Related papers: Respecting Linear Orders for Supermajority Rules
In logic programming under the answer set semantics, preferences on rules are used to choose which of the conflicting rules are applied. Many interesting semantics have been proposed. Brewka and Eiter's Principle I expresses the basic…
Given a linearly ordered set I, every surjective map p: A --> I endows the set A with a structure of set of preferences by "replacing" the elements of I with their inverse images via p considered as "balloons" (sets endowed with an…
We consider the problem of learning the preferences of a heterogeneous population by observing choices from an assortment of products, ads, or other offerings. Our observation model takes a form common in assortment planning applications:…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
Aligning large language models (LLMs) with diverse human preferences is critical for ensuring fairness and informed outcomes when deploying these models for decision-making. In this paper, we seek to uncover fundamental statistical limits…
Social choice theory offers a wealth of approaches for selecting a candidate on behalf of voters based on their reported preference rankings over options. When voters have underlying utilities for these options, however, using preference…
We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…
We study the problem of learning to rank from pairwise preferences, and solve a long-standing open problem that has led to development of many heuristics but no provable results for our particular problem. Given a set $V$ of $n$ elements,…
We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…
Many practical problems are characterized by a preference relation over admissible solutions, where preferred solutions are minimal in some sense. For example, a preferred diagnosis usually comprises a minimal set of reasons that is…
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…
We apply the Inclusion-Exclusion Principle to a unique pair of prime number subsequences to determine whether these subsequences form a small set or a large set and thus whether the infinite sum of the inverse of their terms converges or…
Aggregating preferences under incomplete or constrained feedback is a fundamental problem in social choice and related domains. While prior work has established strong impossibility results for pairwise comparisons, this paper extends the…
When scheduling public works or events in a shared facility one needs to accommodate preferences of a population. We formalize this problem by introducing the notion of a collective schedule. We show how to extend fundamental tools from…
We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…
Robust Ordinal Regression (ROR) is a way of dealing with Multiple Criteria Decision Aiding (MCDA), by considering all sets of parameters of an assumed preference model, that are compatible with preference information given by the Decision…
We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…
We study various orders on countably complete ultrafilters on ordinals that coincide and are wellorders under a hypothesis called the Ultrapower Axiom. Our main focus is on the relationship between the Ultrapower Axiom and the linearity of…
We define and study certain linear orders on chainable continua. Those orders depend on a sequence of chains obtained from definition of chainability and on a fixed non-principal ultrafilter on the set of natural numbers. An alternative…
We study the collective schedules problem, which consists in computing a one machine schedule of a set of tasks, knowing that a set of individuals (also called voters) have preferences regarding the order of the execution of the tasks. Our…