Extending the Description Logic τEL(deg) with Acyclic TBoxes

In a previous paper, we have introduced an extension of the lightweight Description Logic EL that allows us to define concepts in an approximate way. For this purpose, we have defined a graded membership function deg , which for each individual and concept yields a number in the interval [0, 1] expressing the degree to which the individual belongs to the concept. Threshold concepts C∼t for ∼ ∈ {<,≤, >,≥} then collect all the individuals that belong to C with degree ∼ t. We have then investigated the complexity of reasoning in the Description Logic τEL(deg), which is obtained from EL by adding such threshold concepts. In the present paper, we extend these results, which were obtained for reasoning without TBoxes, to the case of reasoning w.r.t. acyclic TBoxes. Surprisingly, this is not as easy as might have been expected. On the one hand, one must be quite careful to define acyclic TBoxes such that they still just introduce abbreviations for complex concepts, and thus can be unfolded. On the other hand, it turns out that, in contrast to the case of EL, adding acyclic TBoxes to τEL(deg) increases the complexity of reasoning by at least on level of the polynomial hierarchy. ∗Supported by DFG Graduiertenkolleg 1763 (QuantLA).