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

Ontology-Mediated Queries for NOSQL Databases

This paper is an extended abstract of the paper with the same title presented at AAAI 2016.International audienceOntology-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

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

Query Rewriting with Disjunctive Existential Rules and Mappings

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.Comment: This report contains the paper accepted at KR 2023 and an appendix with full proofs. 24 page

Supporting Argumentation Systems by Graph Representation and Computation

International audienceArgumentation is a reasoning model based on arguments and on attacks between arguments. It consists in evaluating the acceptability of arguments, according to a given semantics. Due to its generality, Dung's framework for abstract argumentation systems, proposed in 1995, is a reference in the domain. Argumentation systems are commonly represented by graph structures, where nodes and edges respectively represent arguments and attacks between arguments. However beyond this graphical support, graph operations have not been considered as reasoning tools in argumentation systems. This paper proposes a conceptual graph representation of an argumentation system and a computation of argument acceptability relying on conceptual graph default rules

First IJCAI International Workshop on Graph Structures for Knowledge Representation and Reasoning (GKR@IJCAI'09)

International audienceThe development of effective techniques for knowledge representation and reasoning (KRR) is a crucial aspect of successful intelligent systems. Different representation paradigms, as well as their use in dedicated reasoning systems, have been extensively studied in the past. Nevertheless, new challenges, problems, and issues have emerged in the context of knowledge representation in Artificial Intelligence (AI), involving the logical manipulation of increasingly large information sets (see for example Semantic Web, BioInformatics and so on). Improvements in storage capacity and performance of computing infrastructure have also affected the nature of KRR systems, shifting their focus towards representational power and execution performance. Therefore, KRR research is faced with a challenge of developing knowledge representation structures optimized for large scale reasoning. This new generation of KRR systems includes graph-based knowledge representation formalisms such as Bayesian Networks (BNs), Semantic Networks (SNs), Conceptual Graphs (CGs), Formal Concept Analysis (FCA), CPnets, GAI-nets, all of which have been successfully used in a number of applications. The goal of this workshop is to bring together the researchers involved in the development and application of graph-based knowledge representation formalisms and reasoning techniques

Parallelisable Existential Rules: a Story of Pieces

International audienceIn this paper, we consider existential rules, an expressive formalism well suited to the representation of ontological knowledge and 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

A General Modifier-based Framework for Inconsistency-Tolerant Query Answering

We propose a general framework for inconsistency-tolerant query answering within existential rule setting. This framework unifies the main semantics proposed by the state of art and introduces new ones based on cardinality and majority principles. It relies on two key notions: modifiers and inference strategies. An inconsistency-tolerant semantics is seen as a composite modifier plus an inference strategy. We compare the obtained semantics from a productivity point of view