 A consequence relation is a mathematical relation that models what follows logically from what. Consequence relations can be defined in a variety of ways, such as Hilbert, Tarski, and Scott relations. A Hilbert consequence relation is a relation between pairs of formulas, a Tarski relation is a relation between sets of formulas (possibly infinite) and individual formulas, and a Scott relation is a relation between two sets of formulas. In the case of Hilbert and Tarski relations, \(A \vDash B\) or \(\Gamma \vDash B\) mean that the formula \(B\) follows from formula \(A\) or from set of formulas \(\Gamma\). In the case of Scott consequence relations, \(\Gamma \vDash \Delta\) means that the joint truth of all the members of \(\Gamma\) implies (in some sense) the truth of at least one member of \(\Delta\). To this point, studies of nonmonotonic logic have defined nonmonotonic consequence relations in the style of Hilbert or Tarski, rather than Scott.