Related papers: Graded Galois Lattices and Closed Itemsets

We introduce a general unifying framework for the investigation of pointlike sets. The pointlike functors are considered as distinguished elements of a certain lattice of subfunctors of the power semigroup functor; in particular, we exhibit…

We explore a new connection between synthetic domain theory and Grothendieck topoi related to the distributive lattice classifier. In particular, all the axioms of synthetic domain theory (including the inductive fixed point object and the…

Field Arithmetic studies the interplay between arithmetical properties of fields and their absolute Galois groups. Here we studies fields satisfying local global principles for rational points of varieties and profinite groups satisfying…

We introduce the concept of basis for a lattice. This basis plays a vital role to determine the completeness and consistency of the lattice. Weighted lattices are introduced and its complexity is formulated. Some axiomatic systems,…

Constructing lattice isomorphic line arrangements that are not lattice isotopic is a complex yet fundamental task. In this paper, we focus on such pairs but which are not Galois conjugated, referred to as nonarithmetic pairs. Splitting…

The definition of the complement of a fuzzy subset is algebraic in nature and when it is used in the context of fuzzy topological spaces it does not share any similarity with the usual property of topological spaces that the complement of…

We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and sub-formula property. Properness (i.e. closure under uniform substitution of all parametric…

In this exposition we discuss the theory of algebraic extensions of valued fields. Our approach is mostly through Galois theory. Most of the results are well-known, but some are new. No previous knowledge on the theory of valuations is…

Closure system on a finite set is a unifying concept in logic programming, relational data bases and knowledge systems. It can also be presented in the terms of finite lattices, and the tools of economic description of a finite lattice have…

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 an Artinian ring containing the group of…

This is the first paper in a series on intrinsic Donaldson-Thomas theory, where we develop a new framework for enumerative geometry that allows the generalization of constructions and results from linear moduli stacks to general non-linear…

Formal concepts and closed itemsets proved to be of big importance for knowledge discovery, both as a tool for concise representation of association rules and a tool for clustering and constructing domain taxonomies and ontologies.…

Data-driven artificial intelligence (AI) techniques are becoming prominent for learning in support of data compression, but are focused on standard problems such as text compression. To instead address the emerging problem of semantic…

We introduce a neural network architecture and a learning algorithm to produce factorized symbolic representations. We propose to learn these concepts by observing consecutive frames, letting all the components of the hidden representation…

We introduce a novel combinatorial structure called pointed building sets, which can be viewed as families of lattices equipped with compatibility relations. To each pointed building set $\mathsf{B}$, we associate a complete lattice…

We consider problems concerning the partial order structure of the set of spreading models of Banach spaces. We construct examples of spaces showing that the possible structure of these sets include certain classes of finite semi-lattices…

In applications that use knowledge representation (KR) techniques, in particular those that combine data-driven and logic methods, the domain of objects is not an abstract unstructured domain, but it exhibits a dedicated, deep structure of…

Closure space has proven to be a useful tool to restructure lattices and various order structures.This paper aims to provide a novel approach to characterizing some important kinds of continuous domains by means of closure spaces. By…

A rich set of interpretable dimensions has been shown to emerge in the latent space of the Generative Adversarial Networks (GANs) trained for synthesizing images. In order to identify such latent dimensions for image editing, previous…

Structured representation of product information is a major bottleneck for the efficiency of e-commerce platforms, especially in second-hand ecommerce platforms. Currently, most product information are organized based on manually curated…