406 research outputs found
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
Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure
In this work we study a rational extension of the low complexity
description logic SROEL, which underlies the OWL EL ontology language. The
extension involves a typicality operator T, whose semantics is based on Lehmann
and Magidor's ranked models and allows for the definition of defeasible
inclusions. We consider both rational entailment and minimal entailment. We
show that deciding instance checking under minimal entailment is in general
-hard, while, under rational entailment, instance checking can be
computed in polynomial time. We develop a Datalog calculus for instance
checking under rational entailment and exploit it, with stratified negation,
for computing the rational closure of simple KBs in polynomial time.Comment: Accepted for publication on Fundamenta Informatica
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
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
Equality-friendly well-founded semantics and applications to description logics
We tackle the problem of deļ¬ning a well-founded semantics (WFS) for Datalog rules with existentially quantiļ¬ed variables in their heads and nega- tions in their bodies. In particular, we provide a WFS for the recent DatalogĀ± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize DatalogĀ± by non-stratiļ¬ed nonmonotonic nega- tion in rule bodies, and we deļ¬ne a WFS for this generalization via guarded ļ¬xed point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its proļ¬les as well as typical DLs, which also do not make the UNA. We prove that for guarded DatalogĀ± with negation under the equality- friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise deļ¬- nitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering
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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