 In circumscription, given predicates P and Q, we abbreviate \(\forall x(Px \supset Qx)\) as \(P \le Q\); similarly, we abbreviate \(P \le Q \wedge \neg(Q \le P)\) as \(P &lt; Q\). If \(A(P)\) is a formula containing occurrences of a predicate P, then the circumscription of P in A is the second-order sentence \(A^{\star}(P)\): 