As just above this we have said that the rules of inference for propositional logic detailed in the last lecture can also be required in first-order logic. Moreover we just need to clarify that a little. After one important difference between propositional and first-order logic in which the latter has predicates into terms as arguments. However one clarification we need to make such we can apply the inference rules as long as the predicates so the arguments match up. Thus after not only do we have to check for the correct kinds of sentence ahead of we can carry out a rule of inference so we also have to check that the arguments do not forbid the inference.
Here if notice for instance, as suppose in our knowledge base if we have these two statement as;
knows(john,X)→ hates(john, X)
As there is shown and we want to use the Modus Ponens rule to infer something new. Here if notice for instance in this case there is no problem so we can infer that it means john hates everyone he knows, and he knows Mary, so then he must hate Mary that is ,, we can infer that hates to john, mary is true.