Full Idea
A valuation function in predicate logic will assign truth values to formulas relative to variable assignments.
Gist of Idea
Valuations in PC assign truth values to formulas relative to variable assignments
Source
Theodore Sider (Logic for Philosophy [2010], 4.2)
Book Reference
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.94
A Reaction
Sider observes that this is a 'double' relativisation (due to Tarski), since propositional logic truth was already relative to an interpretation. Now we are relative to variable assignments as well.