  The Decision Model and Notation (DMN) is a recent OMG standard for the
elicitation and representation of decision models, and for managing their
interconnection with business processes. DMN builds on the notion of decision
tables, and their combination into more complex decision requirements graphs
(DRGs), which bridge between business process models and decision logic models.
DRGs may rely on additional, external business knowledge models, whose
functioning is not part of the standard. In this work, we consider one of the
most important types of business knowledge, namely background knowledge that
conceptually accounts for the structural aspects of the domain of interest, and
propose decision knowledge bases (DKBs), which semantically combine DRGs
modeled in DMN, and domain knowledge captured by means of first-order logic
with datatypes. We provide a logic-based semantics for such an integration, and
formalize different DMN reasoning tasks for DKBs. We then consider background
knowledge formulated as a description logic ontology with datatypes, and show
how the main verification tasks for DMN in this enriched setting can be
formalized as standard DL reasoning services, and actually carried out in
ExpTime. We discuss the effectiveness of our framework on a case study in
maritime security.
