Summary: Automated support to enterprise modeling has increasingly become a subject of interest for organizations seeking solutions for storage, distribution and analysis of knowledge about business processes. This interest has recently resulted in approving the standard for specifying Semantics of Business Vocabulary and Business Rules (SBVR). Despite the existence of formally grounded notations, up to now SBVR still lacks a sound and consistent logical formalization which would allow developing automated solutions able to check the consistency of a set of business rules. This work reports on the attempt to provide logical foundations for SBVR by the means of defining a specific first-order deontic-alethic logic (FODAL). The connections of FODAL with the modal logic \(\mathbf {QK}\) and the description logic \(\mathcal {ALCQI}\) have been investigated and, on top of the obtained theoretical results, a special tool providing automated support for consistency checks of a set of \(\mathcal {ALCQI}\)-expressible deontic and alethic business rules has been implemented.