|
|
| (6 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| = Additional Exercises for Chapter 2: Predicate Logic = | | = Additional Exercises for Chapter 2: Predicate Logic = |
|
| |
|
| == The syntax of predicate logic == | | == First order models == |
|
| |
|
| <!-- ∀ ∃ ∧ ∨ ⊂ ⊃ ¬ -->
| | Follow the [[Exercise_First_Order_Models|link]]. |
|
| |
|
| For the following exercises we use names and properties from the ''The Lord of the Rings'' novels.
| | == The syntax of predicate logic == |
| | |
| 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''' ∧ '''gandalf'''
| |
| || The connectors "∧" and "∨" 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''')
| |
|
| |
|
| | Follow the [[Exercise_Syntax_of_Predicate_Logic|link]] to get to a set of exercises on the syntax of predicate logic. |
|
| |
|
| {Click on the expressions that are well-formed formulae.
| | == The semantics of predicate logic == |
| }
| |
| - '''hobbit'''
| |
| - '''frodo'''
| |
| + '''hobbit'''('''aragorn''')
| |
| + '''hobbit'''('''frodo''') ∧ '''wizard'''('''gandalf''')
| |
| - '''hobbit'''('''frodo''') ¬ '''wizard'''('''sam''')
| |
| || "¬" combines with '''one''' formula only, not with two.
| |
| </quiz>
| |
|
| |
|
| === Formulae with variables ===
| | Follow the [[Exercise_Semantics_of_Predicate_Logic|link]] |
|
| |
|
| <quiz display="simple">
| | Go to exercises for [[Exercise_Truth_Tables|truth tables]]. |
| {Click on the items that are well-formed expressions of the semantic representation language.
| |
| }
| |
| + ''y''
| |
| - ''x'' ∧ '''frodo'''
| |
| - ∃''x''
| |
| || A quantifier, "∀" or "∃", can only be used with a variable and a formula. For example: ∃''x''('''hobbit'''(''x''))
| |
|
| |
|
| | == Summarizing exercise sheet for Chapter 2 == |
|
| |
|
| {Click on the expressions that are well-formed formulae.
| | The [[Assignmentsheet Logic Summer Term 2013|exercise sheet]] was used in the class ''Introduction to Semantics'', Goethe University Frankfurt, summer term 2013. |
| }
| |
| + ∀''x'' ('''hobbit'''(''x'') ⊃ x = '''gandalf''')
| |
| + ∃''y''('''hobbit'''(''x'') ∨ '''wizard'''(''gandalf''))
| |
| || Note: The variable bound by the quantifier, ''y'', need not occur in the scope of the quantifier.
| |
|
| |
|
| </quiz> | | <hr /> |
| | Back to |
| | * the material for [[Textbook-chapters#Chapter_2:_Predicate_logic|chapter 2]] |
| | * the overview over [[Textbook-chapters|all chapters]] |
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
Go to exercises for truth tables.
Summarizing exercise sheet for Chapter 2
The exercise sheet was used in the class Introduction to Semantics, Goethe University Frankfurt, summer term 2013.
Back to