Exercise Semantics of Predicate Logic: Difference between revisions

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'''father-of-someone'''('''paul''','''lisa''') = ''true'' iff<br />
< I('''paul'''), I('''lisa''') > &isin; I('''father-of-someone''') iff<br />
< ''Paul'', ''Lisa''> &isin; {<''Paul, Tom''>,<''Paul, Lisa''>}.
 
Since this is the case, the formula is true.
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'''blonde(walter)''' = ''true'' iff<br />
< I('''walter''') > &isin; I('''blonde''') iff <br />
< ''Walter'' > &isin; {< ''Alice'' >,< ''Lisa'' >}.
 
Since this is not the case, the overall formula is false.
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'''enjoy-watching-football-togehter(alice,tom)''' = ''true'' iff<br />
< I('''alice'''), I('''tom''') > &isin; I('''enjoy-watching-football-together''') iff<br />
< ''Alice'', ''Tom'' > &isin; {<''Alice, Paul''>,<''Paul, Alice''>,<''Alice, Lisa''>,<''Lisa, Alice''>,<''Alice, Tom''>,<''Tom, Alice''>,<''Paul, Lisa''>,<''Lisa, Paul''>,<''Paul, Tom''>,<''Tom, Paul''>,<''Tom, Lisa''>,<''Lisa, Tom''>}
 
Since this is the case, the formula is true.
 
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Revision as of 21:02, 6 January 2014

Interpretation of atomic formulae

Interpret the following formulae as true or false. If you have not defined these relations or properties in your model use the ones given in a previous exercise.

  • father-of-someone(paul,Lisa)

Check your answers

father-of-someone(paul,lisa) = true iff
< I(paul), I(lisa) > ∈ I(father-of-someone) iff
< Paul, Lisa> ∈ {<Paul, Tom>,<Paul, Lisa>}.

Since this is the case, the formula is true.


  • blonde(walter)

Check your answers

blonde(walter) = true iff
< I(walter) > ∈ I(blonde) iff
< Walter > ∈ {< Alice >,< Lisa >}.

Since this is not the case, the overall formula is false.


  • enjoy-watching-football-together(alice,tom)

Check your answers

enjoy-watching-football-togehter(alice,tom) = true iff
< I(alice), I(tom) > ∈ I(enjoy-watching-football-together) iff
< Alice, Tom > ∈ {<Alice, Paul>,<Paul, Alice>,<Alice, Lisa>,<Lisa, Alice>,<Alice, Tom>,<Tom, Alice>,<Paul, Lisa>,<Lisa, Paul>,<Paul, Tom>,<Tom, Paul>,<Tom, Lisa>,<Lisa, Tom>}

Since this is the case, the formula is true.



Interpretation of formulae with logical connectives

Consider these two natural language sentences. While keeping in mind the scenario given in a previous exercise, create complex formulae with logical connectives and compute the interpretation, respectively.


a.) Alice is a dog and Lisa and Tom enjoy watching football together.

Check your solution


b.) Tom is not Paul's daughter or Tom is tall.

Check your solution



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