Jérôme Euzenat

Jérôme Euzenat

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 manippulated by RCA. We show that RCA returns the least element of the set of acceptable solutions. In addition, it is possible to build dually an operation that generates its greatest element. The set of acceptable solutions is a complete sublattice of the interval between these two elements. Its structure and how the defined functions traverse it are studied in detail.

Jérôme Euzenat

The semantic web has led to the deployment of ontologies on the web connected through various relations and, in particular, alignments of their vocabularies. There exists several semantics for alignments which make difficult interoperation between different interpretation of networks of ontologies. Here we present an abstraction of these semantics which allows for defining the notions of closure and consistency for networks of ontologies independently from the precise semantics. We also show that networks of ontologies with specific notions of morphisms define categories of networks of ontologies.

Jérôme Euzenat

Semantic web information is at the extremities of long pipelines held by human beings. They are at the origin of information and they will consume it either explicitly because the information will be delivered to them in a readable way, or implicitly because the computer processes consuming this information will affect them. Computers are particularly capable of dealing with information the way it is provided to them. However, people may assign to the information they provide a narrower meaning than semantic technologies may consider. This is typically what happens when people do not think their assertions as ambiguous. Model theory, used to provide semantics to the information on the semantic web, is particularly apt at preserving ambiguity and delivering it to the other side of the pipeline. Indeed, it preserves as much interpretations as possible. This quality for reasoning efficiency, becomes a deficiency for accurate communication and meaning preservation. Overcoming it may require either interactive feedback or preservation of the source context. Work from social science and humanities may help solving this particular problem.