Valuation

A function (often called a valuation or truth assignment) that maps propositional variables or atomic formulas to truth values in a given semantic setting and extends to complex formulas according to the logic's semantic clauses.

A function v from a field or a ring to a totally ordered abelian group (often R∪{∞} or Z∪{∞}) that measures size or divisibility, is multiplicative (v(xy)=v(x)+v(y) in additive notation) and satisfies a triangle-like inequality v(x+y) ≥ min(v(x),v(y)) in the non-archimedean case.