Beispiel für die Transformation einer Formel in Klauselform
Transformiere die folgende Formel in Klauselform: $$ (\neg( \neg ((a \land b) \lor c) \lor (b \lor c) ) \land \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) ) $$
$$ \langle $$ | $$ (\neg( \neg ((a \land b) \lor c) \lor (b \lor c) ) \land \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) ) $$ | $$ \rangle $$ | (2) | ||||||||||||
$$ \langle [ $$ | $$ \neg( \neg ((a \land b) \lor c) \lor (b \lor c) $$ | $$ ] , [ $$ | $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ | $$ ] \rangle $$ | (5) | ||||||||||
$$ \langle [ $$ | $$ \neg\neg ((a \land b) \lor c) $$ | $$ ] , [ $$ | $$ \neg (b \lor c) $$ | $$ ] , [ $$ | $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ | $$ ] \rangle $$ | (1) | ||||||||
$$ \langle [ $$ | $$ ((a \land b) \lor c) $$ | $$ ] , [ $$ | $$ \neg (b \lor c) $$ | $$ ] , [ $$ | $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ | $$ ] \rangle $$ | (4) | ||||||||
$$ \langle [ $$ | $$ (a \land b) $$ | $$ , $$ | $$ c~~ $$ | $$ ] , [ $$ | $$ \neg (b \lor c) $$ | $$ ] , [ $$ | $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ | $$ ] \rangle $$ | (2) | ||||||
$$ \langle $$ | $$ [~~a , c~~] $$ | $$ , $$ | $$ [~~b , c~~] $$ | $$ , [ $$ | $$ \neg (b \lor c) $$ | $$ ] , [ $$ | $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ | $$ ] \rangle $$ | (5) | ||||||
$$ \langle $$ | $$ [~~a , c~~] $$ | $$ , $$ | $$ [~~b , c~~] $$ | $$ , $$ | $$ [~~ \neg b~~] $$ | $$ , $$ | $$ [~~\neg c~~] $$ | $$ , [ $$ | $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ | $$ ] \rangle $$ | (3) | ||||
$$ \langle $$ | $$ [~~a , c~~] $$ | $$ , $$ | $$ [~~b , c~~] $$ | $$ , $$ | $$ [~~ \neg b~~] $$ | $$ , $$ | $$ [~~\neg c~~] $$ | $$ , [ $$ | $$ \neg ( a \land b ) $$ | $$ , $$ | $$ \neg ((d \lor c) \lor d) $$ | $$ ] \rangle $$ | (3) | ||
$$ \langle $$ | $$ [~~a , c~~] $$ | $$ , $$ | $$ [~~b , c~~] $$ | $$ , $$ | $$ [~~ \neg b~~] $$ | $$ , $$ | $$ [~~\neg c~~] $$ | $$ , [ $$ | $$ \neg a , \neg b $$ | $$ , $$ | $$ \neg ((d \lor c) \lor d) $$ | $$ ] \rangle $$ | (5) | ||
$$ \langle $$ | $$ [~~a , c~~] $$ | $$ , $$ | $$ [~~b , c~~] $$ | $$ , $$ | $$ [~~ \neg b~~] $$ | $$ , $$ | $$ [~~\neg c~~] $$ | $$ , [ $$ | $$ \neg a, \neg b , $$ | $$ \neg (d \lor c) $$ | $$ ] , [ $$ | $$ \neg a, \neg b, \neg d $$ | $$ ] \rangle $$ | (5) | |
$$ \langle $$ | $$ [~~a , c~~] $$ | $$ , $$ | $$ [~~b , c~~] $$ | $$ , $$ | $$ [~~ \neg b~~] $$ | $$ , $$ | $$ [~~\neg c~~] $$ | $$ , $$ | $$ [ \neg a, \neg b , \neg d ] $$ | $$ , $$ | $$ [ \neg a, \neg b , \neg c ] $$ | $$ , $$ | $$ [ \neg a, \neg b , \neg d ] $$ | $$ \rangle $$ | (Idempotenz) |
$$ \langle $$ | $$ [~~a , c~~] $$ | $$ , $$ | $$ [~~b , c~~] $$ | $$ , $$ | $$ [~~ \neg b~~] $$ | $$ , $$ | $$ [~~\neg c~~] $$ | $$ , $$ | $$ [ \neg a, \neg b , \neg d ] $$ | $$ , $$ | $$ [ \neg a, \neg b , \neg c ] $$ | $$ \rangle $$ |
Beispiel für die Transformation einer Formel in Klauselform. Pro Schritt werden die jeweils betrachteten Teilformeln gelb hinterlegt.
Das Umformungsresultat ist grün hinterlegt.