4,258 research outputs found
Worst-case Optimal Query Answering for Greedy Sets of Existential Rules and Their Subclasses
The need for an ontological layer on top of data, associated with advanced
reasoning mechanisms able to exploit the semantics encoded in ontologies, has
been acknowledged both in the database and knowledge representation
communities. We focus in this paper on the ontological query answering problem,
which consists of querying data while taking ontological knowledge into
account. More specifically, we establish complexities of the conjunctive query
entailment problem for classes of existential rules (also called
tuple-generating dependencies, Datalog+/- rules, or forall-exists-rules. Our
contribution is twofold. First, we introduce the class of greedy
bounded-treewidth sets (gbts) of rules, which covers guarded rules, and their
most well-known generalizations. We provide a generic algorithm for query
entailment under gbts, which is worst-case optimal for combined complexity with
or without bounded predicate arity, as well as for data complexity and query
complexity. Secondly, we classify several gbts classes, whose complexity was
unknown, with respect to combined complexity (with both unbounded and bounded
predicate arity) and data complexity to obtain a comprehensive picture of the
complexity of existential rule fragments that are based on diverse guardedness
notions. Upper bounds are provided by showing that the proposed algorithm is
optimal for all of them
Query inseparability by games
We investigate conjunctive query inseparability of description logic knowledge bases (KBs) with respect to a given signature, a fundamental problem for KB versioning, module extraction, forgetting and knowledge exchange. We develop a game-theoretic technique for checking query inseparability of KBs expressed in fragments of Horn-ALCHI, and show a number of complexity results ranging from P to ExpTime and 2ExpTime. We also employ our results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal UCQ-solutions in knowledge exchange are both ExpTime-complete for combined complexity
Type-elimination-based reasoning for the description logic SHIQbs using decision diagrams and disjunctive datalog
We propose a novel, type-elimination-based method for reasoning in the
description logic SHIQbs including DL-safe rules. To this end, we first
establish a knowledge compilation method converting the terminological part of
an ALCIb knowledge base into an ordered binary decision diagram (OBDD) which
represents a canonical model. This OBDD can in turn be transformed into
disjunctive Datalog and merged with the assertional part of the knowledge base
in order to perform combined reasoning. In order to leverage our technique for
full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that
preserves satisfiability and entailment of positive and negative ground facts.
The proposed technique is shown to be worst case optimal w.r.t. combined and
data complexity and easily admits extensions with ground conjunctive queries.Comment: 38 pages, 3 figures, camera ready version of paper accepted for
publication in Logical Methods in Computer Scienc
Computing Horn Rewritings of Description Logics Ontologies
We study the problem of rewriting an ontology O1 expressed in a DL L1 into an
ontology O2 in a Horn DL L2 such that O1 and O2 are equisatisfiable when
extended with an arbitrary dataset. Ontologies that admit such rewritings are
amenable to reasoning techniques ensuring tractability in data complexity.
After showing undecidability whenever L1 extends ALCF, we focus on devising
efficiently checkable conditions that ensure existence of a Horn rewriting. By
lifting existing techniques for rewriting Disjunctive Datalog programs into
plain Datalog to the case of arbitrary first-order programs with function
symbols, we identify a class of ontologies that admit Horn rewritings of
polynomial size. Our experiments indicate that many real-world ontologies
satisfy our sufficient conditions and thus admit polynomial Horn rewritings.Comment: 15 pages. To appear in IJCAI-1
Approximate Assertional Reasoning Over Expressive Ontologies
In this thesis, approximate reasoning methods for scalable assertional reasoning are provided whose computational properties can be established in a well-understood way, namely in terms of soundness and completeness, and whose quality can be analyzed in terms of statistical measurements, namely recall and precision. The basic idea of these approximate reasoning methods is to speed up reasoning by trading off the quality of reasoning results against increased speed
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