Related papers: Graded Galois Lattices and Closed Itemsets
Laminations are a combinatorial and topological way to study Julia sets. Laminations give information about the structure of parameter space of degree $d$ polynomials with connected Julia sets. We first study fixed point portraits in…
We construct Galois theory for sublattices of certain complete modular lattices and their automorphism groups. A well-known description of the intermediate subgroups of the general linear group over a semilocal ring containing the group of…
There has been a growing adoption of computer vision tools and technologies in architectural design workflows over the past decade. Notable use cases include point cloud generation, visual content analysis, and spatial awareness for robotic…
Lattice-theoretic ideals have been used to define and generate non granular rough approximations over general approximation spaces over the last few years by few authors. The goal of these studies, in relation based rough sets, have been to…
The semantic gap is defined as the difference between the linguistic representations of the same concept, which usually leads to misunderstanding between individuals with different knowledge backgrounds. Since linguistically annotated…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…
Being an unsupervised machine learning and data mining technique, biclustering and its multimodal extensions are becoming popular tools for analysing object-attribute data in different domains. Apart from conventional clustering techniques,…
We propose the design of novel categorical generative AI architectures (GAIAs) using topos theory, a type of category that is ``set-like": a topos has all (co)limits, is Cartesian closed, and has a subobject classifier. Previous theoretical…
In this paper we are concerned with understanding the nature of program metrics for calculi with higher-order types, seen as natural generalizations of program equivalences. Some of the metrics we are interested in are well-known, such as…
Galois slicing is a technique for program slicing for provenance, developed by Perera and collaborators. Galois slicing aims to explain program executions by demonstrating how to track approximations of the input and output forwards and…
In this paper we make explicit an application of the wreath product construction to the Galois groups of field extensions. More precisely, given a tower of fields $F \subseteq K \subseteq L$ with $L/F$ finite and separable, we explicitly…
We present a Galois theory connecting finitary operations with pairs of finitary relations one of which is contained in the other. The Galois closed sets on both sides are characterised as locally closed subuniverses of the full iterative…
The objective of knowledge graph embedding is to encode both entities and relations of knowledge graphs into continuous low-dimensional vector spaces. Previously, most works focused on symbolic representation of knowledge graph with…
Conceptual Graphs (CGs) are a formalism to represent knowledge. However producing a CG database is complex. To the best of our knowledge, existing methods do not fully use the expressivity of CGs. It is particularly troublesome as it is…
The Chip Firing Game (CFG) is a discrete dynamical model used in physics, computer science and economics. It is known that the set of configurations reachable from an initial configuration (this set is called the configuration space) can be…
This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
By applying interpretable machine learning methods such as decision trees, we study how simple models can classify the Galois groups of Galois extensions over $\mathbb{Q}$ of degrees 4, 6, 8, 9, and 10, using Dedekind zeta coefficients. Our…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…