3 Mar 2004
CS3243 - Inference
40
Conversion to CNF
lEveryone who loves all animals is loved by someone:
¡"x ["y Animal(y) Þ Loves(x,y)] Þ [$y Loves(y,x)]
Ÿ
l1. Eliminate biconditionals and implications
¡"x [Ø"y ØAnimal(y) Ú Loves(x,y)] Ú [$y Loves(y,x)]
Ÿ
l2. Move Ø inwards: Ø"x p ≡ $x Øp,  Ø $x p ≡ "x Øp
¡"x [$y Ø(ØAnimal(y) Ú Loves(x,y))] Ú [$y Loves(y,x)]
¡"x [$y ØØAnimal(y) Ù ØLoves(x,y)] Ú [$y Loves(y,x)]
¡"x [$y Animal(y) Ù ØLoves(x,y)] Ú [$y Loves(y,x)]