Related papers: Key (critical) relations preserved by a weak near-…
For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of the other using operations from C. In…
In this paper we present a new class of complexity measures, induced by a new data structure for representing $k$-valued functions (operations), called minor decision diagram. The results are presented in terms of Multi-Valued Logic…
Connections between relations in relation extraction, which we call class ties, are common. In distantly supervised scenario, one entity tuple may have multiple relation facts. Exploiting class ties between relations of one entity tuple…
We define well-connectedness, an order-theoretic notion of largeness whose associated partition relations $\nu\to_{wc}(\mu)_\lambda^2$ formally weaken those of the classical Ramsey relations $\nu\to(\mu)_\lambda^2$. We show that it is…
The Svenonius theorem describes the (first-order) definability in a structure in terms of permutations preserving the relations of elementary extensions of the structure. In the present paper we prove a version of this theorem using…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
Generalizing the notion of a tight almost disjoint family, we introduce the notions of a {\em tight eventually different} family of functions in Baire space and a {\em tight eventually different set of permutations} of $\omega$. Such sets…
In the course of the last decades entropic uncertainty relations have attracted much attention not only due to their fundamental role as manifestation of non-classicality of quantum mechanics, but also as major tools for applications of…
Synonymy and translational equivalence are the relations of sameness of meaning within and across languages. As the principal relations in wordnets and multi-wordnets, they are vital to computational lexical semantics, yet the field suffers…
The near-unanimity-closed minions of Boolean functions, i.e., the clonoids whose target algebra contains a near-unanimity function, are completely described. The key concept towards this result is the minorant-minor partial order and its…
In this article, we prove infinitary version of one to one correspondence theorem between clones and relational clones on a fixed possibly infinite set. We also characterize the relational clone corresponding to the clone of all finitary…
We represent finite join-semilattices and join-preserving morphisms as a category whose objects and morphisms are binary relations. It is a quotient category of $\mathsf{Rel}_f$'s arrow category, where self-duality arises by taking the…
The meaning of a sentence is a function of the relations that hold between its words. We instantiate this relational view of semantics in a series of neural models based on variants of relation networks (RNs) which represent a set of…
This paper unites two problem-solving traditions in computer science: (1) constraint-based reasoning, and (2) formal concept analysis. For basic definitions and properties of networks of constraints, we follow the foundational approach of…
We checked each binary relation on a 5-element set for a given set of properties, including usual ones like asymmetry and less known ones like Euclideanness. Using a poor man's Quine-McCluskey algorithm, we computed prime implicants of…
A clonoid is a set of finitary functions from a set $A$ to a set $B$ that is closed under taking minors. Hence clonoids are generalizations of clones. By a classical result of Post, there are only countably many clones on a 2-element set.…
We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of…
We extend the definition of weak symmetric continuity to be applicable for functions defined on any nonempty subset of $\R$. Then we investigate basic properties of weakly symmetrically continuous functions and compare them with those of…
A clone of functions on a finite domain determines and is determined by its system of invariant relations (=predicates). When a clone is determined by a finite number of relations, we say that the clone is of finite degree. For each Minsky…
Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators…