Michel Leclère

A sound and complete backward chaining algorithm for existential rules

We address the issue of Ontology-Based Data Access which consists of exploiting the semantics expressed in ontologies while querying data. Ontologies are represented in the framework of existential rules, also known as Datalog+/-. We focus on the backward chaining paradigm, which involves rewriting the query (assumed to be a conjunctive query, CQ) into a set of CQs (seen as a union of CQs). The proposed algorithm accepts any set of existential rules as input and stops for so-called finite unification sets of rules (fus). The rewriting step relies on a graph notion, called a piece, which allows to identify subsets of atoms from the query that must be processed together. We first show that our rewriting method computes a minimal set of CQs when this set is finite, i.e., the set of rules is a fus. We then focus on optimizing the rewriting step. First experiments are reported.

Griwes: Generic Model and Preliminary Specifications for a Graph-Based Knowledge Representation Toolkit

Griwes is an initiative to develop a common model and an open-source freeware platform shared by different graph-based frameworks. We provide an overview of its objectives, architecture and specifications. We detail some of the basic mathematical structures that are used to characterize the primitives for graph-based knowledge representation. We then propose to factorize recurrent knowledge representation primitives that can be shared across specific graph-based languages and we provide a proof of concept by showing how two languages (Simple Conceptual Graphs and RDF) can be described in this framework.

On querying simple conceptual graphs with negation

We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of first-order logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG Q to a SG G means that the knowledge represented by Q is deducible from the knowledge represented by G. In this framework, a knowledge base is composed of SGs representing facts and a query is itself a SG. We focus on the issue of querying SGs, which highlights another fundamental problem, namely query answering. Each projection from a query to a fact defines an answer to the query, with an answer being itself a SG. The query answering problem asks for all answers to a query. This paper introduces atomic negation into this framework. Several understandings of negation are explored, which are all of interest in real world applications. In particular, we focus on situations where, in the context of incomplete knowledge, classical negation is not satisfactory because deduction can be proven but there is no answer to the query. We show that intuitionistic deduction captures the notion of an answer and can be solved by projection checking. Algorithms are provided for all studied problems. They are all based on projection. They can thus be combined to deal with several kinds of negation simultaneously. Relationships with problems on conjunctive queries in databases are recalled and extended. Finally, we point out that this discussion can be put in the context of semantic web databases.

Graal: A Toolkit for Query Answering with Existential Rules

This paper presents Graal, a java toolkit dedicated to ontological query answering in the framework of existential rules. We consider knowledge bases composed of data and an ontology expressed by existential rules. The main features of Graal are the following: a basic layer that provides generic interfaces to store and query various kinds of data, forward chaining and query rewriting algorithms, structural analysis of decidability properties of a rule set, a textual format and its parser, and import of OWL 2 files. We describe in more detail the query rewriting algorithms, which rely on original techniques, and report some experiments.

Translations between RDF(S) and conceptual graphs

Though similarities between the Semantic Web language RDF(S) and languages of the Conceptual Graphs family have often been pointed out, the differences between these formalisms have been a source of difficulties while trying to translate objets of a language into the other. In this paper, we present two such transformations, that have been implemented into the CoGUI platform, and discuss their respective strengths and weaknesses.

On the exploration of the query rewriting space with existential rules

We address the issue of Ontology-Based Data Access, with ontologies represented in the framework of existential rules, also known as Datalog+/-. A well-known approach involves rewriting the query using ontological knowledge. We focus here on the basic rewriting technique which consists of rewriting a conjunctive query (CQ) into a union of CQs. We assume that the set of rules is a finite unification set, i.e., for any CQ, there exists a finite sound and complete rewriting of this CQ with the rules. First, we study a generic breadth-first rewriting algorithm, which takes as input any rewriting operator. We define properties of the rewriting operator that ensure the correctness and the termination of this algorithm. Second, we study some operators with respect to the exhibited properties. All these operators have in common to be based on so-called piece-unifiers but they lead to different explorations of the rewriting space. Finally, an experimental comparison of these operators within an implementation of the generic breadth-first rewriting algorithm is presented.

Some algorithmic improvements for the containment problem of conjunctive queries with negation

Query containment is a fundamental problem of databases. Given two queries q1 and q2, it asks whether the set of answers to q1 is included in the set of answers to q2 for any database. In this paper, we investigate this problem for conjunctive queries with negated subgoals. We use graph homomorphism as the core notion, which leads us to extend the results presented in [Ull97] and [WL03]. First, we exhibit sufficient (but not necessary) conditions for query containment based on special subgraphs of q2, which generalize that proposed in [WL03]. As a corollary, we obtain a case where the time complexity of the problem decreases. From a practical viewpoint, these properties can be exploited in algorithms, as shown in the paper. Second, we propose an algorithm based on the exploration of a space of graphs, which improves existing algorithms.

Sound, Complete and Minimal UCQ-Rewriting for Existential Rules

We address the issue of Ontology-Based Data Access, with ontologies represented in the framework of existential rules, also known as Datalog+/-. A well-known approach involves rewriting the query using ontological knowledge. We focus here on the basic rewriting technique which consists of rewriting the initial query into a union of conjunctive queries. First, we study a generic breadth-first rewriting algorithm, which takes as input any rewriting operator, and define properties of rewriting operators that ensure the correctness of the algorithm. Then, we focus on piece-unifiers, which provide a rewriting operator with the desired properties. Finally, we propose an implementation of this framework and report some experiments.

Introducing reasoning into an industrial knowledge management tool

Abstract This paper is devoted to an industrial case study focused on the issue of how to enhance an existing knowledge management tool (ITM) with reasoning capabilities, by introducing a semantic query mechanism as well as validation and inference services. ITM knowledge representation language is based on topic maps. We show that these topic maps (and especially those describing the domain ontology and annotation base) can be naturally mapped to the

Defining Key Semantics for the RDF Datasets: Experiments and Evaluations

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