SoSe 2026: Semantics 1

2026-04-18T10:07:51Z

Manfred: /* Meeting 1 */

2025-12-16T21:05:54Z

Manfred: /* Meeting 9 */

= Meeting 10 =

== Videos ==

This video shows which information is inside a lexcial entry.
<embedvideo service="youtube" dimensions="400">
https://youtu.be/impaNluIyNM
</embedvideo>

The second video shows the HPSG analysis of two simple sentences (37'):
::''Duncan died.'' (the first 18+ minutes)
::''Macbeth killed Duncan.'' (the rest of the video)

<embedvideo service="youtube" dimensions="400">
https://youtu.be/7lLWmA_cmy4
</embedvideo>

= Meeting 9 =

== Videos ==

Watch the following video (33') on the basic step in a syntactic analysis as we need it in our course.

<embedvideo service="youtube" dimensions="400">
https://youtu.be/IN3VsH3Jn1o
</embedvideo>

The next video (14') introduces the way we talk about syntactic trees. Please watch it.

<embedvideo service="youtube" dimensions="400">
https://youtu.be/57TfLZJQgCM
</embedvideo>

The final video is a more general video (12', produced in 2008) on basic steps in a syntactic analysis. Note, only steps 1-5 apply to our course (i.e. the first 9'30'' of the video). Step 6 is based on a different syntactic theory.

<embedvideo service="youtube" dimensions="400">
https://youtu.be/EDbaCAVgHUI
</embedvideo>

= Meeting 7 =

== Video ==

Watch the following video on logical determiners:

<embedvideo service="youtube" dimensions="400">http://youtu.be/5PRL23XcaFY</embedvideo>


== Exercises ==

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

'''Task 1''' Identify the logical 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.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your solutions here:
<div class="mw-collapsible-content">
(a) ''some''

(b) ''every'', ''some''

(c) ''many''</div>
</div>

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

<quiz display=simple>

{''Some Montague who was at the party fell in love with Juliet.''
|type="()"}
- ∃''x'' ('''montague<sub>1</sub>'''(''x'') : ('''at-party<sub>1</sub>'''(''x'') &and; '''fall-in-love-with<sub>2</sub>'''(''x'','''juliet''')))
|| In restricted quantifier notation, the "complete" semantic representation of the noun phrase (NP) appears in the restrictor (-> square brackets).
+ ∃''x'' (('''montague<sub>1</sub>'''(''x'') &and; '''at-party<sub>1</sub>'''(''x'')) : '''fall-in-love-with<sub>2</sub>'''(''x'','''juliet'''))
- ∃''x'' ('''montague<sub>1</sub>'''(''x'') : ('''at-party<sub>1</sub>'''(''x'') &and; '''fall-in-love-with<sub>2</sub>'''(''x'','''juliet'''))
|| In restricted quantifier notation, the semantic representation of the noun phrase (NP) appears in the restrictor.
- ∃''x'' (('''montague<sub>1</sub>'''(''x'') &and; '''fall-in-love-with<sub>2</sub>'''(''x'','''juliet''')) : '''at-party<sub>1</sub>'''(''x''))
|| In restricted quantifier notation, the semantic representation of the noun phrase (NP) appears in the restrictor, that of the VP in the scope.

</quiz>

'''Task 3''' The sentence: ''Some Tybalt loved some Montague.'' is translated into the formula<br>∃ y ('''montague<sub>1</sub>'''(''y'') : '''love<sub>2</sub>'''('''tybalt''',''y'').

<quiz display=simple>
{Mark all the cells in the table that stand for a true statement.
|type="[]"}
| '''montague<sub>1</sub>'''(''y'') <span style="color:white">zwisch</span>| '''love<sub>2</sub>'''('''tybalt''',''y'')<span style="color:white">zwisch</span>
+- ''Romeo''
+- ''Mercutio''
-- ''Juliet''
-- ''Tybalt''
-- ''Laurence''
-- ''Paris''
</quiz>

Given this table, is the overall formula true or false? (Give a reason for your answer.)
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your solutions here:
<div class="mw-collapsible-content">
The formula is false, because there is no individual in our model for which both the restrictor and the scope are true.
</div>
</div>

= Meeting 6 =

(no material)

= Meeting 5 =
'''''Asynchronous!'''''

== Computing the truth value of more complex formulae ==

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) &or; ¬thane(macbeth)'''

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

<embedvideo service="youtube" dimensions="400">http://youtu.be/C1rjU104R54</embedvideo>

== Truth tables ==

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

<embedvideo service="youtube" dimensions="400">http://www.youtube.com/watch?v=ZWdltj5Mqdc</embedvideo>

= Meeting 4 =

== Logical ''or'' ==

The following short video (in German) gives some examples for the difference between the meaning of logical disjunction and the everyday use of the word ''or'' in natural language.

<embedvideo service="youtube" dimensions="400">https://youtu.be/t2-RwzjXSuc?si=nVqvGqcvgqTGQu_3</embedvideo>

(The video is from the youtube playlist [https://tinyurl.com/ventrilinguist ''VentriLinguist: Sprachwissenschaft mit Bauchgefühl''])

== 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) &or; king(lady-macbeth)'''

<embedvideo service="youtube" dimensions="400">http://youtu.be/ABXPMzHFYxU</embedvideo>


== Interpretation of formulae with logical connectives ==
Consider these two natural language sentences. While keeping in mind the scenario given in [[ExerciseFOModels-d|a previous exercise]], create complex formulae with logical connectives and compute the interpretation, respectively.

Consider these two natural language sentences. While keeping in mind the scenario given in [[ExerciseFOModels-d|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
<div class="mw-collapsible-content">Sentence: Alice is a dog and Lisa and Tom enjoy watching football together.

Here the interpretation in predicate logic notation:

<nowiki>[[</nowiki>'''dog (Alice) Ʌ enjoy-watching-football-together (Lisa,Tom)''']] = ''false''<br/>

because <nowiki>[[</nowiki>'''dog (Alice)''']]= ''false'' <br/>

::because I('''Alice''')= <''Alice''> and <''Alice''> is NOT an element of I('''dog''') <br/>

and <nowiki>[[</nowiki>'''enjoy-watching-soccer-together (Lisa,Tom)''']] = ''true'' <br/>

::because I('''Lisa''')= <''Lisa''>, I('''Tom''')= <''Tom''> and <''Lisa,Tom''> '''is''' in the set of I('''enjoy-watching-football-together'''). <br/>

'''Conjunction (Ʌ)''': Both atomic formulae have to be true in order for the complex formula to be true.
</div>
</div>

'''b.)''' Tom is not Paul's daughter or Tom is tall.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
Sentence: Tom is not Paul's daughter or Tom is tall.

Here the interpretation in predicate logic notation:

<nowiki>[[</nowiki>'''¬daughter-of-someone (Tom,Paul) v tall(Tom)''']] = ''true'' <br/>

because <nowiki>[[</nowiki>'''¬daughter-of-someone (Tom,Paul)''']]= ''true'' <br/>

::because I('''Tom''')= <''Tom''>, I('''Paul''')= <''Paul''> and <''Tom,Paul''> is NOT in the set of I('''daughter-of-someone''') <br/>

and <nowiki>[[</nowiki>'''tall(Tom)''']] = ''false'' <br/>

::because I('''Tom''')= <''Tom''> and <''Tom''> is NOT an element of I('''tall'''). <br/>

'''Disjunction (v)''': At least one of the atomic formulae has to be true in order for the complex formula to be true.
</div>
</div>

= 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:
* '''kill2(macbeth,duncan)'''
* '''kill2(lady-macbeth,macbeth)'''

<embedvideo service="youtube" dimensions="400">http://youtu.be/8HGCB9urmbg</embedvideo>

== Syntax of atomic formulae ==

=== Exercise 1 ===
{{CreatedByStudents1213}}<br />''Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], and [[User:IsaB|Isabelle]].''

This exercise is based on the following scenario:
<blockquote>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.
</blockquote>

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.<br />''(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.)''

<quiz display="simple">
{ }
- '''family-dog'''
|| '''family-dog''' is just a predicate symbol. It cannot be interpreted as true or false, as its argument is missing. A possible formula would be: '''family-dog'''('''walter''')

{ }
- '''blonde'''('''alice''','''paul''')
|| It cannot be interpreted as true or false. As '''blonde''' is a property and not a relation it can therefore only have one individual as its argument. A possible formula would be: '''blonde'''('''alice''')

{ }
+ '''father-of'''('''alice''','''lisa)'''
|| '''father-of''' is a relation and therefore requires two individuals as its arguments. Of course, this formula is not true. Alice can never be a father of someone. However, although the interpretation of the formula is wrong, it is still a formula as it can be interpreted as true or false.

{ }
+ '''tall'''('''alice''')
|| As '''tall''' is a property it requires one individual in brackets. This is the case and it can therefore be interpreted as true or false.

{ }
- '''enjoy-watching-football-together'''
|| It cannot be interpreted as true or false. As “enjoy-watching-football-together" is a relation two individuals are required. A possible formula would be: '''enjoy-watching-football-together'''('''walter''','''alice''')
</quiz>

For a general explanation of formulae [[General_Explanation_Formulae|Click here]]
<hr />

=== Exercise 2 ===
For the following exercises we use names and properties from the ''The Lord of the Rings'' novels.

Names: '''frodo''', '''sam''', '''gandalf''', '''aragorn'''<br />
1-place predicates: '''hobbit''', '''wizard'''<br />
2-place predicates: '''know''', '''help'''

<quiz display="simple">
{Click on the items that are well-formed expressions of the semantic representation language.
}
+ '''gandalf'''
+ '''hobbit'''
- '''sauron'''
|| The name '''sauron''' is not included in the non-logical vocabulary.
- '''know'''('''gandalf''')
|| '''know''' is a 2-place predicate. Therefore it must combine with two arguments.
+ '''help'''('''aragorn''','''frodo''')

{Click on the expressions that are well-formed formulae.
}
- '''hobbit'''
- '''frodo'''
+ '''hobbit'''('''aragorn''')
</quiz>

== 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 [[ExerciseFOModels-d|a previous exercise]].

* '''father-of-someone'''('''paul''','''lisa''')
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
<nowiki>[[</nowiki>'''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />
< <nowiki>[[</nowiki>'''paul''']], <nowiki>[[</nowiki>'''lisa''']] > ∈ <nowiki>[[</nowiki>'''father-of-someone''']] iff<br />
< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />
< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.

Since this is the case, the formula is true.
</div>
</div>

* '''blonde'''('''walter''')
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
<nowiki>[[</nowiki>'''blonde(walter)''']] = ''true'' iff<br />
< I('''walter''') > ∈ I('''blonde''') iff <br />
< ''Walter'' > ∈ {< ''Alice'' >,< ''Lisa'' >}.

Since this is not the case, the overall formula is false.
</div>
</div>

* '''enjoy-watching-football-together'''('''alice''','''tom''')
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
<nowiki>[[</nowiki>'''enjoy-watching-football-togehter(alice,tom)''']] = ''true'' iff<br />
< I('''alice'''), I('''tom''') > ∈ I('''enjoy-watching-football-together''') iff<br />
< ''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.

</div>
</div>

= Meeting 2=

== Models ==

{{CreatedByStudents1213}} Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], [[User:IsaB|Isabelle]].

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

<embedvideo service="youtube" dimensions="400">http://youtu.be/4a3mXelw7H4</embedvideo>

Based on this podcast, we can define a scenario as follows:
* Universe: ''U'' = {''LittleRedRidingHood'', ''Grandmother'', ''Wolf''}<br />
* 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'''}<br>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:<br>
:: 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'' > }

= Meeting 1 =

== Video ==

Challenging phenomena at the syntax-semantics interface

<embedvideo service="youtube" dimensions="400">https://youtu.be/zaBC9dKXe5A</embedvideo>

== Scenario ==

The Hunger Games (film, 2012): [https://en.wikipedia.org/wiki/The_Hunger_Games_(film) https://en.wikipedia.org/wiki/The_Hunger_Games_(film)]

2025-10-14T20:17:26Z

Manfred: /* Scenario */

= Meeting 1 =

== Video ==

Challenging phenomena at the syntax-semantics interface

<embedvideo service="youtube" dimensions="400">https://youtu.be/zaBC9dKXe5A</embedvideo>

== Scenario ==

The Hunger Games (film, 2012): [https://en.wikipedia.org/wiki/The_Hunger_Games_(film) https://en.wikipedia.org/wiki/The_Hunger_Games_(film)]

2025-05-21T14:59:15Z

Manfred: /* Logical or */

= 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) =

== Logical ''or'' ==

The following short video (in German) gives some examples for the difference between the meaning of logical disjunction and the everyday use of the word ''or'' in natural language.

<embedvideo service="youtube" dimensions="400">https://youtu.be/t2-RwzjXSuc?si=nVqvGqcvgqTGQu_3</embedvideo>

(The video is from the youtube playlist ''VentriLinguist: Sprachwissenschaft mit Bauchgefuhl'')

== 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) &or; king(lady-macbeth)'''

<embedvideo service="youtube" dimensions="400">http://youtu.be/ABXPMzHFYxU</embedvideo>


== Interpretation of formulae with logical connectives ==
Consider these two natural language sentences. While keeping in mind the scenario given in [[ExerciseFOModels-d|a previous exercise]], create complex formulae with logical connectives and compute the interpretation, respectively.

Consider these two natural language sentences. While keeping in mind the scenario given in [[ExerciseFOModels-d|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
<div class="mw-collapsible-content">Sentence: Alice is a dog and Lisa and Tom enjoy watching football together.

Here the interpretation in predicate logic notation:

<nowiki>[[</nowiki>'''dog (Alice) Ʌ enjoy-watching-football-together (Lisa,Tom)''']] = ''false''<br/>

because <nowiki>[[</nowiki>'''dog (Alice)''']]= ''false'' <br/>

::because I('''Alice''')= <''Alice''> and <''Alice''> is NOT an element of I('''dog''') <br/>

and <nowiki>[[</nowiki>'''enjoy-watching-soccer-together (Lisa,Tom)''']] = ''true'' <br/>

::because I('''Lisa''')= <''Lisa''>, I('''Tom''')= <''Tom''> and <''Lisa,Tom''> '''is''' in the set of I('''enjoy-watching-football-together'''). <br/>

'''Conjunction (Ʌ)''': Both atomic formulae have to be true in order for the complex formula to be true.
</div>
</div>

'''b.)''' Tom is not Paul's daughter or Tom is tall.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
Sentence: Tom is not Paul's daughter or Tom is tall.

Here the interpretation in predicate logic notation:

<nowiki>[[</nowiki>'''¬daughter-of-someone (Tom,Paul) v tall(Tom)''']] = ''true'' <br/>

because <nowiki>[[</nowiki>'''¬daughter-of-someone (Tom,Paul)''']]= ''true'' <br/>

::because I('''Tom''')= <''Tom''>, I('''Paul''')= <''Paul''> and <''Tom,Paul''> is NOT in the set of I('''daughter-of-someone''') <br/>

and <nowiki>[[</nowiki>'''tall(Tom)''']] = ''false'' <br/>

::because I('''Tom''')= <''Tom''> and <''Tom''> is NOT an element of I('''tall'''). <br/>

'''Disjunction (v)''': At least one of the atomic formulae has to be true in order for the complex formula to be true.
</div>
</div>

= 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)'''

<embedvideo service="youtube" dimensions="400">http://youtu.be/8HGCB9urmbg</embedvideo>

== Syntax of atomic formulae ==

=== Exercise 1 ===
{{CreatedByStudents1213}}<br />''Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], and [[User:IsaB|Isabelle]].''

This exercise is based on the following scenario:
<blockquote>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.
</blockquote>

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.<br />''(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.)''

<quiz display="simple">
{ }
- '''family-dog'''
|| '''family-dog''' is just a predicate symbol. It cannot be interpreted as true or false, as its argument is missing. A possible formula would be: '''family-dog'''('''walter''')

{ }
- '''blonde'''('''alice''','''paul''')
|| It cannot be interpreted as true or false. As '''blonde''' is a property and not a relation it can therefore only have one individual as its argument. A possible formula would be: '''blonde'''('''alice''')

{ }
+ '''father-of'''('''alice''','''lisa)'''
|| '''father-of''' is a relation and therefore requires two individuals as its arguments. Of course, this formula is not true. Alice can never be a father of someone. However, although the interpretation of the formula is wrong, it is still a formula as it can be interpreted as true or false.

{ }
+ '''tall'''('''alice''')
|| As '''tall''' is a property it requires one individual in brackets. This is the case and it can therefore be interpreted as true or false.

{ }
- '''enjoy-watching-football-together'''
|| It cannot be interpreted as true or false. As “enjoy-watching-football-together" is a relation two individuals are required. A possible formula would be: '''enjoy-watching-football-together'''('''walter''','''alice''')
</quiz>

For a general explanation of formulae [[General_Explanation_Formulae|Click here]]
<hr />

=== Exercise 2 ===
For the following exercises we use names and properties from the ''The Lord of the Rings'' novels.

Names: '''frodo''', '''sam''', '''gandalf''', '''aragorn'''<br />
1-place predicates: '''hobbit''', '''wizard'''<br />
2-place predicates: '''know''', '''help'''

<quiz display="simple">
{Click on the items that are well-formed expressions of the semantic representation language.
}
+ '''gandalf'''
+ '''hobbit'''
- '''sauron'''
|| The name '''sauron''' is not included in the non-logical vocabulary.
- '''frodo''' &and; '''gandalf'''
|| The connectors "&and;" and "&or;" can only be used to combine two formulae.
- '''know'''('''gandalf''')
|| '''know''' is a 2-place predicate. Therefore it must combine with two arguments.
+ '''help'''('''aragorn''','''frodo''')

{Click on the expressions that are well-formed formulae.
}
- '''hobbit'''
- '''frodo'''
+ '''hobbit'''('''aragorn''')
+ '''hobbit'''('''frodo''') &and; '''wizard'''('''gandalf''')
- '''hobbit'''('''frodo''') ¬ '''wizard'''('''sam''')
|| "¬" combines with '''one''' formula only, not with two.
</quiz>

== 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 [[ExerciseFOModels-d|a previous exercise]].

* '''father-of-someone'''('''paul''','''lisa''')
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
<nowiki>[[</nowiki>'''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />
< <nowiki>[[</nowiki>'''paul''']], <nowiki>[[</nowiki>'''lisa''']] > ∈ <nowiki>[[</nowiki>'''father-of-someone''']] iff<br />
< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />
< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.

Since this is the case, the formula is true.
</div>
</div>

* '''blonde'''('''walter''')
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
<nowiki>[[</nowiki>'''blonde(walter)''']] = ''true'' iff<br />
< I('''walter''') > ∈ I('''blonde''') iff <br />
< ''Walter'' > ∈ {< ''Alice'' >,< ''Lisa'' >}.

Since this is not the case, the overall formula is false.
</div>
</div>

* '''enjoy-watching-football-together'''('''alice''','''tom''')
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
<nowiki>[[</nowiki>'''enjoy-watching-football-togehter(alice,tom)''']] = ''true'' iff<br />
< I('''alice'''), I('''tom''') > ∈ I('''enjoy-watching-football-together''') iff<br />
< ''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.

</div>
</div>

= Meeting 3 (7.5.2025) =

== Models ==

{{CreatedByStudents1213}} Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], [[User:IsaB|Isabelle]].

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

<embedvideo service="youtube" dimensions="400">http://youtu.be/4a3mXelw7H4</embedvideo>

Based on this podcast, we can define a scenario as follows:
* Universe: ''U'' = {''LittleRedRidingHood'', ''Grandmother'', ''Wolf''}<br />
* 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'''}<br>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:<br>
:: 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 ==

{{CreatedByStudents1213}}<br />''Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], and [[User:IsaB|Isabelle]].''

Take a look at the following story:

<blockquote>
'''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.
</blockquote>

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.<br />

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
These are the '''individuals''' of the story:<br/>
Alice<br/>
Paul<br/>
Lisa<br/>
Tom<br/>
Walter<br/>

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''<br />
''I''('''paul''') = ''Paul''<br />
''I''('''lisa''') = ''Lisa''<br />
''I''('''tom''') = ''Tom''<br />
''I''('''walter''') = ''Walter''<br />
</div>
</div>

'''(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!<br />
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
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} = {}''
</div>
</div>

'''(c)''' Write down the possible relations mentioned in the story and map them to the individuals you wrote down in (a).<br />
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
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>''}

</div>
</div>

'''(d)''' Write down the I-functions (interpretation functions) for (a), (b) and (c).<br />'''[[ExerciseFOModels-d|Check your answers]]'''

{{FeedbackExercises}}

= Meeting 1 =

== Video ==

Challenging phenomena at the syntax-semantics interface

<embedvideo service="youtube" dimensions="400">https://youtu.be/zaBC9dKXe5A</embedvideo>

== Scenario ==

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

SoSe25: Semantics 1

2025-05-21T14:58:55Z

Manfred: /* Logical or */

= 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) =

== Logical ''or'' ==

The following short video (in German) gives some examples for the difference between the meaning of logical disjunction and the everyday use of the word ''or'' in natural language.

<embedvideo service="youtube" dimensions="400">https://youtu.be/t2-RwzjXSuc?si=nVqvGqcvgqTGQu_3/embedvideo>

(The video is from the youtube playlist ''VentriLinguist: Sprachwissenschaft mit Bauchgefuhl'')

== 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) &or; king(lady-macbeth)'''

<embedvideo service="youtube" dimensions="400">http://youtu.be/ABXPMzHFYxU</embedvideo>


== Interpretation of formulae with logical connectives ==
Consider these two natural language sentences. While keeping in mind the scenario given in [[ExerciseFOModels-d|a previous exercise]], create complex formulae with logical connectives and compute the interpretation, respectively.

Consider these two natural language sentences. While keeping in mind the scenario given in [[ExerciseFOModels-d|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
<div class="mw-collapsible-content">Sentence: Alice is a dog and Lisa and Tom enjoy watching football together.

Here the interpretation in predicate logic notation:

<nowiki>[[</nowiki>'''dog (Alice) Ʌ enjoy-watching-football-together (Lisa,Tom)''']] = ''false''<br/>

because <nowiki>[[</nowiki>'''dog (Alice)''']]= ''false'' <br/>

::because I('''Alice''')= <''Alice''> and <''Alice''> is NOT an element of I('''dog''') <br/>

and <nowiki>[[</nowiki>'''enjoy-watching-soccer-together (Lisa,Tom)''']] = ''true'' <br/>

::because I('''Lisa''')= <''Lisa''>, I('''Tom''')= <''Tom''> and <''Lisa,Tom''> '''is''' in the set of I('''enjoy-watching-football-together'''). <br/>

'''Conjunction (Ʌ)''': Both atomic formulae have to be true in order for the complex formula to be true.
</div>
</div>

'''b.)''' Tom is not Paul's daughter or Tom is tall.

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
Sentence: Tom is not Paul's daughter or Tom is tall.

Here the interpretation in predicate logic notation:

<nowiki>[[</nowiki>'''¬daughter-of-someone (Tom,Paul) v tall(Tom)''']] = ''true'' <br/>

because <nowiki>[[</nowiki>'''¬daughter-of-someone (Tom,Paul)''']]= ''true'' <br/>

::because I('''Tom''')= <''Tom''>, I('''Paul''')= <''Paul''> and <''Tom,Paul''> is NOT in the set of I('''daughter-of-someone''') <br/>

and <nowiki>[[</nowiki>'''tall(Tom)''']] = ''false'' <br/>

::because I('''Tom''')= <''Tom''> and <''Tom''> is NOT an element of I('''tall'''). <br/>

'''Disjunction (v)''': At least one of the atomic formulae has to be true in order for the complex formula to be true.
</div>
</div>

= 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)'''

<embedvideo service="youtube" dimensions="400">http://youtu.be/8HGCB9urmbg</embedvideo>

== Syntax of atomic formulae ==

=== Exercise 1 ===
{{CreatedByStudents1213}}<br />''Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], and [[User:IsaB|Isabelle]].''

This exercise is based on the following scenario:
<blockquote>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.
</blockquote>

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.<br />''(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.)''

<quiz display="simple">
{ }
- '''family-dog'''
|| '''family-dog''' is just a predicate symbol. It cannot be interpreted as true or false, as its argument is missing. A possible formula would be: '''family-dog'''('''walter''')

{ }
- '''blonde'''('''alice''','''paul''')
|| It cannot be interpreted as true or false. As '''blonde''' is a property and not a relation it can therefore only have one individual as its argument. A possible formula would be: '''blonde'''('''alice''')

{ }
+ '''father-of'''('''alice''','''lisa)'''
|| '''father-of''' is a relation and therefore requires two individuals as its arguments. Of course, this formula is not true. Alice can never be a father of someone. However, although the interpretation of the formula is wrong, it is still a formula as it can be interpreted as true or false.

{ }
+ '''tall'''('''alice''')
|| As '''tall''' is a property it requires one individual in brackets. This is the case and it can therefore be interpreted as true or false.

{ }
- '''enjoy-watching-football-together'''
|| It cannot be interpreted as true or false. As “enjoy-watching-football-together" is a relation two individuals are required. A possible formula would be: '''enjoy-watching-football-together'''('''walter''','''alice''')
</quiz>

For a general explanation of formulae [[General_Explanation_Formulae|Click here]]
<hr />

=== Exercise 2 ===
For the following exercises we use names and properties from the ''The Lord of the Rings'' novels.

Names: '''frodo''', '''sam''', '''gandalf''', '''aragorn'''<br />
1-place predicates: '''hobbit''', '''wizard'''<br />
2-place predicates: '''know''', '''help'''

<quiz display="simple">
{Click on the items that are well-formed expressions of the semantic representation language.
}
+ '''gandalf'''
+ '''hobbit'''
- '''sauron'''
|| The name '''sauron''' is not included in the non-logical vocabulary.
- '''frodo''' &and; '''gandalf'''
|| The connectors "&and;" and "&or;" can only be used to combine two formulae.
- '''know'''('''gandalf''')
|| '''know''' is a 2-place predicate. Therefore it must combine with two arguments.
+ '''help'''('''aragorn''','''frodo''')

{Click on the expressions that are well-formed formulae.
}
- '''hobbit'''
- '''frodo'''
+ '''hobbit'''('''aragorn''')
+ '''hobbit'''('''frodo''') &and; '''wizard'''('''gandalf''')
- '''hobbit'''('''frodo''') ¬ '''wizard'''('''sam''')
|| "¬" combines with '''one''' formula only, not with two.
</quiz>

== 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 [[ExerciseFOModels-d|a previous exercise]].

* '''father-of-someone'''('''paul''','''lisa''')
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
<nowiki>[[</nowiki>'''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />
< <nowiki>[[</nowiki>'''paul''']], <nowiki>[[</nowiki>'''lisa''']] > ∈ <nowiki>[[</nowiki>'''father-of-someone''']] iff<br />
< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />
< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.

Since this is the case, the formula is true.
</div>
</div>

* '''blonde'''('''walter''')
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
<nowiki>[[</nowiki>'''blonde(walter)''']] = ''true'' iff<br />
< I('''walter''') > ∈ I('''blonde''') iff <br />
< ''Walter'' > ∈ {< ''Alice'' >,< ''Lisa'' >}.

Since this is not the case, the overall formula is false.
</div>
</div>

* '''enjoy-watching-football-together'''('''alice''','''tom''')
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
Check your answers
<div class="mw-collapsible-content">
<nowiki>[[</nowiki>'''enjoy-watching-football-togehter(alice,tom)''']] = ''true'' iff<br />
< I('''alice'''), I('''tom''') > ∈ I('''enjoy-watching-football-together''') iff<br />
< ''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.

</div>
</div>

= Meeting 3 (7.5.2025) =

== Models ==

{{CreatedByStudents1213}} Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], [[User:IsaB|Isabelle]].

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

<embedvideo service="youtube" dimensions="400">http://youtu.be/4a3mXelw7H4</embedvideo>

Based on this podcast, we can define a scenario as follows:
* Universe: ''U'' = {''LittleRedRidingHood'', ''Grandmother'', ''Wolf''}<br />
* 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'''}<br>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:<br>
:: 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 ==

{{CreatedByStudents1213}}<br />''Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], and [[User:IsaB|Isabelle]].''

Take a look at the following story:

<blockquote>
'''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.
</blockquote>

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.<br />

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These are the '''individuals''' of the story:<br/>
Alice<br/>
Paul<br/>
Lisa<br/>
Tom<br/>
Walter<br/>

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''<br />
''I''('''paul''') = ''Paul''<br />
''I''('''lisa''') = ''Lisa''<br />
''I''('''tom''') = ''Tom''<br />
''I''('''walter''') = ''Walter''<br />
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'''(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!<br />
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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} = {}''
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'''(c)''' Write down the possible relations mentioned in the story and map them to the individuals you wrote down in (a).<br />
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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>''}

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'''(d)''' Write down the I-functions (interpretation functions) for (a), (b) and (c).<br />'''[[ExerciseFOModels-d|Check your answers]]'''

{{FeedbackExercises}}

= Meeting 1 =

== Video ==

Challenging phenomena at the syntax-semantics interface

<embedvideo service="youtube" dimensions="400">https://youtu.be/zaBC9dKXe5A</embedvideo>

== Scenario ==

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