  Semantic data fuels many different applications, but is still lacking proper
integration into programming languages. Untyped access is error-prone while
mapping approaches cannot fully capture the conceptualization of semantic data.
In this paper, we present $\lambda_{DL}$,a $\lambda$-calculus with a modified
type system to provide type-safe integration of semantic data. This is achieved
by the integration of description logics into the $\lambda$-calculus for typing
and data access. It is centered around several key design principles. Among
these are (1) the usage of semantic conceptualizations as types, (2) subtype
inference for these types, and (3) type-checked query access to the data by
both ensuring the satisfiability of queries as well as typing query results
precisely in $\lambda_{DL}$. The paper motivates the use of a modified type
system for semantic data and it provides the theoretic foundation for the
integration of description logics as well as the core formal specifications of
$\lambda_{DL}$ including a proof of type safety.
