Exercise-ch2: Difference between revisions

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= Additional Exercises for Chapter 2: Predicate Logic =
= Additional Exercises for Chapter 2: Predicate Logic =
== First order models ==
Follow the [[Exercis_First_Order_Models|link]].


== The syntax of predicate logic ==
== The syntax of predicate logic ==
Line 5: Line 9:
Follow the [[Exercise_Syntax_of_Predicate_Logic|link]] to get to a set of exercises on the syntax of predicate logic.
Follow the [[Exercise_Syntax_of_Predicate_Logic|link]] to get to a set of exercises on the syntax of predicate logic.


<!-- &forall; &exist; &and; &or; &sub; &sup; &not; -->
== The semantics of predicate logic ==
 
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'''
 
=== Formulae without variables ===
 
<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''') &not; '''wizard'''('''sam''')
|| "&not;" combines with '''one''' formula only, not with two.
</quiz>
 
=== Formulae with variables ===
 
<quiz display="simple">
{Click on the items that are well-formed expressions of the semantic representation language.
}
+ ''y''
- ''x'' &and; '''frodo'''
- &exist;''x''
|| A quantifier, "&forall;" or "&exist;", can only be used with a variable and a formula. For example: &exist;''x''('''hobbit'''(''x''))
 
 
{Click on the expressions that are well-formed formulae.
}
+ &forall;''x'' ('''hobbit'''(''x'') &sup; x = '''gandalf''')
+ &exist;''y''('''hobbit'''(''x'') &or; '''wizard'''(''gandalf''))
|| Note: The variable bound by the quantifier, ''y'', need not occur in the scope of the quantifier.


</quiz>
Follow the [[Exercise_Semantics_of_Predicate_Logic|link]]


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Revision as of 10:00, 5 April 2013

Additional Exercises for Chapter 2: Predicate Logic

First order models

Follow the link.

The syntax of predicate logic

Follow the link to get to a set of exercises on the syntax of predicate logic.

The semantics of predicate logic

Follow the link

Back to

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