RDF to Conceptual Graphs Translations

International audienceIn this paper we will discuss two different translations between RDF (Resource Description Format) and Conceptual Graphs (CGs). These translations will allow tools like Cogui and Cogitant to be able to import and export RDF(S) documents. The first translation is sound and complete from a reasoning view point but is not visual nor a representation in the spirit of Conceptual Graphs (CGs). The second translation has the advantage of being natural and fully exploiting the CG features, but, on the other hand it does not apply to the whole RDF(S). We aim this paper as a preliminary report of ongoing work looking in detail at different pro and the cons of each approach

Bringing existential variables in answer set programming and bringing non-monotony in existential rules: two sides of the same coin

This article deals with the combination of ontologies and rules by means of existential rules and answer set programming. Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Furthermore Answer Set Programming (ASP) is an appropriate formalism to represent various problems issued from Artificial Intelligence and arising when available information is incomplete. The combination of the two formalisms requires to extend existential rules with nonmonotonic negation and to extend ASP with existential variables. In this article, we present the syntax and semantics of Existential Non Monotonic Rules (ENM-rules) using skolemization which join together the two frameworks. We formalize its links with standard ASP. Moreover, since entailment with existential rules is undecidable, we present conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase and we discuss extension of these results in the nonmonotonic case

Simple conceptual graphs revisited: hypergraphs and conjunctive types for efficient projection algorithms

baget2003aInternational audienceSimple Conceptual Graphs (SGs) form the cornerstone for the "Conceptual Graphs" family of languages. In this model, the subsumptio operation is called projection; it is a labelled graphs homomorphism (a NP-hard problem). Designing efficient algorithms to compute projections between two SGs is thus of uttermost importance for the community building languages on top of this basic model. This paper presents some such algorithms, inspired by those developped for Constraint Satisfaction Problems. In order to benefit from the optimization work done in this community, we have chosen to present an alternate version of SGs, differences being the definition of these graphs as hypergraphs and the use of conjunctive types

Towards Efficient Reasoning under Guarded-based Disjunctive Existential Rules

International audienceThe complete picture of the complexity of answering (unions of) conjunctive queries under the main guarded-based classes of disjunc- tive existential rules has been recently settled. It has been shown that the problem is very hard, namely 2ExpTime-complete, even for fixed sets of rules expressed in lightweight formalisms. This gives rise to the question whether its complexity can be reduced by restricting the query language. Several subclasses of conjunctive queries have been proposed with the aim of reducing the complexity of classical database problems such as query evaluation and query containment. Three of the most prominent subclasses of this kind are queries of bounded hypertree-width, queries of bounded treewidth and acyclic queries. The central objective of the present paper is to understand whether the above query languages have a positive impact on the complexity of query answering under the main guarded-based classes of disjunctive existential rules. We show that (unions of) conjunctive queries of bounded hypertree- width and of bounded treewidth do not reduce the complexity of our problem, even if we focus on predicates of bounded arity, or on fixed sets of disjunctive existential rules. Regarding acyclic queries, although our problem remains 2ExpTime-complete in general, in some relevant set- tings the complexity reduces to ExpTime-complete; in fact, this requires to bound the arity of the predicates, and for some expressive guarded- based formalisms, to fix the set of rules

Default Conceptual Graph Rules, Atomic Negation and Tic-Tac-Toe

International audienceIn this paper, we explore the expressivity of default CG rules (a CG-oriented subset of Reiter's default logics) through two applications. In the first one, we show that default CG rules provide a unifying framework for CG rules as well as polarized CGs (CGs with atomic negation). This framework allows us to study decidable subclasses of a new language mixing CG rules with atomic negation. In the second application, we use default CG rules as a formalism to model a game, an application seldom explored by the CG community. This model puts into light the conciseness provided by defaults, as well as the possibilities they offer to achieve efficient reasonings

Introducing graph-based reasoning into a knowledge management tool: An industrial case study

Abstract. This paper is devoted to an industrial case study focused on the issue of how to enhance ITM, a knowledge management tool, with reasoning capabilities, primarily by introducing a semantic query mechanism. ITM knowledge representation language is based on topic maps. We show that these topic maps (and especially those describing the domain ontology and the annotation base) can be naturally mapped to the SG family, a sublanguage of conceptual graphs. As this mapping is reversible, ITM can be equipped with a graph-based query language equivalent to conjunctive queries and it can be enriched with inference rules.

Towards Farsighted Dependencies for Existential Rules

International audienceWe consider existential rules (also called Tuple-Generating Dependencies or Datalog+/- rules). These rules are particularly well-suited to the topical ontological query answering problem, which consists of querying data while taking terminological knowledge into account. Since this problem is not decidable in general, various conditions ensuring decidability have been proposed in the literature. In this paper, we focus on conditions that restrict the way rules may interact to ensure that the forward chaining mechanism is finite. After a review of existing proposals, we propose a generalization of the notion of rule dependency, namely k-dependency, that allows to enlarge halting cases. It can also be used to compile the rule base, which leads to improve query answering algorithms

Concrete Results on Abstract Rules

Abstract. There are many different notions of “rule ” in the literature. A key feature and main intuition of any such notion is that rules can be “applied ” to derive conclusions from certain premises. More formally, a rule is viewed as a function that, when invoked on a set of known facts, can produce new facts. In this paper, we show that this extreme simplification is still sufficient to obtain a number of useful results in concrete cases. We define abstract rules as a certain kind of functions, provide them with a semantics in terms of (abstract) stable models, and explain how concrete normal logic programming rules can be viewed as abstract rules in a variety of ways. We further analyse dependencies between abstract rules to recognise classes of logic programs for which stable models are guaranteed to be unique.

Ontological Query Answering with Existential Rules

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. To tackle this problem, we consider a logical framework based on existential rules, also called Tuple-Generating Dependencies or Datalog+/- rules. This framework can also be defined in graph terms. Query entailment with existential rules is not decidable, thus a crucial issue is to define decidable classes of rules as large as possible. This paper is a survey of decidable classes of rules, including a review of the main complexity results. It mostly relies on previous work presented at IJCAI’2009 [BLMS09] and KR’2010 [BLM10] (and developed in a journal paper [BLMS11]), updated to include very recent results