Related papers: Computably Enumerable Equivalence Relations
Causal nets (CNs) are Petri nets where causal dependencies are modelled via inhibitor arcs. They play the role of occurrence nets when representing the behaviour of a concurrent and distributed system, even when reversibility is considered.…
Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has…
A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We…
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…
Cohesive powers of computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let $\omega$, $\zeta$, and $\eta$ denote the respective order-types of the natural numbers, the integers, and…
Neural relation extraction discovers semantic relations between entities from unstructured text using deep learning methods. In this study, we present a comprehensive review of methods on neural network based relation extraction. We discuss…
We introduce and study several amenability properties for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability or co-amenability of such groups. As a background for this…
The topic of this paper is the subtle interplay between countability and representations. In particular, we establish that the definition of countability of a certain set $X$ crucially hinges on the associated equivalence relation $=_{X}$.…
Entities and relationships between entities are vital in the real world. Essentially, we understand the world by understanding entities and relations. For instance, to understand a field, e.g., computer science, we need to understand the…
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…
The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…
Model Multiplicity (MM) arises when multiple, equally performing machine learning models can be trained to solve the same prediction task. Recent studies show that models obtained under MM may produce inconsistent predictions for the same…
We discuss combinatorial conditions for the existence of various types of reductions between equivalence relations, and in particular identify necessary and sufficient conditions for the existence of injective reductions.
Discourse relations bind smaller linguistic units into coherent texts. However, automatically identifying discourse relations is difficult, because it requires understanding the semantics of the linked arguments. A more subtle challenge is…
We count the number of countable homogeneous colored linear orderings in $k$ colors. Relatedly, we count the number of countable $C_{n,m}$-homogeneous linear orderings. $C_{n,m}$-homogeneity is a strong homogeneity notion that approximates…
Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely…
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…
Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge and probabilistic reasoning.
In this paper, we extend some classes of structured matrices to higher order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a…
The same method that creates adversarial examples (AEs) to fool image-classifiers can be used to generate counterfactual explanations (CEs) that explain algorithmic decisions. This observation has led researchers to consider CEs as AEs by…