How to Approximate Ontology-Mediated Queries
This work addresses computational efficiency issues for ontology-mediated queries in knowledge representation, but it is incremental as it builds on existing approximation methods.
The paper tackles the problem of approximating ontology-mediated queries in description logics ALC and ALCI by introducing two kinds of approximations: replacing the ontology with a tractable language or the database with a tractable class, and it results in reducing data complexity from coNP-complete to PTime, sometimes to fixed-parameter tractable or linear time.
We introduce and study several notions of approximation for ontology-mediated queries based on the description logics ALC and ALCI. Our approximations are of two kinds: we may (1) replace the ontology with one formulated in a tractable ontology language such as ELI or certain TGDs and (2) replace the database with one from a tractable class such as the class of databases whose treewidth is bounded by a constant. We determine the computational complexity and the relative completeness of the resulting approximations. (Almost) all of them reduce the data complexity from coNP-complete to PTime, in some cases even to fixed-parameter tractable and to linear time. While approximations of kind (1) also reduce the combined complexity, this tends to not be the case for approximations of kind (2). In some cases, the combined complexity even increases.