9 research outputs found
First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries
Aiming at ontology-based data access to temporal data, we design
two-dimensional temporal ontology and query languages by combining logics from
the (extended) DL-Lite family with linear temporal logic LTL over discrete time
(Z,<). Our main concern is first-order rewritability of ontology-mediated
queries (OMQs) that consist of a 2D ontology and a positive temporal instance
query. Our target languages for FO-rewritings are two-sorted FO(<) -
first-order logic with sorts for time instants ordered by the built-in
precedence relation < and for the domain of individuals - its extension FOE
with the standard congruence predicates t \equiv 0 mod n, for any fixed n > 1,
and FO(RPR) that admits relational primitive recursion. In terms of circuit
complexity, FOE- and FO(RPR)-rewritability guarantee answering OMQs in uniform
AC0 and NC1, respectively.
We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL
ontology languages and investigate the FO-rewritability of OMQs with atomic
queries by constructing projections onto 1D LTL OMQs and employing recent
results on the FO-rewritability of propositional LTL OMQs. As the projections
involve deciding consistency of ontologies and data, we also consider the
consistency problem for our languages. While the undecidability of consistency
for 2D ontology languages with expressive Boolean role inclusions might be
expected, we also show that, rather surprisingly, the restriction to Krom and
Horn role inclusions leads to decidability (and ExpSpace-completeness), even if
one admits full Booleans on concepts. As a final step, we lift some of the
rewritability results for atomic OMQs to OMQs with expressive positive temporal
instance queries. The lifting results are based on an in-depth study of the
canonical models and only concern Horn ontologies
Saturation-based Boolean conjunctive query answering and rewriting for the guarded quantification fragments
Query answering is an important problem in AI, database and knowledge
representation. In this paper, we develop saturation-based Boolean conjunctive
query answering and rewriting procedures for the guarded, the loosely guarded
and the clique-guarded fragments. Our query answering procedure improves
existing resolution-based decision procedures for the guarded and the loosely
guarded fragments and this procedure solves Boolean conjunctive query answering
problems for the guarded, the loosely guarded and the clique-guarded fragments.
Based on this query answering procedure, we also introduce a novel
saturation-based query rewriting procedure for these guarded fragments. Unlike
mainstream query answering and rewriting methods, our procedures derive a
compact and reusable saturation, namely a closure of formulas, to handle the
challenge of querying for distributed datasets. This paper lays the theoretical
foundations for the first automated deduction decision procedures for Boolean
conjunctive query answering and the first saturation-based Boolean conjunctive
query rewriting in the guarded, the loosely guarded and the clique-guarded
fragments
A tetrachotomy of ontology-mediated queries with a covering axiom
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by descrip- tion logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology- based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple cov- ering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Π2p-complete for combined complexity and can be in AC0 or L-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups be- ing 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d- sirups. Our main technical result is a complete and transparent syntactic AC0 / NL / P / coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL
A tetrachotomy of ontology-mediated queries with a covering axiom
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by descrip- tion logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology- based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple cov- ering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Π2p-complete for combined complexity and can be in AC0 or L-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups be- ing 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d- sirups. Our main technical result is a complete and transparent syntactic AC0 / NL / P / coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL