 When defining semantic notions such as joint satisfiability or logical consequence, contemporary logicians generally work with formal languages, the specification of which involves a separation of logical and non-logical elements. Consequence and other semantic relations are then defined in terms of the behaviour of formulas when arbitrary semantic values of the appropriate kinds are assigned to all of the non-logical parameters (usually including a tacit parameter for the domain of quantification). On this view, consequence is a dyadic relation between a set of premises and a conclusion or set of conclusions.