Related papers: Weyl and intuitionistic infinitesimals
Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl…
Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced…
In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the…
In this paper, we construct a bialgebra theory for associative conformal algebras, namely antisymmetric infinitesimal conformal bialgebras. On the one hand, it is an attempt to give conformal structures for antisymmetric infinitesimal…
We study fractional variants of the quasi-norms introduced by Brezis, Van Schaftingen, and Yung in the study of the Sobolev space $\dot W^{1,p}$. The resulting spaces are identified as a special class of real interpolation spaces of…
Penrose conjectured a connection between entropy and Weyl curvature of the Universe. This is plausible, as the almost homogeneous and isotropic Universe at the onset of structure formation has negligible Weyl curvature, which then grows…
For any closed smooth Riemannian manifold H. Weyl has defined a sequence of numbers called today intrinsic volumes. They include volume, Euler characteristic, and integral of the scalar curvature. We conjecture that absolute values of all…
We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the…
The usual interpretation of Weyl geometry is modified in two senses. First, both the additive Weyl connection and its variation are treated as (1, 2) tensors under the action of Weyl covariant derivative. Second, a modified covariant…
In arXiv:0905.1675, Nik Weaver proposed a novel intuitionistic formal theory of third-order arithmetic as a formalisation of his philosophical position known as mathematical conceptualism. In this paper, we will construct a realisability…
We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by G\"odel and others. Using Bayesian-inspired arguments we build a normative model of fair bets under deductive uncertainty which draws…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
We study almost complete intersections ideals whose Rees algebras are extremal in the sense that some of their fundamental metrics---depth or relation type---have maximal or minimal values in the class. The focus is on those ideals that…
This is an expositary article telling a short story made from the leaves of quantum probability with the following ingredients: (i) A special projective, unitary, irreducible and factorizable representation of the euclidean group of a…
We obtain a double exponential bound in Brauer's generalisation of van der Waerden's theorem, which concerns progressions with the same colour as their common difference. Such a result has been obtained independently and in much greater…
Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except for special cases, previous work has…
Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into…
The axiomatic foundations of Bentham and Rawls solutions are discussed within the broader domain of cardinal preferences. It is unveiled that both solution concepts share all four of the following axioms: Nonemptiness, Anonymity, Unanimity,…
We present a complete review of the quantum-to-classical limit of open systems by means of the theory of decoherence and the use of the Weyl-Wigner-Moyal (WWM) transformation. We show that the analytical extension of the Hamiltonian…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…