LittleRedRidingHood,Grandmother > }

I(afternoon-snack-of2) = AfternoonSnackOf = { <x,y> | x is y 's afternoon snack } = { <LittleRedRidingHood,Wolf > }

Exercises

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, and Isabelle.

Take a look at the following story:

Scenario:

At the time Alice, Paul, Tom and Lisa live in Berlin, but they rather want to live in Munich. Alice is married to Paul. They are Tom and Lisa's parents. Both Lisa and her father are tall, while Alice and Tom are rather small. Lisa and her mom share the same hair color, which is blonde. The family enjoys watching American football games together. But while the girls also like watching soccer, the boys get bored of it. Walter, the family's dog, doesn't care about sports at all, he likes to eat the familiy members´ shoes.

Using predicate logic terms and notation we now want to define the world described in the story. First we need our individuals, their relations and possible properties. You will need a pen and paper to write down your answers!

Note: As in the textbook, the expressions of the World will be written in italics and the ones of the predicate logic in bold.

(a) Define the universe described in the scenario. Introduce appropriate name symbols and define their interpretation. Make sure you use the correct notation.

Check your answers

These are the individuals of the story:
Alice
Paul
Lisa
Tom
Walter

This is how is this is stated in predicate logic:

U= {Alice, Paul, Lisa, Tom, Walter}

Name symbols: alice, paul, lisa, tom, walter

Interpretation of the name symbols:

I(alice) = Alice
I(paul) = Paul
I(lisa) = Lisa
I(tom) = Tom
I(walter) = Walter

(b) Choose three individuals from those mentioned in the story and map them to three properties mentioned in the story. Don't forget: empty sets are possible!

Check your answers

These are some possible answers:

rather-small: { <x> | x is rather small} = {<Tom>,<Alice>}

tall: { <x> | x is tall} = {<Paul>, <Lisa>}

blonde:{ <x> | x is blonde} = {<Alice>, <Lisa>}

female: {<x> |x is female} = {<Lisa>,<Alice>}

male: {<x> | x is male} = {<Tom>,<Paul>}

bored-watching-soccer: {<x> | x gets bored watching soccer} = {<Tom>,<Paul>}

enjoys-watching-soccer: {<x> | x enjoys watching soccer} = {<Alice>,<Lisa>}

enjoys-watching-football: {<x> | x enjoys watching football} = {<Tom>,<Alice>, <Lisa>, <Paul>}

doesn't-care-about-sports: {<x> | x doesn’t care about sports} = {<Walter>}

likes-eating-shoes: {<x> | x likes eating shoes} = {<Walter>}

lives-in-Berlin: {<x> | x lives in Berlin} = {<Tom>, <Alice>, <Lisa>, <Paul>}

want-to-live-in-Munich: {<x> | x wants to live in Munich} = {<Tom>, <Alice>, <Paul>, <Lisa>}

lives-in-Munich: {<x>| x lives in Munich} = {}

(c) Write down the possible relations mentioned in the story and map them to the individuals you wrote down in (a).

Check your answers

Here are examples of some relations:

son-of-someone: {<x,y> | x is the son of y} = {<Tom, Paul>, <Tom, Alice>}

father-of-someone: {<x, y> | x is the father of y} ={<Paul, Tom>, <Paul,Lisa>}

daughter-of-someone: {<x, y> | x is the daughter of y} = {<Lisa, Paul>, <Lisa, Alice>}

mother-of-someone: {<x, y> | x is the mother of y} ={<Alice, Lisa>, <Alice, Paul>}

brother-of-someone: {<x, y> | x is the brother of y} = {<Tom, Lisa>}

sister-of-someone: is the sister of y} = {<Lisa, Tom>}

dog-of-someone: {<x, y> | x is the dog of y} = {<Walter, Alice>, <Walter, Paul>, <Walter, Tom>, <Walter, Lisa>}

married-to-eachother: {<x, y> | x is married to y} = {<Alice, Paul>, <Paul, Alice}

enjoy-watching-football-together: {<x, y> | x enjoys watching football with y} = {<Alice, Paul>, <Paul, Alice>, <Alice, Lisa>, <Lisa, Alice>, <Alice, Tom>, <Tom, Alice>, <Paul, Lisa>, <Lisa, Paul>, <Paul, Tom>, <Tom, Paul>, <Tom, Lisa>, <Lisa, Tom>}

(d) Write down the I-functions (interpretation functions) for (a), (b) and (c).
Check your answers

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

Meeting 1

Video

Challenging phenomena at the syntax-semantics interface

Scenario

Shrek (film, 2001): https://en.wikipedia.org/wiki/Shrek