Exercise Syntax of Predicate Logic: Difference between revisions

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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. To check your answers click on single expressions.
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">
<quiz display="simple">
{Is the following a well-formed formula?}
{ }
- '''family-dog'''
- '''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''')
|| '''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''')
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|| 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''')
|| 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''')


{Is the following a well-formed formula?}
{ }
+ '''father-of'''('''alice''','''lisa)'''
+ '''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.  
|| '''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.  


{Is the following a well-formed formula?}
{ }
+ '''tall'''('''alice''')
+ '''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.  
|| 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.  


{Is the following a well-formed formula?}
{ }
- '''enjoy-watching-football-together'''
- '''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''')
|| 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''')

Latest revision as of 15:49, 5 May 2013

Formulae without variables

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

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)

Formulae with variables

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.

y
x ∧ frodo
∃x

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

∀x (hobbit(x) ⊃ x = gandalf)
∃y(hobbit(x) ∨ wizard(gandalf))


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