Ontology-mediated Query Answering Research Articles

Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic

Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC0, ACC0 and NC1 coincides with FO(<,≡)-rewritability using unary predicates x ≡ 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We prove that, similarly to known PSᴘᴀᴄᴇ-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,≡)- and FO(<,MOD)-definability is also PSᴘᴀᴄᴇ-complete (unless ACC0 = NC1). We then use this result to show that deciding FO(<)-, FO(<,≡)- and FO(<,MOD)-rewritability of LTL OMQs is ExᴘSᴘᴀᴄᴇ-complete, and that these problems become PSᴘᴀᴄᴇ-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,≡)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSᴘᴀᴄᴇ-, Π2p- and coNP-complete.

Comparative Analysis of Logic Reasoning and Graph Neural Networks for Ontology-Mediated Query Answering With a Covering Axiom

Comparative Analysis of Logic Reasoning and Graph Neural Networks for Ontology-Mediated Query Answering With a Covering Axiom

Answering regular path queries mediated by unrestricted [formula omitted] ontologies

A prime application of description logics is ontology-mediated query answering, with the query language often reaching far beyond instance queries. Here, we investigate this task for positive existential two-way regular path queries and ontologies formulated in the expressive description logic SQu, where SQu denotes the extension of the basic description logic ALC with transitive roles (S) and qualified number restrictions (Q) which can be unrestrictedly applied to both non-transitive and transitive roles (⋅u). Notably, the latter is usually forbidden in expressive description logics. As the main contribution, we show decidability of ontology-mediated query answering in that setting and establish tight complexity bounds, namely 2ExpTime-completeness in combined complexity and coNP-completeness in data complexity. Since the lower bounds are inherited from the fragment ALC, we concentrate on providing upper bounds. As main technical tools we establish a tree-like countermodel property and a characterization of when a query is not satisfied in a tree-like interpretation. Together, these results allow us to use an automata-based approach to query answering.

Preference-based inconsistency-tolerant query answering under existential rules

Ontology-mediated query answering (OMQA) emerged as a paradigm to enhance querying of data sources with an ontology that encodes background knowledge. In applications involving large amounts of data from multiple data sources, it might well be the case that inconsistency arises, making standard query answering useless, since everything is entailed by an inconsistent knowledge base. Being able to provide meaningful query answers in the presence of inconsistency is thus a critical issue to make OMQA systems successful in practice. The problem of querying inconsistent knowledge has attracted a great deal of interest over the years. Different inconsistency-tolerant semantics of query answering have been proposed, that is, approaches to answer queries in a meaningful way despite the knowledge at hand being inconsistent. Most of the semantics in the literature are based on the notion of repair, that is, a “maximal” consistent subset of the database. In general, there can be several repairs, so it is often natural and desirable to express preferences among them. In this paper, we propose a framework for querying inconsistent knowledge bases under user preferences for existential rule languages. Specifically, we introduce preference rules, a declarative formalism which enable users to express (i) preferences over both the database and the knowledge that can be derived from it via an ontology, and (ii) preconditions for preferences to hold. We then define two notions of preferred repairs which take preference rules into account. This naturally leads us to introducing preference-aware counterparts of popular inconsistency-tolerant semantics, where only preferred repairs are considered for query answering. We provide a thorough analysis of the data and combined complexity of different relevant problems for a wide range of existential rule languages.

Characterizing the Program Expressive Power of Existential Rule Languages

Existential rule languages are a family of ontology languages that have been widely used in ontology-mediated query answering (OMQA). However, for most of them, the expressive power of representing domain knowledge for OMQA, known as the program expressive power, is not well-understood yet. In this paper, we establish a number of novel characterizations for the program expressive power of several important existential rule languages, including tuple-generating dependencies (TGDs), linear TGDs, as well as disjunctive TGDs. The characterizations employ natural model-theoretic properties, and automata-theoretic properties sometimes, which thus provide powerful tools for identifying the definability of domain knowledge for OMQA in these languages.

Efficient Datalog Rewriting for Query Answering in TGD Ontologies

Tuple-generating dependencies (TGDs or existential rules) are an expressive constraint language for ontology-mediated query answering and thus query answering is of high complexity. Existing systems based on first-order rewriting methods can lead to queries too large for DBMS to handle. It is shown that datalog rewriting can result in more compact queries, yet previously proposed datalog rewriting methods are mostly inefficient for implementation. In this paper, we fill the gap by proposing an efficient datalog rewriting approach for answering conjunctive queries over TGDs, and identify and combine existing fragments of TGDs for which our rewriting method terminates. We implemented a prototype system Drewer, and experiments show that it is able to handle a wide range of benchmarks in the literature. Moreover, Drewer shows superior performance over state-of-the-art systems on both the compactness of rewriting and the efficiency of query answering.

Ontology-Mediated SPARQL Query Answering over Knowledge Graphs

Abstract Ontology-Mediated Query Answering (OMQA) is a well-established framework to answer queries over Knowledge Graphs (KGs), enriched with rdfs or owl ontologies. OMQA was originally designed for Unions of Conjunctive Queries (UCQs), and based on certain answers. More recently, OMQA has been extended to sparql queries, but to our knowledge, none of the efforts made in this direction (either in the literature, or the so-called W3C sparql entailment regimes) is able to capture both certain answers for UCQs and the standard interpretation of sparql over a plain graph. We formalize these as requirements to be met by any semantics that aims at conciliating certain answers and sparql answers, and extend these with three additional requirements. Then we define two semantics that satisfies all requirements for sparql queries with select , union , join , and optional . Finally, we investigate the combined complexity of query answering under these semantics over a KG enriched with a DL-Lite R ontology, showing that for several fragments of sparql , known upper-bounds for query answering over a plain KG are matched.

Deploying spatial-stream query answering in C-ITS scenarios1

Cooperative Intelligent Transport Systems (C-ITS) play an important role for providing the means to collect and exchange spatio-temporal data via V2X-based communication between vehicles and the infrastructure, which will become a central enabler for road safety of (semi)-autonomous vehicles. The Local Dynamic Map (LDM) is a key concept for integrating static and streamed data in a spatial context. The LDM has been semantically enhanced to allow for an elaborate domain model that is captured by a mobility ontology, and for queries over data streams that cater for semantic concepts and spatial relationships. Our approach for semantic enhancement is in the context of ontology-mediated query answering (OQA) and features conjunctive queries over DL-LiteA ontologies that support window operators over streams and spatial relations between spatial objects. In this paper, we show how this approach can be extended to address a wider range of use cases in the three C-ITS scenarios traffic statistics, traffic events detection, and advanced driving assistance systems. We define for the mentioned use cases requirements derived from necessary domain-specific features and report, based on them, on extensions of our query language and ontology model. The extensions include temporal relations, numeric predictions and trajectory predictions as well as optimization strategies such as caching. An experimental evaluation of queries that reflect the requirements has been conducted using the real-world traffic simulation tool PTV Vissim. It provides evidence for the feasibility/efficiency of our approach in the new scenarios.

A Short Survey on Inconsistency Handling in Ontology-Mediated Query Answering

This paper provides a concise overview of the literature on inconsistency handling for ontology-mediated query answering, a topic which has grown into an active area of research over the last decade. The focus of this survey is on the case where errors are localized in the data (i.e., the ontology is deemed reliable) and where inconsistency-tolerant semantics are employed with the aim of obtaining meaningful information from inconsistent knowledge bases.

Rewriting Approaches for Ontology-Mediated Query Answering

A most promising approach to answering queries in ontology-based data access (OBDA) is through query rewriting. In this paper we present novel rewriting approaches for several extensions of OBDA. The goal is to understand their relative expressiveness and to pave the way for efficient query answering algorithms.

Characterizing Boundedness in Chase Variants

AbstractExistential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

Ontology-Mediated Query Answering over Log-Linear Probabilistic Data

Large-scale knowledge bases are at the heart of modern information systems. Their knowledge is inherently uncertain, and hence they are often materialized as probabilistic databases. However, probabilistic database management systems typically lack the capability to incorporate implicit background knowledge and, consequently, fail to capture some intuitive query answers. Ontology-mediated query answering is a popular paradigm for encoding commonsense knowledge, which can provide more complete answers to user queries. We propose a new data model that integrates the paradigm of ontology-mediated query answering with probabilistic databases, employing a log-linear probability model. We compare our approach to existing proposals, and provide supporting computational results.

Ontology-mediated query answering over temporal and inconsistent data

Stream-based reasoning systems process data stemming from different sources that are received over time. In this kind of applications, reasoning needs to cope with the temporal dimension and should be resilient against inconsistencies in the data. Motivated by such settings, this paper addresses the problem of handling inconsistent data in a temporal version of ontology-mediated query answering. We consider a recently proposed temporal query language that combines conjunctive queries with operators of propositional linear temporal logic (LTL), and consider these under three inconsistency-tolerant semantics that have been introduced for querying inconsistent description logic knowledge bases. We investigate their complexity for temporal EL ⊥ and DL-LiteR knowledge bases. In particular, we consider two different cases, depending on the presence of negations in the query. Furthermore, we complete the complexity picture for the consistent case. We also provide two approaches toward practical algorithms for inconsistency-tolerant temporal query answering.