Note that we do not include here the results from Souhila Kaci and Tjitze Rienstra since they joined the team in September 2011.

In collaboration with:Sebastian Rudolph (Karlsruhe Institute of Technology)

We have developed a framework based on rules that have the ability of generating unknown individuals, an ability sometimes called value invention in databases. These rules are of the form body $\to$ head, where the body and the head are conjunctions of atoms (without function symbols except constants) and variables that occur only in the head are existentiallyquantified, hence their name existential rules hereafter. E.g., $\forall x\left(Human\right(x)\to \exists y(isParent(y,x)\wedge Human\left(y\right)\left)\right)$. These rules can be seen as the logical translation of conceptual graph rules, historically a main focus of the team . Existential rules have the same logical form as the well-known Tuple-Generating Dependencies (TGDs) in databases . TGDs have been extensively used as a high-level generalization of different kinds of constraints, e.g., for data exchange . Recently, there has been renewed interest for TGDs seen as rules in the context of ontological query answering. Indeed, the value inventionfeature has been recognized as crucial in an open-world perspective, where it cannot be assumed that all individuals are known in advance. The deductive database language Datalog allows to express some ontological knowledge but it does not allow for value invention. This motivated the recent extension of Datalog to TGDs (i.e., existential rules), which gave rise to the Datalog +/- family , , . In KRR and in the Semantic Web, ontological knowledge is often represented with formalisms based on description logics (DLs). However, DLs traditionally focused on reasoning tasks about the ontology itself (the so-called TBox), for instance classifying concepts; querying tasks were restricted to ground atom entailment. Conjunctive query answering with classical DLs has appeared to be extremely complex, hence less expressive DLs more adapted to conjunctive query answering on large amounts of data have been designed recently, namely DL-Lite , $\mathrm{ℰℒ}$ , , and more generally Horn DLs (see e.g., ), cf. also the tractable profiles of the Semantic Web language OWL2. Existential rules cover the core of lightweight DLs dedicated to query answering, while being more powerful and flexible , , . In particular, they have unrestricted predicate arity (while DLs consider unary and binary predicates only), which allows for a natural coupling with database schemas, in which relations may have any arity; moreover, adding pieces of information, for instance to take contextual knowledge into account, is made easy by the unrestricted predicate arity, since these pieces can be added as new predicate arguments.

Building on our previous work on conceptual graphs, while meeting this new trend, we have developed a knowledge representation framework centered on existential rules, which can be seen both as logic-based and graph-based.

Entailment, hence query answering, with existential rules is not decidable, thus finding decidable classes of rules as expressive as possible is a crucial issue. We have pursued our previous work on better understanding the border between decidability and undecidability. We have also extended rule dependency to k-dependency, which takes into account sequences of rule applications.

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For newly exhibited decidable classes (namely, “frontier-one”, “frontier-guarded” and “weakly-frontier-guarded” rules), the problem complexity was unknown, moreover there was no algorithm for computing entailment. First, we have classified these classes with respect to combined complexity (i.e., usual complexity) with both unbounded and bounded predicate arity, and data complexity (i.e., restricting the input of the decision problem to the facts). An interesting result is that some of the new classes (namely frontier-one and frontier-guarded rules) have a polynomial time data complexity. Secondly, we have provided a generic algorithm for query entailment with a large class of rules including these classes, which is worst-case optimal for combined complexity (with or without bounded predicate arity) as well as for data complexity.

Conjunctive queries have long been recognized as the basic queries in database and knowledge-based systems. The fundamental decision problems on these queries, namely query inclusion checking (given two queries $q_1$and $q_2$, is $q_1$included in $q_2$, i.e., is the set of answers to $q_1$included in the set of answers to $q_2$for all databases) and query entailment (is a given query entailed by the database) are NP-complete. When atomic negation is added to queries and databases, these problems become ${\Pi }_2^P$-complete (with the open world assumption for the query entailment problem). Note that these problems can be recast as entailment in the FOL fragment of existentially closed conjunction of literals (without function symbols except constants). On the one hand, we have led a theoretical complexity study: we have investigated the role of pairs of literals called “exchangeable” (which generalizes the notion of unifiable literals) in the complexity increase. The main results are that when the number of exchangeable pairs is bounded, say by $k$, then the complexity falls from ${\Pi }_2^P$-complete to $P_{\left|\right|}^{NP}$-complete for any $k\ge 3$, and is NP-complete for $k\le 1$(the case $k=2$being open).

In collaboration with:Geneviève Simonet (LIRMM Algeco team)

On the other hand, we have proposed, refined and compared experimentally several algorithms. This study follows first results of us in and is the core of Khalil Ben Mohamed's PhD thesis defended in December 2010 .

Let us point out that both theoretical and practical results still hold when the predicates are preordered, which allows to take very light ontologies into account, i.e., where concepts and relations are organized in a specialization preorder.

In collaboration with:Joël Abecassis (IATE/INRA), Jean-Rémi Bourguet (UM3), Patrice Buche (IATE/INRA), Sébastien Destercke (IATE/CIRAD) Nir Oren (Univ. of Aberdeen, Scotland)

Scientific investigations in this axis are guided by applications of our partners in agronomy (IATE laboratory). Substantial part of the work has consisted of analyzing the proposed applications and the techniques they require in order to select appropriate applications with respect to our team project.

Argumentation is a reasoning model based on the construction and the evaluation of arguments. In his seminal paper, Dung has proposed an abstract argumentation framework . In that framework, arguments are assumed to have the same strength. This assumption is unfortunately strong and often unsatisfied. Consequently, several generalizations of the framework have been proposed in the literature. In and , we have led a comparative study of these generalizations. It clearly shows under which conditions two proposals are equivalent. We have also integrated those generalizations into a common more expressive framework.

An instantiation of Dung's abstract framework with the conceptual graph framework has been proposed. This representation uses default conceptual graph rules, an extension of classical conceptual graph rules (equivalent to existential rules, see Axis 1) with Reiter's defaults allowing for non-monotonic reasoning, that we developed independently of the argumentation framework , . In the conceptual graph representation, arguments are represented as nested graphs, attacks between arguments can be computed from the structure of arguments and default rules allow to compute several kinds of extensions (i.e., maximal sets of arguments jointly acceptable according to a given semantics).

This approach has been applied to agrifood chain analysis, which is a highly complex procedure since it relies on numerous criteria of various types: environmental, economical, functional, sanitary, etc. Quality objectives imply different stakeholders, technicians, managers, professional organizations, end-users, public organizations, etc. Since the goals of the implied stakeholders may be divergent, decision-making raises arbitration issues. Arbitration can be done through a compromise—a solution that satisfies, at least partially, all the actors— or favor some of the actors, depending on the decision-maker's priorities. We have analyzed a case study concerning risks/benefits within the wheat-to-bread chain. It concerns the controversy about the possible change in the ash content of the flour used for commonly used French bread. Several stakeholders of the chain are concerned, in particular the Ministry of Health through its recommendations in a national nutrition and health program, millers, bakers and consumers.

As already pointed out, the proposed approach is novel both for theoretical and application aspects.

Let us mention additional results related to the applications in agronomy on decision making combining machine learning based on decision trees and ontologies , , as well as results obtained by our collaborators on semi-automatic data extraction from web data (tables), data reliability, and the representation and flexible querying of imprecise data with fuzzy sets , , , , , , , , . These investigations are complementary to the above mentioned results on argumentation and generally relate to other aspects in the same applicative projects.

It often happens that different references (i.e. data descriptions), possibly coming from heterogeneous data sources, concern the same real world entity. In such cases, it is necessary: (i) to detect whether different data descriptions really refer to the same real world entity and (ii) to fuse them into a unique representation. Since the seminal paper , this issue has been been studied under various names:“record linking”, “entity resolution”,“reference resolution”, ”de-duplication”, “object identification”, “data reconciliation”, etc., mostly in databases (cf. the bibliography by William E. Winckler http:// www. hcp. med. harvard. edu/ statistics/ survey-soft/ docs/ WinklerReclinkRef. pdf). It has become one of the major challenges in the Web of Data, where the objective is to link data published on the web and to process them as a single distributed database. Most entity resolution methods are based on classification techniques; Fatiha Saïs, Nathalie Pernelle and Marie-Christine Rousset proposed the first logical approach . Many experiments on public data are underway, in France (cf. DataLift DataLift, http:// datalift. org/ and ISIDORE ISIDORE, http:// www. rechercheisidore. fr/ projects) or internationally (e.g., VIAF project The Virtual International Authority File, http:// www. oclc. org/ research/ activities/ viaf/ led by OCLC Online Computer Library Center, http:// www. oclc. org, whose aim is to interconnect authority files coming from 18 national organizations).

Two years ago, we began a collaboration with ABES (National Bibliographic Agency for Universities, which takes part in the VIAF project). The aim of this collaboration is to enable the publication of ABES metadata bases on the Web of Data and to provide an identification service dedicated to bibliographic notices. ABES bibliographic bases, and more generally document metadata bases, appear to be a privileged application domain for the representation and reasoning formalisms developed by the team. This work has an interdisciplinary dimension, as it also requires experts in the Library and Information Science domain. We think that a logical approach is able to provide a generic solution for entity resolution in document metedata bases, even though it is generally admitted in Library and Information Science that “there is no single paradigmatic author name disambiguation task—each bibliographic database, each digital library, and each collection of publications, has its own unique set of problems and issues” .