32 research outputs found
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
Combining Rewriting and Incremental Materialisation Maintenance for Datalog Programs with Equality
Materialisation precomputes all consequences of a set of facts and a datalog
program so that queries can be evaluated directly (i.e., independently from the
program). Rewriting optimises materialisation for datalog programs with
equality by replacing all equal constants with a single representative; and
incremental maintenance algorithms can efficiently update a materialisation for
small changes in the input facts. Both techniques are critical to practical
applicability of datalog systems; however, we are unaware of an approach that
combines rewriting and incremental maintenance. In this paper we present the
first such combination, and we show empirically that it can speed up updates by
several orders of magnitude compared to using either rewriting or incremental
maintenance in isolation.Comment: All proofs contained in the appendix. 7 pages + 4 pages appendix. 7
algorithms and one table with evaluation result
On the Decidability of Connectedness Constraints in 2D and 3D Euclidean Spaces
We investigate (quantifier-free) spatial constraint languages with equality,
contact and connectedness predicates as well as Boolean operations on regions,
interpreted over low-dimensional Euclidean spaces. We show that the complexity
of reasoning varies dramatically depending on the dimension of the space and on
the type of regions considered. For example, the logic with the
interior-connectedness predicate (and without contact) is undecidable over
polygons or regular closed sets in the Euclidean plane, NP-complete over
regular closed sets in three-dimensional Euclidean space, and ExpTime-complete
over polyhedra in three-dimensional Euclidean space.Comment: Accepted for publication in the IJCAI 2011 proceeding