Related papers: Semantics of Division for Polynomial Solvers
We introduce the completeness problem for Modal Logic and examine its complexity. For a definition of completeness for formulas, given a formula of a modal logic, the completeness problem asks whether the formula is complete for that logic.…
Existing efforts to formulate computational definitions of fairness have largely focused on distributional notions of equality, where equality is defined by the resources or decisions given to individuals in the system. Yet existing…
This paper considers a novel variant of the online fair division problem involving multiple agents in which a learner sequentially observes an indivisible item that has to be irrevocably allocated to one of the agents while satisfying a…
For models of concurrent and distributed systems, it is important and also challenging to establish correctness in terms of safety and/or liveness properties. Theories of distributed systems consider equivalences fundamental, since they (1)…
The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fields cannot be defined by equations, the theory of…
A computably presented algebraic field $F$ has a \emph{splitting algorithm} if it is decidable which polynomials in $F[X]$ are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of…
Binary classification based on predicted probabilities (scores) is a fundamental task in supervised machine learning. While thresholding scores is Bayes-optimal in the unconstrained setting, using a single threshold generally violates…
This article considers the problem of solving a system of $n$ real polynomial equations in $n+1$ variables. We propose an algorithm based on Newton's method and subdivision for this problem. Our algorithm is intended only for nondegenerate…
We explore the following question: Is a decision-making program fair, for some useful definition of fairness? First, we describe how several algorithmic fairness questions can be phrased as program verification problems. Second, we discuss…
In Machine Learning, an accepted definition of fairness of a decision taken by a classifier is that it should not depend on protected features, such as gender. Unfortunately, when constraints exist between features, such dependencies can be…
This paper summarises the current state-of-the art in the study of compositionality in distributional semantics, and major challenges for this area. We single out generalised quantifiers and intensional semantics as areas on which to focus…
Mechanism design is addressed in the context of fair allocations of indivisible goods with monetary compensation. Motivated by a real-world social choice problem, mechanisms with verification are considered in a setting where (i) agents'…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Algorithmic fairness, and in particular the fairness of scoring and classification algorithms, has become a topic of increasing social concern and has recently witnessed an explosion of research in theoretical computer science, machine…
Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…
A new and relatively elementary approach is proposed for solving the problem of fair division of a continuous resource (measurable space, pie, etc.) between several participants, the selection criteria of which are described by charges…
In this paper we investigate fair computations in the pi-calculus. Following Costa and Stirling's approach for CCS-like languages, we consider a method to label process actions in order to filter out unfair computations. We contrast the…
We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework…