Related papers: Construction schemes: transferring structures from…
While a great effort has concerned the development of fully integrated modular understanding systems, few researches have focused on the problem of unifying existing linguistic formalisms with cognitive processing models. The Situated…
This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set $A$ containing $\Omega(|A|^{3/2})$ three-term arithmetic progressions.
We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
We construct a C*-algebra that has only one irreducible representation up to unitary equivalence but is not isomorphic to the algebra of compact operators on any Hilbert space. This answers an old question of Naimark. Our construction uses…
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…
The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah. The corresponding completely proper forcing which…
We prove equivalence of certain axiom sets for affine buildings. Along the lines a purely combinatorial proof of the existence of a spherical building at infinity is given. As a corollary we obtain that ``being an affine building'' is…
Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem.…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
Examples of the construction of Hamiltonian structures for dynamical systems in field theory (including one reputedly non-Hamiltonian problem) without using Lagrangians, are presented. The recently developed method used requires the…
A new construction is given of non-standard uniserial modules over certain valuation domains; the construction resembles that of a special Aronszajn tree in set theory. A consequence is the proof of a sufficient condition for the existence…
We discuss the connections between the failure of the axiom of choice in set theory, and certain model-theoretic structures with enough symmetry.
We present a general framework for carrying out some constructions. The unifying factor is a combinatorial principle which we present in terms of a game in which the first player challenges the second player to carry out constructions which…
Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects…
We analyze the schema theorem and the building block hypothesis using a recently derived, exact schemata evolution equation. We derive a new schema theorem based on the concept of effective fitness showing that schemata of higher than…
Sequence to Sequence models struggle at compositionality and systematic generalisation even while they excel at many other tasks. We attribute this limitation to their failure to internalise constructions conventionalised form meaning…
We investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize…
Construction grammar posits that constructions, or form-meaning pairings, are acquired through experience with language (the distributional learning hypothesis). But how much information about constructions does this distribution actually…