8 research outputs found
On (in)tractability of OBDA with OWL 2 QL
We show that, although conjunctive queries over OWL 2 QL ontologies are reducible to database queries, no algorithm can construct such a reduction in polynomial time without changing the data. On the other hand, we give a polynomial reduction for OWL2QL ontologies without role inclusions
Polynomial conjunctive query rewriting under unary inclusion dependencies
Ontology-based data access (OBDA) is widely accepted as an important ingredient of the new generation of information systems. In the OBDA paradigm, potentially incomplete relational data is enriched by means of ontologies, representing intensional knowledge of the application domain. We consider the problem of conjunctive query answering in OBDA. Certain ontology languages have been identified as FO-rewritable (e.g., DL-Lite and sticky-join sets of TGDs), which means that the ontology can be incorporated into the user's query, thus reducing OBDA to standard relational query evaluation. However, all known query rewriting techniques produce queries that are exponentially large in the size of the user's query, which can be a serious issue for standard relational database engines. In this paper, we present a polynomial query rewriting for conjunctive queries under unary inclusion dependencies. On
the other hand, we show that binary inclusion dependencies do not admit
polynomial query rewriting algorithms
Exponential Lower Bounds and Separation for Query Rewriting
We establish connections between the size of circuits and formulas computing
monotone Boolean functions and the size of first-order and nonrecursive Datalog
rewritings for conjunctive queries over OWL 2 QL ontologies. We use known lower
bounds and separation results from circuit complexity to prove similar results
for the size of rewritings that do not use non-signature constants. For
example, we show that, in the worst case, positive existential and nonrecursive
Datalog rewritings are exponentially longer than the original queries;
nonrecursive Datalog rewritings are in general exponentially more succinct than
positive existential rewritings; while first-order rewritings can be
superpolynomially more succinct than positive existential rewritings
The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs
We study the problem of probabilistic query evaluation on probabilistic
graphs, namely, tuple-independent probabilistic databases on signatures of
arity two. Our focus is the class of queries that is closed under
homomorphisms, or equivalently, the infinite unions of conjunctive queries. Our
main result states that all unbounded queries from this class are #P-hard for
probabilistic query evaluation. As bounded queries from this class are
equivalent to a union of conjunctive queries, they are already classified by
the dichotomy of Dalvi and Suciu (2012). Hence, our result and theirs imply a
complete data complexity dichotomy, between polynomial time and #P-hardness,
for evaluating infinite unions of conjunctive queries over probabilistic
graphs. This dichotomy covers in particular all fragments of infinite unions of
conjunctive queries such as negation-free (disjunctive) Datalog, regular path
queries, and a large class of ontology-mediated queries on arity-two
signatures. Our result is shown by reducing from counting the valuations of
positive partitioned 2-DNF formulae for some queries, or from the
source-to-target reliability problem in an undirected graph for other queries,
depending on properties of minimal models. The presented dichotomy result
applies to even a special case of probabilistic query evaluation called
generalized model counting, where fact probabilities must be 0, 0.5, or 1.Comment: 30 pages. Journal version of the ICDT'20 paper
https://drops.dagstuhl.de/opus/volltexte/2020/11939/. Submitted to LMCS. The
previous version (version 2) was the same as the ICDT'20 paper with some
minor formatting tweaks and 7 extra pages of technical appendi
Tree-like Queries in OWL 2 QL: Succinctness and Complexity Results
This paper investigates the impact of query topology on the difficulty of
answering conjunctive queries in the presence of OWL 2 QL ontologies. Our first
contribution is to clarify the worst-case size of positive existential (PE),
non-recursive Datalog (NDL), and first-order (FO) rewritings for various
classes of tree-like conjunctive queries, ranging from linear queries to
bounded treewidth queries. Perhaps our most surprising result is a
superpolynomial lower bound on the size of PE-rewritings that holds already for
linear queries and ontologies of depth 2. More positively, we show that
polynomial-size NDL-rewritings always exist for tree-shaped queries with a
bounded number of leaves (and arbitrary ontologies), and for bounded treewidth
queries paired with bounded depth ontologies. For FO-rewritings, we equate the
existence of polysize rewritings with well-known problems in Boolean circuit
complexity. As our second contribution, we analyze the computational complexity
of query answering and establish tractability results (either NL- or
LOGCFL-completeness) for a range of query-ontology pairs. Combining our new
results with those from the literature yields a complete picture of the
succinctness and complexity landscapes for the considered classes of queries
and ontologies.Comment: This is an extended version of a paper accepted at LICS'15. It
contains both succinctness and complexity results and adopts FOL notation.
The appendix contains proofs that had to be omitted from the conference
version for lack of space. The previous arxiv version (a long version of our
DL'14 workshop paper) only contained the succinctness results and used
description logic notatio