相关论文: Selection principles related to $\alpha_i$-propert…
Arhangelskii's properties $\alpha_2$ and $\alpha_4$ defined for convergent sequences may be characterized in terms of Scheeper's selection principles. We generalize these results to hold for more general collections and consider these…
In this paper we investigate the properties of function spaces using the selection principles.
Selectional preference learning methods have usually focused on word-to-class relations, e.g., a verb selects as its subject a given nominal class. This papers extends previous statistical models to class-to-class preferences, and presents…
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
We present a selection principle $S_1(\mathcal{O},\mathcal{H})$ that characterizes the $G_{\delta}$-diagonal property. We also present a topological game induced by this selection principle and we study the relations between this game and…
We study the problem of fair sequential decision making given voter preferences. In each round, a decision rule must choose a decision from a set of alternatives where each voter reports which of these alternatives they approve. Instead of…
This tutorial deal with the Axiom of Choice and some of its applications to topics related to Computer Science. We will see that the Axiom of Choice is equivalent to some well-known proof principles like Zorn's Lemma or Tuckey's Maximality…
Motivated by a recent result of Sakai, we define a new selection operator for covers of topological spaces, inducing new selection hypotheses. We initiate a systematic study of the new hypotheses. Some intriguing problems remain open.
Building on a specific formalization of analogical relationships of the form "A relates to B as C relates to D", we establish a connection between two important subfields of artificial intelligence, namely analogical reasoning and…
I provide simplified proofs for each of the following fundamental theorems regarding selection principles: 1. The Quasinormal Convergence Theorem, due to the author and Zdomskyy, asserting that a certain, important property of the space of…
We consider different choice procedures such as scoring rules, rules, using majority relation, value function and tournament matrix, which are used in social and multi-criteria choice problems. We focus on the study of the properties that…
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider…
We survey some of the major open problems involving selection principles, diagonalizations, and covering properties in topology and infinite combinatorics. Background details, definitions and motivations are also provided.
Several rules for social choice are examined from a unifying point of view that looks at them as procedures for revising a system of degrees of belief in accordance with certain specified logical constraints. Belief is here a social…
We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces,…
Random variables $X^i$, $i=1,2$ are 'probabilistically equivalent' if they have the same law. Moreover, in any class of equivalent random variables it is easy to select canonical representatives. The corresponding questions are more…
In the {\em Many Worlds Interpretation} of quantum mechanics, the range of possible worlds (or histories) provides variation, and the Anthropic Principle is a selective principle analogous to natural selection. When looked on in this way,…
We study a class of {\em aggregation rules} that could be applied to ethical AI decision-making. These rules yield the decisions to be made by automated systems based on the information of profiles of preferences over possible choices. We…
Natural selection acts on traits at different scales, often with opposing consequences. This article identifies the particular forces that act at each scale and how those forces combine to determine the overall evolutionary outcome. A…
The Shapley value has become popular in the Explainable AI (XAI) literature, thanks, to a large extent, to a solid theoretical foundation, including four "favourable and fair" axioms for attribution in transferable utility games. The…