Motivated by applications to relational databases, N. Alechina proposed in 2000 a many-sorted first-order logic with specialized models (called fd-models), where an ordinary first-order structure was equipped with a system of functions realizing functional dependences between variables (interpreted as attributes). Due to these constraints, only a restricted set of assignments is available in such a model. This factor may rouse some undesirable effects when formulas of the language are evaluated. We develop for the relevant first-order languages another, assignment-free algebraic semantics based on improved fd-models.