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

Polynomial conjunctive query rewriting under unary inclusion dependencies

Ontology-based data access (OBDA) is widely accepted as an important ingredient of the new generation of information systems. In the OBDA paradigm, potentially incomplete relational data is enriched by means of ontologies, representing intensional knowledge of the application domain. We consider the problem of conjunctive query answering in OBDA. Certain ontology languages have been identified as FO-rewritable (e.g., DL-Lite and sticky-join sets of TGDs), which means that the ontology can be incorporated into the user's query, thus reducing OBDA to standard relational query evaluation. However, all known query rewriting techniques produce queries that are exponentially large in the size of the user's query, which can be a serious issue for standard relational database engines. In this paper, we present a polynomial query rewriting for conjunctive queries under unary inclusion dependencies. On the other hand, we show that binary inclusion dependencies do not admit polynomial query rewriting algorithms

Conjunctive Query Answering for the Description Logic SHIQ

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP

On (in)tractability of OBDA with OWL 2 QL

We show that, although conjunctive queries over OWL 2 QL ontologies are reducible to database queries, no algorithm can construct such a reduction in polynomial time without changing the data. On the other hand, we give a polynomial reduction for OWL2QL ontologies without role inclusions

Querying the Guarded Fragment

Evaluating a Boolean conjunctive query Q against a guarded first-order theory F is equivalent to checking whether "F and not Q" is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since Q may not be guarded, well known results about the decidability, complexity, and finite-model property of the guarded fragment do not obviously carry over to conjunctive query answering over guarded theories, and had been left open in general. By investigating finite guarded bisimilar covers of hypergraphs and relational structures, and by substantially generalising Rosati's finite chase, we prove for guarded theories F and (unions of) conjunctive queries Q that (i) Q is true in each model of F iff Q is true in each finite model of F and (ii) determining whether F implies Q is 2EXPTIME-complete. We further show the following results: (iii) the existence of polynomial-size conformal covers of arbitrary hypergraphs; (iv) a new proof of the finite model property of the clique-guarded fragment; (v) the small model property of the guarded fragment with optimal bounds; (vi) a polynomial-time solution to the canonisation problem modulo guarded bisimulation, which yields (vii) a capturing result for guarded bisimulation invariant PTIME.Comment: This is an improved and extended version of the paper of the same title presented at LICS 201

DL-lite with attributes and datatypes

We extend the DL-Lite languages by means of attributes and datatypes. Attributes -- a notion borrowed from data models -- associate concrete values from datatypes to abstract objects and in this way complement roles, which describe relationships between abstract objects. The extended languages remain tractable (with a notable exception) even though they contain both existential and (a limited form of) universal quantification. We present complexity results for two most important reasoning problems in DL-Lite: combined complexity of knowledge base satisfiability and data complexity of positive existential query answering