Related papers: Introducer Concepts in n-Dimensional Contexts
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging…
Bioinformatic data sources available on the web are multiple and heterogenous. The lack of documentation and the difficulty of interaction with these data sources require users competence in both informatics and biological fields for an…
Description Logics (DLs) are appropriate, widely used, logics for managing structured knowledge. They allow reasoning about individuals and concepts, i.e. set of individuals with common properties. Typically, DLs are limited to dealing with…
This paper defines a constraint-based model dedicated to multidimensional databases. The model we define represents data through a constellation of facts (subjects of analyse) associated to dimensions (axis of analyse), which are possibly…
The present paper reviews and discusses work from computer science that proposes to identify concepts in internal representations (hidden layers) of DNNs. It is examined, first, how existing methods actually identify concepts that are…
In this paper we describe a mechanism to improve Information Retrieval (IR) on the web. The method is based on Formal Concepts Analysis (FCA) that it is makes semantical relations during the queries, and allows a reorganizing, in the shape…
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…
For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant under the network adjacency matrix. The complete lattice of synchrony subspaces of an $n$-cell regular network can be seen as an…
Matrices of (approximate) low rank are pervasive in data science, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a vast literature on how to exploit low rank structure in…
While studying some properties of linear operators in a Euclidean Jordan algebra, Gowda, Sznajder and Tao have introduced generalized lattice operations based on the projection onto the cone of squares. In two recent papers of the authors…
We consider hyperplane arrangements generated by generic points and study their intersection lattices. These arrangements are known to be equivalent to discriminantal arrangements. We show a fundamental structure of the intersection…
The ability to summarize and organize knowledge into abstract concepts is key to learning and reasoning. Many industrial applications rely on the consistent and systematic use of concepts, especially when dealing with decision-critical…
A five-dimensional lattice space can be decomposed into a number of four-dimens ional lattices called as layers. The five-dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with…
Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three…
Images are composed as a hierarchy of object parts. We use this insight to create a generative graphical model that defines a hierarchical distribution over image parts. Typically, this leads to intractable inference due to loops in the…
Automating the extraction of concept hierarchies from free text is advantageous because manual generation is frequently labor- and resource-intensive. Free result, the whole procedure for concept hierarchy learning from free text entails…
In the process of knowledge discovery and representation in large datasets using formal concept analysis, complexity plays a major role in identifying all the formal concepts and constructing the concept lattice(digraph of the concepts).…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…
Traditional knowledge graphs are constrained by fixed ontologies that organize concepts within rigid hierarchical structures. The root cause lies in treating domains as implicit context rather than as explicit, reasoning-level components.…
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…