Maximal Ordinal Two-Factorizations

Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and Glodeanu proposed a biplot based on two ordinal factors. For the biplot to be useful, it is important that these factors comprise as much data points as possible, i.e., that they cover a large part of the incidence relation. In this work, we investigate such ordinal two-factorizations. First, we investigate for formal contexts that omit ordinal two-factorizations the disjointness of the two factors. Then, we show that deciding on the existence of two-factorizations of a given size is an NP-complete problem which makes computing maximal factorizations computationally expensive. Finally, we provide the algorithm Ord2Factor that allows us to compute large ordinal two-factorizations.Comment: 15 pages, 6 figures, 2 algorithms, 28th International Conference on Conceptual Structure

Learning General Concept Inclusions in Probabilistic Description Logics

Probabilistic interpretations consist of a set of interpretations with a shared domain and a measure assigning a probability to each interpretation. Such structures can be obtained as results of repeated experiments, e.g., in biology, psychology, medicine, etc. A translation between probabilistic and crisp description logics is introduced and then utilised to reduce the construction of a base of general concept inclusions of a probabilistic interpretation to the crisp case for which a method for the axiomatisation of a base of GCIs is well-known

Formal Concepts and Residuation on Multilattices}

Let $\mathcal{A}_i: =(A_i,\le_i,\top_i,\odot_i,\to_i,\bot_i)$, $i=1,2$ be two complete residuated multilattices, $G$ (set of objects) and $M$ (set of attributes) be two nonempty sets and $(\varphi, \psi)$ a Galois connection between $A_1^G$ and $A_2^M$. In this work we prove that $$\mathcal{C}: =\{(h,f)\in A_1^G\times A_2^M \mid \varphi(h)=f \text{ and } \psi(f)=h \}$$ is a complete residuated multilattice. This is a generalization of a result by Ruiz-Calvi{\~n}o and Medina \cite{RM12} saying that if the (reduct of the) algebras $\mathcal{A}_i$, $i=1,2$ are complete multilattices, then $\mathcal{C}$ is a complete multilattice.Comment: 14 pages, 3 figure

Combining Concept Annotation and Pattern Structures for Guiding Ontology Mapping

International audienceFormal Concept Analysis (FCA) is a mathematical framework classifying in formal concepts a set of objects w.r.t. their common attributes. To this aim, FCA relies on a binary incidence relationship indicating whether an object has an attribute. On one hand, in order to consider more complex descriptions for objects (e.g., intervals, graphs), FCA has been extended with Pattern Structures. On the other hand, in a previous work, we introduced the notion of Concept Annotation, adding a third dimension to formal concepts, computed over the extent, without modifying the original classification. In this paper, we combine Concept Annotation with the formalism of Pattern Structures and we consider multiple annotation possibilities, i.e., multiple annotations for one concept and computing the annotation over the intent. We illustrate our approach and its interest with two use cases: (i) suggesting mappings between ontology classes and (ii) finding specific classes frequently associated as domain and range of a predicate

Discovering and Comparing Relational Knowledge, the Example of Pharmacogenomics

Article in Proceedings of the EKAW Doctoral Consortium 2018 co-located with the 21st International Conference on Knowledge Engineering and Knowledge Management (EKAW 2018)Pharmacogenomics (PGx) studies the influence of the genome in drug response, with knowledge units of the form of ternary relationships genomic variation-drug-phenotype. State-of-the-art PGx knowledge is available in the biomedical literature as well as in specialized knowledge bases. Additionally, Electronic Health Records of hospitals can be mined to discover such knowledge units that can then be compared with the state of the art, in order to confirm or temper relationships lacking validation or clinical counterpart. However, both discovering and comparing PGx relationships face multiple challenges: heterogeneous descriptions of knowledge units (languages, vocabularies and granularities), missing values and importance of the time dimension. In this research, we aim at proposing a framework based on Semantic Web technologies and Formal Concept Analysis to discover, represent and compare PGx knowledge units. We present the first results, consisting of creating an integrated knowledge base of PGx knowledge units from various sources and defining comparison methods, as well as the remaining issues to tackle

Model Exploration by Confidence with Completely Specified Counterexamples

We present an extensions of our previous work on axiomatizing confident general concept inclusions in given finite interpretations. Within this extension we allow external experts to interactively provide counterexamples to general concept inclusions with otherwise enough confidence in the given data. This extensions allows us to distinguish between erroneous counterexamples in the data and rare, but valid counterexamples

Efficient Axiomatization of OWL 2 EL Ontologies from Data by means of Formal Concept Analysis: (Extended Version)

We present an FCA-based axiomatization method that produces a complete EL TBox (the terminological part of an OWL 2 EL ontology) from a graph dataset in at most exponential time. We describe technical details that allow for efficient implementation as well as variations that dispense with the computation of extremely large axioms, thereby rendering the approach applicable albeit some completeness is lost. Moreover, we evaluate the prototype on real-world datasets.This is an extended version of an article accepted at AAAI 2024

La fusion des ontologies

La fusion des ontologies est une filière du domaine de la gestion des connaissances qui est en relation étroite avec d'autres domaines informatiques comme l'intelligence artificielle, le Web sémantique et le traitement du langage naturel. Cette filière prend une part de plus en plus accentuée dans la gestion des ontologies tout en considérant l'évolution rapide de la technologie des connaissances. La naissance de la fusion d'ontologies a conduit à la menée de plusieurs travaux de recherches et le développement de différentes approches concrètes, mais qui présentent certaines faiblesses, notamment au niveau de l'analyse des données relationnelles. La majorité de ces travaux se concentrent principalement sur l'alignement et la détection des similarités, mais ils négligent les informations qu'on pourrait dégager à partir de l'analyse formelle et relationnelle des concepts. Dans ce projet, nous proposons une approche de fusion d'ontologies, au sein de la plateforme INUKHUK, basée sur l'application d'analyses formelles et relationnelles des concepts (AFC et ARC). Ainsi, le principe de notre approche s'articule sur la factorisation des deux ontologies sources. Cette factorisation engendre une structure qui sera nettoyée à l'aide d'un outil d'alignement. Nous appliquons les analyses avec le moteur ARC sur la structure générée précédemment pour dégager un ensemble de treillis. Nous déduisons l'ontologie fusionnée à partir de l'ensemble de treillis dégagé. Avec notre approche, nous exploitons également la notion de la ré-ingénierie puisque nous factorisons, puis nous restructurons les ontologies.\ud ______________________________________________________________________________ \ud MOTS-CLÉS DE L’AUTEUR : fusion d'ontologies, alignement d'ontologies, factorisation des ontologies, analyse relationnelle des concepts, analyse formelle des concepts, génération des treillis, restructuration des ontologies