112 research outputs found
On the first-order rewritability of conjunctive queries over binary guarded existential rules
We study conjunctive query answering and first-order rewritability of conjunctive queries for binary guarded existential rules. In particular, we prove that the problem of establishing whether a given set of binary guarded existential rules is such that all conjunctive queries admit a first-order rewriting is decidable, and present a technique for solving this problem. These results have a important practical impact, since they make it possible to identify those sets of binary guarded existential rules for which it is possible to answer every conjunctive query through query rewriting and standard evaluation of a first-order query (actually, a union of conjunctive queries) over a relational database system
Computing FO-Rewritings in EL in Practice: from Atomic to Conjunctive Queries
A prominent approach to implementing ontology-mediated queries (OMQs) is to
rewrite into a first-order query, which is then executed using a conventional
SQL database system. We consider the case where the ontology is formulated in
the description logic EL and the actual query is a conjunctive query and show
that rewritings of such OMQs can be efficiently computed in practice, in a
sound and complete way. Our approach combines a reduction with a decomposed
backwards chaining algorithm for OMQs that are based on the simpler atomic
queries, also illuminating the relationship between first-order rewritings of
OMQs based on conjunctive and on atomic queries. Experiments with real-world
ontologies show promising results
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
Datalog Rewritability of Disjunctive Datalog Programs and its Applications to Ontology Reasoning
We study the problem of rewriting a disjunctive datalog program into plain
datalog. We show that a disjunctive program is rewritable if and only if it is
equivalent to a linear disjunctive program, thus providing a novel
characterisation of datalog rewritability. Motivated by this result, we propose
weakly linear disjunctive datalog---a novel rule-based KR language that extends
both datalog and linear disjunctive datalog and for which reasoning is
tractable in data complexity. We then explore applications of weakly linear
programs to ontology reasoning and propose a tractable extension of OWL 2 RL
with disjunctive axioms. Our empirical results suggest that many non-Horn
ontologies can be reduced to weakly linear programs and that query answering
over such ontologies using a datalog engine is feasible in practice.Comment: 14 pages. To appear at AAAI-1
Rewritability in Monadic Disjunctive Datalog, MMSNP, and Expressive Description Logics
We study rewritability of monadic disjunctive Datalog programs, (the
complements of) MMSNP sentences, and ontology-mediated queries (OMQs) based on
expressive description logics of the ALC family and on conjunctive queries. We
show that rewritability into FO and into monadic Datalog (MDLog) are decidable,
and that rewritability into Datalog is decidable when the original query
satisfies a certain condition related to equality. We establish
2NExpTime-completeness for all studied problems except rewritability into MDLog
for which there remains a gap between 2NExpTime and 3ExpTime. We also analyze
the shape of rewritings, which in the MMSNP case correspond to obstructions,
and give a new construction of canonical Datalog programs that is more
elementary than existing ones and also applies to formulas with free variables
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