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Register a new userHow to Approximate Ontology-Mediated Queries
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Added by
Carsten Lutz
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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.
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We consider ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and (unions) of conjunctive queries, studying the rewritability into OMQs based on instance queries (IQs). Our results include exact characterizations of when such a rewriting is possible and tight complexity bounds for deciding rewritability. We also give a tight complexity bound for the related problem of deciding whether a given MMSNP sentence is equivalent to a CSP.
We consider the problem of evaluating certain types of functional aggregation queries on relational data subject to additive inequalities. Such aggregation queries, with a smallish number of additive inequalities, arise naturally/commonly in many applications, particularly in learning applications. We give a relatively complete categorization of the computational complexity of such problems. We first show that the problem is NP-hard, even in the case of one additive inequality. Thus we turn to approximating the query. Our main result is an efficient algorithm for approximating, with arbitrarily small relative error, many natural aggregation queries with one additive inequality. We give examples of natural queries that can be efficiently solved using this algorithm. In contrast, we show that the situation with two additive inequalities is quite different, by showing that it is NP-hard to evaluate simple aggregation queries, with two additive inequalities, with any bounded relative error.
We focus on ontology-mediated queries (OMQs) based on (frontier-)guarded existential rules and (unions of) conjunctive queries, and we investigate the problem of FO-rewritability, i.e., whether an OMQ can be rewritten as a first-order query. We adopt two different approaches. The first approach employs standard two-way alternating parity tree automata. Although it does not lead to a tight complexity bound, it provides a transparent solution based on widely known tools. The second approach relies on a sophisticated automata model, known as cost automata. This allows us to show that our problem is 2ExpTime-complete. In both approaches, we provide semantic characterizations of FO-rewritability that are of independent interest.
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