Exercise Syntax of Predicate Logic - Revision history

Manfred: /* Exercise 1 */

2013-05-05T15:49:40Z

Exercise 1

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	</blockquote>		</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 on '''submit''', you will see a suggestion for the second part of the question.)''		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">

Manfred: /* Exercise 1 */

2013-05-05T15:49:19Z

Exercise 1

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	</blockquote>		</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.		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 on '''submit''', you will see a suggestion for the second part of the question.)''
	(Click on the box if the expressionis a formula. When you press on ''submit'', you will see a suggestion for the second part of the question.)

	<quiz display="simple">		<quiz display="simple">

Manfred: /* Exercise 1 */

2013-05-05T15:48:30Z

Exercise 1

← Older revision		Revision as of 15:48, 5 May 2013
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	</blockquote>		</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. ~~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.
			(Click on the box if the expressionis a formula. When you press on ''submit'', 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''')

	{		{ }
	- '''blonde'''('''alice''','''paul''')		- '''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''')		\|\| 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''')

Manfred: /* Exercise 1 */

2013-05-05T15:45:33Z

Exercise 1

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	\|\| '''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''')

	{ }		{
	- '''blonde'''('''alice''','''paul''')		- '''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''')		\|\| 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''')

Manfred: /* Exercise 1 */

2013-05-05T15:45:21Z

Exercise 1

← Older revision		Revision as of 15:45, 5 May 2013
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	\|\| '''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''')

	{}		{ }
	- '''blonde'''('''alice''','''paul''')		- '''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''')		\|\| 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''')

Manfred: /* Exercise 1 */

2013-05-05T15:44:17Z

Exercise 1

← Older revision		Revision as of 15:44, 5 May 2013
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	\|\| '''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''')

	{~~Is the following a well-formed formula?~~}		{}
	- '''blonde'''('''alice''','''paul''')		- '''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''')		\|\| 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''')

Manfred at 15:17, 5 May 2013

2013-05-05T15:17:21Z

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	<!-- ∀ ∃ &and; &or; ⊂ ⊃ ¬ -->		<!-- ∀ ∃ &and; &or; ⊂ ⊃ ¬ -->
	=== Formulae without variables ===		== Formulae without variables ==


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

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	<hr />		<hr />

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

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	<hr />		<hr />

	=== Formulae with variables ===		== Formulae with variables ==


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

Manfred: /* Formulae without variables */

2013-05-05T15:16:15Z

Formulae without variables

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 === Formulae without variables ===
 {{CreatedByStudents1213}}<br />''Involved participants: [[User:Lisa| Lisa]], [[User:Marthe| Marthe]], [[User:Elisabeth.krall| Elisabeth]], and [[User:IsaB|Isabelle]].''
@@ Line 64: / Line 34: @@
 For a general explanation of formulae [[General_Explanation_Formulae|Click here]]
 <hr />

Manfred: /* Formulae without variables */

2013-05-05T15:14:54Z

Formulae without variables

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	{Is the following a well-formed formula?}		{Is the following a well-formed formula?}
	+ '''father-of~~-someone~~'''('''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.

	{Is the following a well-formed formula?}		{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.

	{Is the following a well-formed formula?}		{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''')
	</quiz>		</quiz>

Manfred at 15:11, 5 May 2013

2013-05-05T15:11:53Z

← Older revision		Revision as of 15:11, 5 May 2013
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	<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''')

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

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

	{}		{Is the following a well-formed formula?}
	- '''enjoy-watching-football-together'''		- '''enjoy-watching-football-together'''
	</quiz>		</quiz>