542 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
Magic Sets for Disjunctive Datalog Programs
In this paper, a new technique for the optimization of (partially) bound
queries over disjunctive Datalog programs with stratified negation is
presented. The technique exploits the propagation of query bindings and extends
the Magic Set (MS) optimization technique.
An important feature of disjunctive Datalog is nonmonotonicity, which calls
for nondeterministic implementations, such as backtracking search. A
distinguishing characteristic of the new method is that the optimization can be
exploited also during the nondeterministic phase. In particular, after some
assumptions have been made during the computation, parts of the program may
become irrelevant to a query under these assumptions. This allows for dynamic
pruning of the search space. In contrast, the effect of the previously defined
MS methods for disjunctive Datalog is limited to the deterministic portion of
the process. In this way, the potential performance gain by using the proposed
method can be exponential, as could be observed empirically.
The correctness of MS is established thanks to a strong relationship between
MS and unfounded sets that has not been studied in the literature before. This
knowledge allows for extending the method also to programs with stratified
negation in a natural way.
The proposed method has been implemented in DLV and various experiments have
been conducted. Experimental results on synthetic data confirm the utility of
MS for disjunctive Datalog, and they highlight the computational gain that may
be obtained by the new method w.r.t. the previously proposed MS methods for
disjunctive Datalog programs. Further experiments on real-world data show the
benefits of MS within an application scenario that has received considerable
attention in recent years, the problem of answering user queries over possibly
inconsistent databases originating from integration of autonomous sources of
information.Comment: 67 pages, 19 figures, preprint submitted to Artificial Intelligenc
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 disjunctive datalog
Datalog is a declarative logic programming language that uses classical logical reasoning as its basic form of reasoning. Defeasible reasoning is a form of non-classical reasoning that is able to deal with exceptions to general assertions in a formal manner. The KLM approach to defeasible reasoning is an axiomatic approach based on the concept of plausible inference. Since Datalog uses classical reasoning, it is currently not able to handle defeasible implications and exceptions. We aim to extend the expressivity of Datalog by incorporating KLM-style defeasi- ble reasoning into classical Datalog. We present a systematic approach to extending the KLM properties and a well-known form of defeasible entailment: Rational Closure. We conclude by exploring Datalog exten- sions of less conservative forms of defeasible entailment: Relevant and Lexicographic Closure
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
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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