Related papers: Logical Characterization of Contextual Hidden-Vari…
In this paper from 2011 we approach some questions about quantum contextuality with tools from formal logic. In particular, we consider an experiment associated with the Peres-Mermin square. The language of all possible sequences of…
In this paper we show that if $(X,\mathcal{A})$ is a measurable space and if $Y$ is a topological model of a Lawvere theory $\mathcal{T}$ equipped with $\mathcal{B}$ the Borel $\sigma$-algebra on $Y$, then the set of…
We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related. (T.1) A basic property of Cantor space $2^{\mathbb{N}}$…
The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…
In his book \textit{The Mathematical Foundations of Quantum Mechanics}, published in 1932, J. von Neumann performed an analysis of the consequences of introducing hidden parameters (hidden variables) into quantum mechanics. He showed that…
We propose a principle for exploring context in machine learning models. Starting with a simple assumption that each observation may or may not depend on its context, a conditional probability distribution is decomposed into two parts:…
Elements of a novel theory of quantum physics are developed, synthesising the role of symbolism in describing quantum measurement and in the topological representation of fractal invariant sets in nonlinear dynamical systems theory. In this…
I propose a new class of interpretations, {\it real world interpretations}, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one…
The denotational semantics of the untyped lambda-calculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
We show that the embeddability relations for countable quandles and for countable fields of any given characteristic other than 2 are maximally complex in a strong sense: they are invariantly universal. This notion from the theory of Borel…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems, but are there different forms of infinite entanglement? To understand entanglement in such systems, we use a…
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…
For an arbitrary simple Lie algebra $\g$ and an arbitrary root of unity $q,$ the closed subsets of the Weyl alcove of the quantum group $U_q(\g)$ are classified. Here a closed subset is a set such that if any two weights in the Weyl alcove…
We give characterizations for the (in ZFC unprovable) sentences ``Every $\Sb{1}{2}$--set is measurable" and ``Every $\Db{1}{2}$--set is measurable" for various notions of measurability derived from well--known forcing partial orderings.
A general theory of resource-bounded measurability and measure is developed. Starting from any feasible probability measure $\nu$ on the Cantor space $\C$ and any suitable complexity class $C \subseteq \C$, the theory identifies the subsets…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and…
Contextuality has long been associated with topological properties. In this work, such a relationship is elevated to identification in the broader framework of generalized contextuality. We employ the usual identification of states,…