Regular path queries in expressive description logics with nominals (original) (raw)
Related papers
Answering regular path queries in expressive Description Logics via alternating tree-automata
Information and Computation, 2014
Automata on infinite trees Expressive Description Logics (DLs) have been advocated as formalisms for modeling the domain of interest in various application areas, including the Semantic Web, data and information integration, peer-to-peer data management, and ontology-based data access. An important requirement there is the ability to answer complex queries beyond instance retrieval, taking into account constraints expressed in a knowledge base. We consider this task for positive 2-way regular path queries (P2RPQs) over knowledge bases in the expressive DL ZIQ. P2RPQs are more general than conjunctive queries, union of conjunctive queries, and regular path queries from the literature. They allow regular expressions over roles and data joins that require inverse paths. The DL ZIQ extends the core DL ALC with qualified number restrictions, inverse roles, safe Boolean role expressions, regular expressions over roles, and concepts of the form ∃S.Self in the style of the DL SRIQ. Using techniques based on two-way tree-automata, we first provide as a stepping stone an elegant characterization of TBox and ABox satisfiability testing which gives us a tight ExpTime bound for this problem (under unary number encoding). We then establish a double exponential upper bound for answering P2RPQs over ZIQ knowledge bases; this bound is tight. Our result significantly pushes the frontier of 2ExpTime decidability of query answering in expressive DLs, both with respect to the query language and the considered DL. Furthermore, by reducing the well known DL SRIQ to ZIQ (with an exponential blow-up in the size of the knowledge base), we also provide a tight 2ExpTime upper bound for knowledge base satisfiability in SRIQ and establish the decidability of query answering for this significant fragment of the new OWL 2 standard.
Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
Among the most expressive knowledge representation formalisms are the description logics of the Z family. For well-behaved fragments of ZOIQ, entailment of positive two-way regular path queries is well known to be 2EXPTIME-complete under the proviso of unary encoding of numbers in cardinality constraints. We show that this assumption can be dropped without an increase in complexity and EXPTIME-completeness can be achieved when bounding the number of query atoms, using a novel reduction from query entailment to knowledge base satisfiability. These findings allow to strengthen other results regarding query entailment and query containment problems in very expressive description logics. Our results also carry over to GC2, the two-variable guarded fragment of first-order logic with counting quantifiers, for which hitherto only conjunctive query entailment has been investigated.
Containment of regular path queries under description logic constraints
2011
Abstract Query containment has been studied extensively in KR and databases, for different kinds of query languages and domain constraints. We address the longstanding open problem of containment under expressive description logic (DL) constraints for two-way regular path queries (2RPQs) and their conjunctions, which generalize conjunctive queries with the ability to express regular navigation. We show that, surprisingly, functionality constraints alone make containment of 2RPQs already EXPTIME-hard.
Characterizing Data Complexity for Conjunctive Query Answering In Expressive Description Logics
PROCEEDINGS OF THE NATIONAL …, 2006
Description Logics (DLs) are the formal foundations of the standard web ontology languages OWL-DL and OWL-Lite. In the Semantic Web and other domains, ontologies are increasingly seen also as a mechanism to access and query data repositories. This novel context poses an original combination of challenges that has not been addressed before: (i) sufficient expressive power of the DL to capture common data modeling constructs; (ii) well established and flexible query mechanisms such as Conjunctive Queries (CQs); (iii) optimization of inference techniques with respect to data size, which typically dominates the size of ontologies. This calls for investigating data complexity of query answering in expressive DLs. While the complexity of DLs has been studied extensively, data complexity has been characterized only for answering atomic queries, and was still open for answering CQs in expressive DLs. We tackle this issue and prove a tight CONP upper bound for the problem in SHIQ, as long as no transitive roles occur in the query. We thus establish that for a whole range of DLs from AL to SHIQ, answering CQs with no transitive roles has CONP-complete data complexity. We obtain our result by a novel tableaux-based algorithm for checking query entailment, inspired by the one in , but which manages the technical challenges of simultaneous inverse roles and number restrictions (which leads to a DL lacking the finite model property).
Practical reasoning for expressive description logics
1999
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles, role hierarchies, and qualifying number restrictions. Early experiments indicate that this algorithm is well-suited for implementation.
Finite Query Answering in Expressive Description Logics with Transitive Roles
ArXiv, 2018
We study the problem of finite ontology mediated query answering (FOMQA), the variant of OMQA where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We adopt the most typical setting with unions of conjunctive queries and ontologies expressed in description logics (DLs). The study of FOMQA is relevant in settings that are not finitely controllable. This is the case not only for DLs without the finite model property, but also for those allowing transitive role declarations. When transitive roles are allowed, evaluating queries is challenging: FOMQA is undecidable for SHOIF and only known to be decidable for the Horn fragment of ALCIF. We show decidability of FOMQA for three proper fragments of SOIF: SOI, SOF, and SIF. Our approach is to characterise models relevant for deciding finite query entailment. Relying on a certain regularity of these models, we develop automata-based decision procedures with optimal complexity bounds.
Conjunctive queries for a tractable fragment of OWL 1.1
The Semantic Web, 2007
Despite the success of the Web Ontology Language OWL, the development of expressive means for querying OWL knowledge bases is still an open issue. In this paper, we investigate how a very natural and desirable form of queries-namely conjunctive ones-can be used in conjunction with OWL such that one of the major design criteria of the latter-namely decidability-can be retained. More precisely, we show that querying the tractable fragment EL ++ of OWL 1.1 is decidable. We also provide a complexity analysis and show that querying unrestricted EL ++ is undecidable.
Finite Entailment of UCRPQs over ALC Ontologies
arXiv (Cornell University), 2022
We investigate the problem of finite entailment of ontologymediated queries. We consider the expressive query language, unions of conjunctive regular path queries (UCR-PQs), extending the well-known class of union of conjunctive queries, with regular expressions over roles. We look at ontologies formulated using the description logic ALC, and show a tight 2EXPTIME upper bound for entailment of UCR-PQs. At the core of our decision procedure, there is a novel automata-based technique introducing a stratification of interpretations induced by the deterministic finite automaton underlying the input UCRPQ.
Reducing OWL entailment to description logic satisfiability
2003
We show how to reduce ontology entailment for the OWL DL and OWL Lite ontology languages to knowledge base satisfiability in (respectively) the SHOIN SHOIN (D) and SHIF SHIF (D) description logics. This is done by first establishing a correspondence between OWL ontologies and description logic knowledge bases and then by showing how knowledge base entailment can be reduced to knowledge base satisfiability.