36 research outputs found
Revisiting acyclicity and guardedness criteria for decidability of existential rules
Abstract. Existential rules, i.e. Datalog extended with existential quantifiers in rule heads, are currently studied under a variety of names such as Datalog+/-, ââ-rules, and tuple-generating dependencies. The renewed interest in this formalism is fuelled by a wealth of recently discovered language fragments for which query answering is decidable. This paper extends and consolidates two of the main approaches in this field -acyclicity and guardedness -by providing (1) complexitypreserving generalisations of weakly acyclic and weakly (frontier-)guarded rules, and (2) a novel formalism of glut-(frontier-)guarded rules that subsumes both. This builds on an insight that acyclicity can be used to extend any existential rule language while retaining decidability. Besides decidability, combined query complexities are established in all cases
Tractable Query Answering and Optimization for Extensions of Weakly-Sticky Datalog+-
We consider a semantic class, weakly-chase-sticky (WChS), and a syntactic
subclass, jointly-weakly-sticky (JWS), of Datalog+- programs. Both extend that
of weakly-sticky (WS) programs, which appear in our applications to data
quality. For WChS programs we propose a practical, polynomial-time query
answering algorithm (QAA). We establish that the two classes are closed under
magic-sets rewritings. As a consequence, QAA can be applied to the optimized
programs. QAA takes as inputs the program (including the query) and semantic
information about the "finiteness" of predicate positions. For the syntactic
subclasses JWS and WS of WChS, this additional information is computable.Comment: To appear in Proc. Alberto Mendelzon WS on Foundations of Data
Management (AMW15
Bounded Implication for Existential Rules
The property of boundedness in Datalog formalizes whether a set of rules can be equivalently expressed by a non-recursive set of rules. Existential rules extend Datalog to the presence of existential variables in rule heads. In this paper, we introduce and study notions of boundedness for existential rules. We provide a notion of weak boundedness and a notion of strong boundedness for a rule set, and show that they correspond, respectively, to the notions of first-order rewritability of atomic queries and first-order rewritability of conjunctive queries over the set. While weak and strong boundedness are in general not equivalent, we show that, for some notable subclasses of existential rules, i.e., Datalog, single-head binary rules, and frontier-guarded rules, the two notions coincide
Revisiting Chase Termination for Existential Rules and their Extension to Nonmonotonic Negation
Existential rules have been proposed for representing ontological knowledge,
specifically in the context of Ontology- Based Data Access. Entailment with
existential rules is undecidable. We focus in this paper on conditions that
ensure the termination of a breadth-first forward chaining algorithm known as
the chase. Several variants of the chase have been proposed. In the first part
of this paper, we propose a new tool that allows to extend existing acyclicity
conditions ensuring chase termination, while keeping good complexity
properties. In the second part, we study the extension to existential rules
with nonmonotonic negation under stable model semantics, discuss the relevancy
of the chase variants for these rules and further extend acyclicity results
obtained in the positive case.Comment: This paper appears in the Proceedings of the 15th International
Workshop on Non-Monotonic Reasoning (NMR 2014
Loop Restricted Existential Rules and First-order Rewritability for Query Answering
In ontology-based data access (OBDA), the classical database is enhanced with
an ontology in the form of logical assertions generating new intensional
knowledge. A powerful form of such logical assertions is the tuple-generating
dependencies (TGDs), also called existential rules, where Horn rules are
extended by allowing existential quantifiers to appear in the rule heads. In
this paper we introduce a new language called loop restricted (LR) TGDs
(existential rules), which are TGDs with certain restrictions on the loops
embedded in the underlying rule set. We study the complexity of this new
language. We show that the conjunctive query answering (CQA) under the LR TGDs
is decid- able. In particular, we prove that this language satisfies the
so-called bounded derivation-depth prop- erty (BDDP), which implies that the
CQA is first-order rewritable, and its data complexity is in AC0 . We also
prove that the combined complexity of the CQA is EXPTIME complete, while the
language membership is PSPACE complete. Then we extend the LR TGDs language to
the generalised loop restricted (GLR) TGDs language, and prove that this class
of TGDs still remains to be first-order rewritable and properly contains most
of other first-order rewritable TGDs classes discovered in the literature so
far.Comment: Full paper version of extended abstrac