Computing Optimal Repairs of Quantified ABoxes w.r.t. Static $$\mathcal {EL}$$ TBoxes

Abstract

The application of automated reasoning approaches to Description Logic (DL) ontologies may produce certain consequences that either are deemed to be wrong or should be hidden for privacy reasons. The question is then how to repair the ontology such that the unwanted consequences can no longer be deduced. An optimal repair is one where the least amount of other consequences is removed. Most of the previous approaches to ontology repair are of a syntactic nature in that they remove or weaken the axioms explicitly present in the ontology, and thus cannot achieve semantic optimality. In previous work, we have addressed the problem of computing optimal repairs of (quantified) ABoxes, where the unwanted consequences are described by concept assertions of the lightweight DL $$\mathcal {EL}$$ EL . In the present paper, we improve on the results achieved so far in two ways. First, we allow for the presence of terminological knowledge in the form of an $$\mathcal {EL}$$ EL TBox. This TBox is assumed to be static in the sense that it cannot be changed in the repair process. Second, the construction of optimal repairs described in our previous work is best case exponential. We introduce an optimized construction that is exponential only in the worst case. First experimental results indicate that this reduces the size of the computed optimal repairs considerably.

Pushing Optimal ABox Repair from EL Towards More Expressive Horn-DLs

“…the empty terminology. The rules in Figure 1 extend the CQ-saturation rules in (Baader et al 2021) such that nominals, inverse roles, and RIs are taken into account. Note that, during saturation, the matrix B may contain complex concept assertions, but after termination all concept assertions are again restricted to concept names.…”

“…In general, application of the saturation rules need not terminate, already in the EL setting considered in (Baader et al 2021). But there the restriction to cycle-restricted TBoxes guarantees termination, where an EL TBox T is cycle-restricted if there is no concept C and roles r 1 , .…”

“…In (Baader et al 2021), we extended this approach to a setting where, in addition to the qABox, the ontology contains an EL TBox, which is assumed to be correct, and thus cannot be changed during repair. To add consequences implied by the TBox, we saturate the qABox by using the concept inclusions as rewrite rules before repairing the qABox.…”

“…This is not just a problem of our repair approach, but may prevent the existence of optimal repairs (see Example 9 below). In (Baader et al 2021), two approaches are considered to overcome this problem. On the one hand, one can restrict the attention to TBoxes that are cycle-restricted as introduced in (Baader, Borgwardt, and Morawska 2012).…”

“…However, even disregarding the impracticality of an algorithm that computes the optimal repairs by looking at all qABoxes up to a certain size bound, this does not lead to a viable methods for choosing an appropriate optimal repair since it would require the knowledge engineer to choose among exponentially many repairs of exponential size. In contrast, the canonical repairs (which cover all optimal repairs) constructed by our extension of the repair approach in (Baader et al 2021) are characterized by so-called repair seeds, which are of polynomial size. The knowledge engineer can choose among these by answering a polynomial number of instance queries (i.e., queries about which instance relationships hold in the application domain).…”