Exercise-ch2: Difference between revisions
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1-place predicates: '''hobbit''', '''wizard'''<br /> | 1-place predicates: '''hobbit''', '''wizard'''<br /> | ||
2-place predicates: '''know''', '''help''' | 2-place predicates: '''know''', '''help''' | ||
=== Formulae without variables === | |||
<quiz display="simple"> | <quiz display="simple"> | ||
| Line 32: | Line 34: | ||
- '''frodo''' | - '''frodo''' | ||
+ '''hobbit'''('''aragorn''') | + '''hobbit'''('''aragorn''') | ||
+ ∀''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> | |||
=== Formulae with variables === | |||
<quiz display="simple"> | |||
{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'')) | |||
{Click on the expressions that are well-formed formulae. | |||
} | |||
+ ∀''x'' ('''hobbit'''(''x'') ⊃ x = '''gandalf''') | + ∀''x'' ('''hobbit'''(''x'') ⊃ x = '''gandalf''') | ||
+ ∃''y''('''hobbit'''(''x'') ∨ '''wizard'''(''gandalf'')) | + ∃''y''('''hobbit'''(''x'') ∨ '''wizard'''(''gandalf'')) | ||
Revision as of 20:53, 15 March 2013
Additional Exercises for Chapter 2: Predicate Logic
The syntax 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
1-place predicates: hobbit, wizard
2-place predicates: know, help
Formulae without variables
Formulae with variables