Related papers: The Thins Ordering on Relations
Many practical scenarios make it necessary to evaluate top-k queries over data items with partially unknown values. This paper considers a setting where the values are taken from a numerical domain, and where some partial order constraints…
Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original…
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…
We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…
We investigate lifted inference on ordered domains with predecessor relations, where the elements of the domain respect a total (cyclic) order, and every element has a distinct (clockwise) predecessor. Previous work has explored this…
In higher education, data is collected that indicate the term(s) that a course is taken and when it is passed. Often, study plans propose a suggested course order to students. Study planners can adjust these based on detected deviations…
Quasiminimal structures play an important role in non-elementary categoricity. In this paper we explore possibilities of constructing quasiminimal models of a given first-order theory. We present several constructions with increasing…
We use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of…
We extend Berge's Maximum Theorem to allow for incomplete preferences. We first provide a simple version of the Maximum Theorem for convex feasible sets and a fixed preference. Then, we show that if, in addition to the traditional…
We study an alternative model of infinitary term rewriting. Instead of a metric on terms, a partial order on partial terms is employed to formalise convergence of reductions. We consider both a weak and a strong notion of convergence and…
Ferrer-i-Cancho (2015) presents a mathematical model of both the synchronic and diachronic nature of word order based on the assumption that memory costs are a never decreasing function of distance and a few very general linguistic…
As a fundamental component in location-based services, inferring the relationship between points-of-interests (POIs) is very critical for service providers to offer good user experience to business owners and customers. Most of the existing…
Ranking individuals based on their performance in different coalitions is a problem emerging in various domains (teams sports, scientific evaluation, argumentation, etc.). Often, for practical reasons, the number of comparable coalitions is…
Some general properties of abstract relations are closely examined. These include generalizations of linearity, and properties based on `pinning' an inequality by a pair of families of endomorphisms.To each property we try to associate a…
We initiate the study of fairness for ordinal regression. We adapt two fairness notions previously considered in fair ranking and propose a strategy for training a predictor that is approximately fair according to either notion. Our…
In fair division of indivisible goods, using sequences of sincere choices (or picking sequences) is a natural way to allocate the objects. The idea is the following: at each stage, a designated agent picks one object among those that…
Theory of relations is the framework of this thesis. It is about enumeration of finite structures. Let $\mathscr C$ be a class of finite combinatorial structures, the \emph{profile} of $\mathscr C$ is the function $\varphi_{\mathscr C}$…
To study discrimination in automated decision-making systems, scholars have proposed several definitions of fairness, each expressing a different fair ideal. These definitions require practitioners to make complex decisions regarding which…
We show that the category of partially ordered sets $\mathsf{Pos}$ is equivalent to the free conservative cocompletion of the category of finite non-empty totally ordered sets $\Delta$, which is also known as the simplex category.
We determine upper bounds for the maximum order of an element of a finite almost simple group with socle T in terms of the minimum index m(T) of a maximal subgroup of T: for T not an alternating group we prove that, with finitely many…