In: Computer Science
Everyone who is nice to all dogs is loved by somebody.
∀x (∀y dog(y) ⇒ Kind(x,y)) ⇒ (∃y Loves(y,x))
Demonstrate how to convert it to CNF.
You should get:
( dog(F(x)) v (Loves(G(x),x)) ^ (~nice(x,F(x)) v Loves(G(x),x))
Step 1: Remove the biconditionals and implications.
Step 2: Move the negations inward.
Step 3: Standardize variables
Step 4: Skolemize
Step 5: Drop universal quantifiers
Step 6: Distribute v over ^