difference between first order and second order logic
Second-order logic First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence   ∀ P ∀ x ( x ∈ P ∨ x ∉ P )  {\displaystyle \forall P\,\forall x(x\in P\lor x\notin P)}  says that for every unary relation (or set) P of individuals, and every individual x, either x is in P or it is not (this is the principle of bivalence). Second-order logic also includes quantification over sets, functions, and other variables as explained in the section Syntax and fragments. Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.
German sentence structure German sentence structure is somewhat more complex than that of many other European languages, but similar to Dutch, with phrases regularly inverted for both questions and subordinate phrases. The main sentence structure rule is that the conjugated verb is the second element in a main clause or the last in a subordinate clause. Verbs in the infinitive are generally placed after their respective objects.