A Proposal for Extending Formal Concept Analysis to Knowledge Graphs

International audienceKnowledge graphs offer a versatile knowledge representation, and have been studied under different forms, such as conceptual graphs or Datalog databases. With the rise of the Semantic Web, more and more data are available as knowledge graphs. FCA has been successful for analyzing, mining, learning, and exploring tabular data, and our aim is to help transpose those results to graph-based data. Previous FCA approaches have already addressed relational data, hence graphs, but with various limits. We propose G-FCA as an extension of FCA where the formal context is a knowledge graph based on n-ary relationships. The main contributions is the introduction of " n-ary concepts " , i.e. concepts whose extents are n-ary relations of objects. Their intents, " projected graph patterns " , mix relationships of different arities, objects, and variables. In this paper, we lay first theoretical results, in particular the existence of a concept lattice for each concept arity, and the role of rela-tional projections to connect those different lattices

Stepwise functional refoundation of relational concept analysis

Relational concept analysis (RCA) is an extension of formal concept analysis allowing to deal with several related contexts simultaneously. It has been designed for learning description logic theories from data and used within various applications. A puzzling observation about RCA is that it returns a single family of concept lattices although, when the data feature circular dependencies, other solutions may be considered acceptable. The semantics of RCA, provided in an operational way, does not shed light on this issue. In this report, we define these acceptable solutions as those families of concept lattices which belong to the space determined by the initial contexts (well-formed), cannot scale new attributes (saturated), and refer only to concepts of the family (self-supported). We adopt a functional view on the RCA process by defining the space of well-formed solutions and two functions on that space: one expansive and the other contractive. We show that the acceptable solutions are the common fixed points of both functions. This is achieved step-by-step by starting from a minimal version of RCA that considers only one single context defined on a space of contexts and a space of lattices. These spaces are then joined into a single space of context-lattice pairs, which is further extended to a space of indexed families of context-lattice pairs representing the objects manipComment: euzenat2023

Conceptual Navigation in Large Knowledge Graphs

International audienceA growing part of Big Data is made of knowledge graphs. Major knowledge graphs such as Wikidata, DBpedia or the Google Knowledge Graph count millions of entities and billions of semantic links. A major challenge is to enable their exploration and querying by end-users. The SPARQL query language is powerful but provides no support for exploration by endusers. Question answering is user-friendly but is limited in expressivity and reliability. Navigation in concept lattices supports exploration but is limited in expressivity and scalability. In this paper, we introduce a new exploration and querying paradigm, Abstract Conceptual Navigation (ACN), that merges querying and navigation in order to reconcile expressivity, usability, and scalability. ACN is founded on Formal Concept Analysis (FCA) by defining the navigation space as a concept lattice. We then instantiate the ACN paradigm to knowledge graphs (Graph-ACN) by relying on Graph-FCA, an extension of FCA to knowledge graphs. We continue by detailing how Graph-ACN can be efficiently implemented on top of SPARQL endpoints, and how its expressivity can be increased in a modular way. Finally, we present a concrete implementation available online, Sparklis, and a few application cases on large knowledge graphs

Workshop Notes of the Sixth International Workshop "What can FCA do for Artificial Intelligence?"

International audienc

FCAIR 2012 Formal Concept Analysis Meets Information Retrieval Workshop co-located with the 35th European Conference on Information Retrieval (ECIR 2013) March 24, 2013, Moscow, Russia

International audienceFormal Concept Analysis (FCA) is a mathematically well-founded theory aimed at data analysis and classifiation. The area came into being in the early 1980s and has since then spawned over 10000 scientific publications and a variety of practically deployed tools. FCA allows one to build from a data table with objects in rows and attributes in columns a taxonomic data structure called concept lattice, which can be used for many purposes, especially for Knowledge Discovery and Information Retrieval. The Formal Concept Analysis Meets Information Retrieval (FCAIR) workshop collocated with the 35th European Conference on Information Retrieval (ECIR 2013) was intended, on the one hand, to attract researchers from FCA community to a broad discussion of FCA-based research on information retrieval, and, on the other hand, to promote ideas, models, and methods of FCA in the community of Information Retrieval