 In classical logic and in positive free logic any substitution instance of a valid formula (or form of inference) is itself a valid formula (or form of inference). But in negative or neutral free logic this is not the case. A substitution instance is the result of replacing primitive non-logical symbols by possibly more complex ones of the same semantic type—\(n\)-place predicates with open formulas in \(n\) variables, and individual constants with singular terms—each occurrence of the same primitive symbol being replaced by the same possibly complex symbol. The replacement of an occurrence of a primitive \(n\)-place predicate \(P\) in some formula \(B\) by an open formula \(A\) with free variables \(x_1 ,\ldots ,x_n\) is performed as follows: where \(t_1 ,\ldots ,t_n\) are the individual constants or variables immediately following \(P\) in that occurrence, replace P\(t_1 \ldots t_n\) in \(B\) by \(A(t_i /x_i)\)—the result of replacing \(x_i\) by \(t_i\) in \(A\), for each \(i\), \(1\le i\le n\).