Universal instantiation (UI) Every instantiation of a universally quantified sentence is entailed by it: Vu a SUBST({v/g},a) for any variable v and ground term g Eg,Vx King(x)AGreedy(x）→Evil(x)yields King(John)A Greedy(John)Evil(John) King(Richard)A Greedy(Richard)Evil(Richard) King(Father(John))A Greedy(Father(John))Evil(Father(John)) Chapter 9 4 Universal instantiation (UI) Every instantiation of a universally quantified sentence is entailed by it: ∀ v α Subst({v/g}, α) for any variable v and ground term g E.g., ∀ x King(x) ∧ Greedy(x) ⇒ Evil(x) yields King(John) ∧ Greedy(John) ⇒ Evil(John) King(Richard) ∧ Greedy(Richard) ⇒ Evil(Richard) King(Father(John)) ∧ Greedy(Father(John)) ⇒ Evil(Father(John)) . . . Chapter 9 4