Related papers: Invariance under permutations as a semantic motiva…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
An infinite permutation $\alpha$ is a linear ordering of $\mathbb N$. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this…
A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…
The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…
This paper examines the category theory of stratified set theory (NF and KF). We work out the properties of the relevant categories of sets, and introduce a functorial analogue to Specker's T-operation. Such a development leads one to…
Given a morphism from an affine semigroup Q to an arbitrary commutative monoid, it is shown that every fiber possesses an affine stratification: a partition into a finite disjoint union of translates of normal affine semigroups. The proof…
This paper allows one to obtain a criterion for the existence of a projectively invariant measure formulated in terms of combinatorial properties of a group (amenability of some canonical quotient group). Such necessary and sufficient…
We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…
This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…
We present a taxonomy of the variability mechanisms offered by modeling languages. The definition of a formal language encompasses a syntax and a semantic domain as well as the mapping that relates them, thus language variabilities are…
We explore indefinite causal order between events in the context of quasiclassical spacetimes in superposition. We introduce several new quantifiers to measure the degree of indefiniteness of the causal order for an arbitrary finite number…
In this paper I argue that infinities in the classical computation theory such as the unsolvability of the Halting Problem can be addressed in the same way as Feynman divergences in Quantum Field Theory, and that meaningful versions of…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
We propose to condition a generative model by a given image classifier uncertainty in order to analyze and explain its behavior. Preliminary experiments on synthetic data and a corrupted version of MNIST dataset illustrate the idea.
Let $\mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with…
We study the problem of learning fair prediction models for unseen test sets distributed differently from the train set. Stability against changes in data distribution is an important mandate for responsible deployment of models. The domain…
In this sequel to my previous paper, "Is String Theory in Knots?" I explore ways of constructing symmetries through an algebraic stepping process using knotted graphs. The hope is that this may lead to an algebraic formulation of string…
All languages have a noun category, but its realisation varies considerably. Depending on the language, semantic and/or morphosyntactic differences may be more or less pronounced. This paper explores these variations, using Riffian as a…
Language learners must learn the meanings of many thousands of words, despite those words occurring in complex environments in which infinitely many meanings might be inferred by the learner as a word's true meaning. This problem of…
Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…