80 research outputs found
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
Queries with Guarded Negation (full version)
A well-established and fundamental insight in database theory is that
negation (also known as complementation) tends to make queries difficult to
process and difficult to reason about. Many basic problems are decidable and
admit practical algorithms in the case of unions of conjunctive queries, but
become difficult or even undecidable when queries are allowed to contain
negation. Inspired by recent results in finite model theory, we consider a
restricted form of negation, guarded negation. We introduce a fragment of SQL,
called GN-SQL, as well as a fragment of Datalog with stratified negation,
called GN-Datalog, that allow only guarded negation, and we show that these
query languages are computationally well behaved, in terms of testing query
containment, query evaluation, open-world query answering, and boundedness.
GN-SQL and GN-Datalog subsume a number of well known query languages and
constraint languages, such as unions of conjunctive queries, monadic Datalog,
and frontier-guarded tgds. In addition, an analysis of standard benchmark
workloads shows that most usage of negation in SQL in practice is guarded
negation
Expressive Completeness of Existential Rule Languages for Ontology-based Query Answering
Existential rules, also known as data dependencies in Databases, have been
recently rediscovered as a promising family of languages for Ontology-based
Query Answering. In this paper, we prove that disjunctive embedded dependencies
exactly capture the class of recursively enumerable ontologies in
Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness
result does not rely on any built-in linear order on the database. To establish
the expressive completeness, we introduce a novel semantic definition for OCQA
ontologies. We also show that neither the class of disjunctive tuple-generating
dependencies nor the class of embedded dependencies is expressively complete
for recursively enumerable OCQA ontologies.Comment: 10 pages; the full version of a paper to appear in IJCAI 2016.
Changes (regarding to v1): a new reference has been added, and some typos
have been correcte
Model-theoretic Characterizations of Existential Rule Languages
Existential rules, a.k.a. dependencies in databases, and Datalog+/- in
knowledge representation and reasoning recently, are a family of important
logical languages widely used in computer science and artificial intelligence.
Towards a deep understanding of these languages in model theory, we establish
model-theoretic characterizations for a number of existential rule languages
such as (disjunctive) embedded dependencies, tuple-generating dependencies
(TGDs), (frontier-)guarded TGDs and linear TGDs. All these characterizations
hold for arbitrary structures, and most of them also work on the class of
finite structures. As a natural application of these characterizations,
complexity bounds for the rewritability of above languages are also identified.Comment: 17 pages, 2 figures, the full version of a paper submitted to IJCAI
202
Goal-Driven Query Answering for Existential Rules with Equality
Inspired by the magic sets for Datalog, we present a novel goal-driven
approach for answering queries over terminating existential rules with equality
(aka TGDs and EGDs). Our technique improves the performance of query answering
by pruning the consequences that are not relevant for the query. This is
challenging in our setting because equalities can potentially affect all
predicates in a dataset. We address this problem by combining the existing
singularization technique with two new ingredients: an algorithm for
identifying the rules relevant to a query and a new magic sets algorithm. We
show empirically that our technique can significantly improve the performance
of query answering, and that it can mean the difference between answering a
query in a few seconds or not being able to process the query at all
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