Modal definability of first-order formulas with free variables and query answering

We present an algorithmically efficient criterion of modal definability for first-order existential conjunctive formulas with several free variables. Then we apply it to establish modal definability of some family of first-order ∀∃-formulas. Finally, we use our definability results to show that, in any expressive description logic, the problem of answering modally definable conjunctive queries is polynomially reducible to the problem of knowledge base consistency.