Related papers: Boolean Substructures in Formal Concept Analysis
What factors contribute to the relative success and corresponding difficulties of in-context learning for Large Language Models (LLMs)? Drawing on insights from the literature on human concept learning, we test LLMs on carefully designed…
We introduce a fundamental concept -- closed sets of correlations -- for studying non-local correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical…
A lattice is called well-rounded, if its lattice vectors of minimal length span the ambient space. We show that there are interesting connections between the existence of well-rounded sublattices and coincidence site lattices (CSLs).…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
Negation in natural language does not follow Boolean logic and is therefore inherently difficult to model. In particular, it takes into account the broader understanding of what is being negated. In previous work, we proposed a framework…
We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
After some background on lattices, the locality framework introduced in earlier work by the authors is extended to cover posets and lattices. We then extend the correspondence between Euclidean structures on vector spaces and orthogonal…
The finite set of subsystems of a finite quantum system with variables in ${\mathbb Z}(n)$, is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that understands a rich shared code. A semantic embedding is a form of…
A ballean $\mathcal{B}$ (or a coarse structure) on a set $X$ is a family of subsets of $X$ called balls (or entourages of the diagonal in $X\times X$) defined in such a way that $\mathcal{B}$ can be considered as the asymptotic counterpart…
Given subsets $\mathcal{C},\mathcal{F}$ of a preorder $\mathcal{A}$, we give necessary and sufficient conditions for $\mathcal{A}$ to admit the structure of a model category whose cofibrant objects are $\mathcal{C}$ and whose fibrant…
We prove a tangle-tree theorem and a tangle duality theorem for abstract separation systems $\vec S$ that are submodular in the structural sense that, for every pair of oriented separations, $\vec S$ contains either their meet or their join…
The role of background in bosonic quantum statistics is discussed in the frame of a new approach in terms of coherent states. Bosons are indeed detected in different physical situations where they exhibit different and apparently…
In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one components, namely interlaced solitons. These are waveforms in which in the relevant anti-continuum limit, i.e.…
For a positive integer n, we denote by SUB (resp., SUBn) the class of all lattices that can be embedded into the lattice Co(P) of all order-convex subsets of a partially ordered set P (resp., P of length at most n). We prove the following…
The aim of this note is to show that every subset of a given topological space is the intersection of a preopen and a preclosed set, therefore $\beta$-locally closed, and that every topological space is $\beta$-submaximal.
Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these…
We develop the idea that a natural link between Boltzmann schemes and finite volumes exists naturally: the conserved mass and momentum during the collision phase of the Boltzmann scheme induces general expressions for mass and momentum…