judgment (mathematical logic)

In mathematical logic, a judgment can be an assertion about occurrence of a free variable in an expression of the object language, or about provability of a proposition (either as a tautology or from a given context), but judgments can be also other inductively definable assertions in the metatheory. Judgments are used for example in formalizing deduction systems: a logical axiom expresses a judgment, premises of a rule of inference are formed as a sequence of judgments, and their conclusion is a judgment as well. Also the result of a proof expresses a judgment, and the used hypotheses are formed as a sequence of judgments.