In logic and model theory, a valuation can be: In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema.
In this context, a valuation begins with an assignment of a truth value to each propositional variable.
A structure consists of a set (domain of discourse) that determines the range of the quantifiers, along with interpretations of the constant, function, and relation symbols in the language.
Corresponding to each structure is a unique truth assignment for all sentences (formulas with no free variables) in the language.
, then the double-bracket notation is commonly used to denote a valuation; that is,