 According to this approach, one can use a \(\lambda\) to treat essentially any formula, even complex ones, as if they were atomic. We see the principle of \(\beta\)-reduction in the deductive and semantic parts. That this approach adheres to the relational reading of \(\lambda\) terms can be seen clearly in the semantics: according to the standard Tarski-style semantics for first-order logic, the interpretation of a formula (possibly with free variables) denotes a set of tuples of elements of the structure, as we vary the variable assignment that assigns elements of the structure to the variables.