Folding of set-theoretical solutions of the Yang-Baxter equation

We establish a correspondence between the invariant subsets of a non-degenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside structure. Moreover, we introduce the notion of a foldable solution, which extends the one of a decomposable solution

SEMANTIC CLASSIFICATION OF INSTANCES IN A FRAME-BASED REPRESENTATION

The topic of this paper is classification reasoning in frame-based representations. In these representations, an object designates either a concept (which is represented by a class) or a concrete entity which illustrates one or more classes (represented by an instance). Our objective is to define an instance classification method, which gives a more important place to the semantics of the Object To Classify (OTC) than other works in this area. We have studied cognitive psychology works concerning categorization. These works are focused on the identific:ation of the elements which are concerned with the categorization process. We have taken into account certain results of cognitive psychology to define our classification system. The theme of this paper is the following: in the section 2, the general problem of classification in the frame-based representations is presented. Then, in section 3, critical review of these representations is proposed. The section 4 presents the main results of the cognitive psychology concerning categorization and the section 5 details the more important points of our classification system. Then, the general approach of our system is given (section 6). Finally, we give the elements of knowledge participating into the classification process (section 7) and the matching step is described, specially important in the defined method (section 8)

CONSTRUCTION OF FRAME HIERARCHIES USING MACHINE LEARNING

In this paper, we describe an architecture for helping frame hierarchy conception. This architecture is based on machine learning and cognitive psychological studies on categorizotion. Our basic assumption is that categorization should be considered as a goal-driven, context--dependent process and therefore the hierarchical organization of categories should be represented in different perspectives. The core of our architecture is a learning system of categorization that generates multi.perspective hierarchies. Concept hierarchies are, at first, generated in a probabilistic representation and after translated into a frame one