In ontology-based data access (OBDA), multiple data sources are integrated via mappings to an ontology. We consider an OBDA setting based on existential rules and the certain answer semantics. We address the recent issue of query abstraction, which consists of abstracting data queries by translating them to the ontology layer. Since a perfect abstraction may not exist, the notions of minimally complete and maximally sound abstractions have been introduced. We study abstractions within an extension of UCQs with a limited form of inequality and a special predicate marking database constants. While this extension does not lead to an increased complexity of the problems of interest, it is able to express minimally complete abstractions, hence perfect abstractions when they exist. We also characterize maximally sound abstractions by making a new connection with the notion of maximum recovery stemming from data exchange.

We consider the issue of answering unions of conjunctive queries (UCQs) with disjunctive existential rules and mappings. While this issue has already been well studied from a chase perspective, query rewriting within UCQs has hardly been addressed yet. We first propose a sound and complete query rewriting operator, which has the advantage of establishing a tight relationship between a chase step and a rewriting step. The associated breadth-first query rewriting algorithm outputs a minimal UCQ-rewriting when one exists. Second, we show that for any ``truly disjunctive'' nonrecursive rule, there exists a conjunctive query that has no UCQ-rewriting. It follows that the notion of finite unification sets (fus), which denotes sets of existential rules such that any UCQ admits a UCQ-rewriting, seems to have little relevance in this setting. Finally, turning our attention to mappings, we show that the problem of determining whether a UCQ admits a UCQ-rewriting through a disjunctive mapping is undecidable. We conclude with a number of open problems.

The core chase, a popular algorithm for answering conjunctive queries (CQs) over existential rules, is guaranteed to terminate and compute a finite universal model whenever one exists, leading to the equivalence of the universal-model-based and the chase-based definitions of finite expansion sets (fes) -- a class of rulesets featuring decidable CQ entailment. In case of non-termination, however, it is non-trivial to define a ''result'' of the core chase, due to its non-monotonicity. This causes complications when dealing with advanced decidability criteria based on the existence of (universal) models of finite treewidth. For these, sufficient chase-based conditions have only been established for weaker, monotonic chase variants. This paper investigates the -- prima facie plausible -- hypothesis that the existence of a treewidth-bounded universal model and the existence of a treewidth-bounded core-chase sequence coincide -- which would conveniently entail decidable CQ entailment whenever the latter holds. Perhaps surprisingly, carefully crafted examples show that both directions of this hypothesized correspondence fail. On a positive note, we are still able to define an aggregation scheme for the infinite core chase that preserves treewidth bounds and produces a finitely universal model, i.e., one that satisfies exactly the entailed CQs. This allows us to prove that the existence of a treewidth-bounded core-chase sequence does warrant decidability of CQ entailment (yet, on other grounds than expected). Hence, for the first time, we are able to define a chase-based notion of bounded treewidth sets of rules that subsumes fes.

Data trees, typically encoded in JSON, are ubiquitous in data-driven applications. This ubiquity makes urgent the development of novel techniques for querying heterogeneous JSON data in a flexible manner. We propose a rule language for JSON, called constrained tree-rules, whose purpose is to provide a high-level unified view of heterogeneous JSON data and infer implicit information. As reasoning with constrained tree-rules is undecidable, we identify a relevant subset featuring tractable query answering, for which we design an automata-based query rewriting algorithm. Our approach consists of leveraging NoSQL document stores by means of a novel instance-aware query-rewriting technique. We present an extensive experimental analysis on large collections of several million JSON records. Our results show the importance of instance-aware rewriting as well as the efficiency and scalability of our approach.

In this paper, we consider existential rules, an expressive formalism well adapted to the representation of ontological knowledge, as well as data-to-ontology mappings in the context of ontology-based data integration. The chase is a fundamental tool to do reasoning with existential rules as it computes all the facts entailed by the rules from a database instance. We introduce parallelisable sets of existential rules, for which the chase can be computed in a single breadth-first step from any instance. The question we investigate is the characterization of such rule sets. We show that parallelisable rule sets are exactly those rule sets both bounded for the chase and belonging to a novel class of rules, called pieceful. The pieceful class includes in particular frontier-guarded existential rules and (plain) datalog. We also give another characterization of parallelisable rule sets in terms of rule composition based on rewriting.

Abstract Existential 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.

International audience

We consider the problem of integrating heterogeneous data (relational, JSON, key-values, graphs etc.) and querying it efficiently. Traditional data integration systems fall into two classes: data warehousing , where all data source content is materialized in a single repository, and mediation , where data remains in their original stores and all data can be queried through a mediator. We propose to demonstrate Obi-Wan, a novel mediator following the Ontology-Based Data access (OBDA) paradigm. Obi-Wan integrates data sources of many data models under an interface based on RDF graphs and ontologies (classes, properties, and relations between them). The novelty of Obi-Wan is to combine maximum integration power (GLAV mappings, see below) with the highest query answering power supported by an RDF mediator: RDF queries not only over the data but also over the integration ontologies. This makes it more flexible and powerful than comparable systems.

Query answering in RDF knowledge bases has traditionally been performed either through graph saturation, i.e., adding all implicit triples to the graph, or through query reformulation, i.e., modifying the query to look for the explicit triples entailing precisely what the original query asks for. The most expressive fragment of RDF for which Reformulation-based query answering exists is the so-called database fragment [ 13 ], in which implicit triples are restricted to those entailed using an RDFS ontology. Within this fragment, query answering was so far limited to the interrogation of data triples (non-RDFS ones); however, a powerful feature specific to RDF is the ability to query data and schema triples together. In this paper, we address the general query answering problem by reducing it, through a pre-query reformulation step, to that solved by the query reformulation technique of [ 13 ]. We also report on experiments demonstrating the low cost of our reformulation algorithm.

Existential rules, long known as tuple-generating dependencies in database theory, have been intensively studied in the last decade as a powerful formalism to represent ontological knowledge in the context of ontology-based query answering. A knowledge base is then composed of an instance that contains incomplete data and a set of existential rules, and answers to queries are logically entailed from the knowledge base. This brought again to light the fundamental chase tool, and its different variants that have been proposed in the literature. It is well-known that the problem of determining, given a chase variant and a set of existential rules, whether the chase will halt on any instance, is undecidable. Hence, a crucial issue is whether it becomes decidable for known subclasses of existential rules. In this work, we consider linear existential rules with atomic head, a simple yet important subclass of existential rules that generalizes inclusion dependencies. We show the decidability of the all-instance chase termination problem on these rules for three main chase variants, namely semi-oblivious, restricted and core chase. To obtain these results, we introduce a novel approach based on so-called derivation trees and a single notion of forbidden pattern. Besides the theoretical interest of a unified approach and new proofs for the semi-oblivious and core chase variants, we provide the first positive decidability results concerning the termination of the restricted chase, proving that chase termination on linear existential rules with atomic head is decidable for both versions of the problem: Does every chase sequence terminate? Does some chase sequence terminate?

We study the notion of boundedness in the context positive existential rules, that is, wether there exists an upper bound to the depth of the chase procedure, that is independent from the initial instance. By focussing our attention on the oblivious and the semi-oblivious chase variants, we give a characterization of boundedness in terms of FO-rewritability and chase termination. We show that it is decidable to recognize if a set of rules is bounded for several classes of rules and outline the complexity of the problem.

Ontology-mediated query answering is concerned with the problem of answering queries over knowledge bases consisting of a database instance and an ontology. While most work in the area focuses on conjunctive queries, navigational queries are gaining increasing attention. In this paper, we investigate the complexity of answering two-way conjunctive regular path queries (CRPQs) over knowledge bases whose ontology is given by a set of guarded existential rules. We first consider the subclass of linear existential rules and show that CRPQ answering is EXPTIME-complete in combined complexity and NL-complete in data complexity, matching the recently established bounds for answering non-conjunctive RPQs. For guarded rules, we provide a non-trivial reduction to the linear case, which allows us to show that the complexity of CRPQ answering is the same as for plain conjunctive queries, namely, 2EXPTIME-complete in combined complexity and PTIME-complete in data complexity.

We propose a novel rule-based ontology language for JSON records and investigate its computational properties. After providing a natural translation into first-order logic, we identify relationships to existing ontology languages, which yield decidability of query answering but only rough complexity bounds. By establishing an interesting and non-trivial connection to word rewriting, we are able to pinpoint the exact combined complexity of query answering in our framework and obtain tractability results for data complexity. The upper bounds are proven using a query reformulation technique, which can be implemented on top of key-value stores, thereby exploiting their querying facilities.

Ontology-Based Data Access has been studied so far for relational structures and deployed on top of relational databases. This paradigm enables a uniform access to heterogeneous data sources, also coping with incomplete information. Whether OBDA is suitable also for non-relational structures, like those shared by increasingly popular NOSQL languages, is still an open question. In this paper, we study the problem of answering ontology-mediated queries on top of key-value stores. We formalize the data model and core queries of these systems, and introduce a rule language to express lightweight ontologies on top of data. We study the decidability and data complexity of query answering in this setting.

Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. 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. First, we propose a new tool that allows to extend existing acyclicity conditions ensuring chase termination, while keeping good complexity properties. Second, we consider the extension to existential rules with nonmonotonic negation under stable model semantics and further extend acyclicity results obtained in the positive case.

International audience

Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given in terms of positive, conjunctive, existential FOL. We present here a family of extensions of this model, based on rules and constraints, keeping graph homomorphism as the basic operation. We focus on the formal definitions of the different models obtained, including their operational semantics and relationships with FOL, and we analyze the decidability and complexity of the associated problems (consistency and deduction). As soon as rules are involved in reasonings, these problems are not decidable, but we exhibit a condition under which they fall in the polynomial hierarchy. These results extend and complete the ones already published by the authors. Moreover we systematically study the complexity of some particular cases obtained by restricting the form of constraints and/or rules.

We study the expressiveness of Nested Graphs, an extension of conceptual graphs. Nesting is introduced as a formal version of the intuitive “zooming in” on descriptions of individuals. Projections are defined inductively as the formal tool for “reasoning with nested graphs.” Nested graphs are translated to “colored” formulas. Coloring represents anaphoras in a way similar to conceptual graphs. A system of Gentzen sequents is shown to be adequate and complete with respect to projections of nested graphs.

This paper centres on the generalization/specialization relation in the framework of conceptual graphs (this relation corresponds to logical subsumption when considering logical formulas associated with conceptual graphs). Results given here apply more generally to any model where knowledge is described by labelled graphs and reasoning is based on graph subsumption, as in semantic networks or in structural machine learning. The generalization/specialization relation, as defined by Sowa, is first precisely analysed, in particular its links with a graph morphism, called projection. Besides Sowa's specialization relation (which is a preorder), another one is actually used in some practical applications (which is an order). These are comparatively studied. The second topic of this paper is the design of efficient algorithms for computing these specialization relations. Since the associated problems are NP-hard, the form of the graphs is restricted in order to arrive at polynomial algorithms. In particular, polynomial algorithms are presented for computing a projection from a conceptual ‘tree’ to any conceptual graph, and for counting the number of such projections. The algorithms are also described in a generic way, replacing the projection by a parametrized graph morphism, and conceptual graphs by directed labelled graphs.

Previous studies concerning multiple inheritance convinced us that a better analysis of conflict resolution mechanisms was necessary. In [DHHM92], we stated properties that a sound mechanism has to respect. Among them, a monotonicity principle plays a critical role, ensuring that the inheritance mechanism behaves “naturally” relative to the incremental design of the inheritance hierarchy. We focus here on linearizations and present an intrinsically monotonic linearization, whereas currently used linearizations are not. This paper describes the algorithm in detail, explains the design choices, and compares it to other linearizations, with LOOPS and CLOS taken as references. In particular, this new linearization extends CLOS and LOOPS linearizations, producing the same results when these linearizations are sound.

The main topic of this paper is multiple inheritance and conflict resolution methods in Object Oriented Programming. Our aim is to develop sound mechanisms easily understandable to any user. For this purpose, coherent behaviors of conflict resolution methods for multiple inheritance (such as supporting incrementality-monotonicity and stability under link subdivision) are introduced. We present interesting examples in which multiple inheritance known linearization algorithms (such as in CLOS [2] and LOOPS [19]) behave badly. Then we carefully study the conditions (on the inheritance graph) which assure good linearizations. We end with some suggestions for an incremental inheritance algorithm.