Related papers: Boolean Substructures in Formal Concept Analysis
We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation's characterization of a hierarchy of pseudovarieties of finite lattices,…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
We prove a number of dualities between posets and (pseudo)bases of open sets in locally compact Hausdorff spaces. In particular, we show that (1) Relatively compact basic sublattices are finitely axiomatizable. (2) Relatively compact basic…
Generating a long, coherent text such as a paragraph requires a high-level control of different levels of relations between sentences (e.g., tense, coreference). We call such a logical connection between sentences as a (paragraph) flow. In…
The notion of pseudocategory, as considered in [11], is extended from the context of a 2-category to the more general one of a sesquicategory, which is considered as a category equipped with a 2-cell structure. Some particular examples of…
One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
Human understanding of text depends on general semantic concepts of words rather than their superficial forms. To what extent does our human intuition transfer to language models? In this work, we study the degree to which current…
We find tight estimates for the minimum number of proper subspaces needed to cover all lattice points in an n-dimensional convex body symmetric about the origin. We also find the order of magnitude of the number of (n-1)-dimensional…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
We propose to compose dynamic tree structures that place the objects in an image into a visual context, helping visual reasoning tasks such as scene graph generation and visual Q&A. Our visual context tree model, dubbed VCTree, has two key…
Lexical semantics is concerned with both the multiple senses a word can adopt in different contexts, and the semantic relations that exist between meanings of different words. To investigate them, Contextualized Language Models are a…
We consider some distinguished classes of elements of a multiplicative lattice endowed with coarse lower topologies, and call them lower spaces. The primary objective of this paper is to study the topological properties of these lower…
A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
A $t$-$(n,d,\lambda)$ design over ${\mathbb F}_q$, or a subspace design, is a collection of $d$-dimensional subspaces of ${\mathbb F}_q^n$, called blocks, with the property that every $t$-dimensional subspace of ${\mathbb F}_q^n$ is…
A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition. We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence,…
A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…
A non-distributive two-sorted hypersequent calculus \textbf{PDBL} and its modal extension \textbf{MPDBL} are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…