Abstract
In the area of Description Logic (DL) based knowledge representation, two desirable features of DL systems have as yet been incompatible: firstly, the support of general TBoxes containing general concept inclusion (GCI) axioms, and secondly, non-standard inference services facilitating knowledge engineering tasks, such as build-up and maintenance of terminologies (TBoxes). In order to make non-standard inferences available without sacrificing the convenience of GCIs, the present paper proposes hybrid TBoxes consisting of a pair of a general TBox $\mathcal{F}$ interpreted by descriptive semantics, and a (possibly) cyclic TBox $\mathcal{T}$ interpreted by fixpoint semantics. $\mathcal{F}$ serves as a foundation of $\mathcal{T}$ in the sense that the GCIs in $\mathcal{F}$ define relationships between concepts used as atomic concept names in the definitions in $\mathcal{T}$. Our main technical result is a polynomial time subsumption algorithm for hybrid $\mathcal{EL}$-TBoxes based on a polynomial reduction to subsumption w.r.t. cyclic $\mathcal{EL}$-TBoxes with fixpoint semantics. By virtue of this reduction, all non-standard inferences already available for cyclic $\mathcal{EL}$-TBoxes become available for hybrid ones.
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