since if formulas are satisfied by teams and formulas of classical logics are satisfied by assignments, there is no obvious intertranslation between if formulas and formulas of some classical logic system. however, there is a translation procedure of if formulas into "sentences" of "relational" formula_368 (actually, one distinct translation formula_401 for each finite formula_159 and for each choice of a predicate symbol formula_251 of arity formula_404). in this kind of translation, an extra n-ary predicate symbol formula_251 is used to represent an n-variable team formula_150. this is motivated by the fact that, once an ordering formula_407 of the variables of formula_151 has been fixed, it is possible to associate a relation formula_409 to the team formula_150. with this conventions, an if formula is related to its translation thus: