相关论文: Classification aggregation: a quantitative impossi…

We establish several results on the word problem for just infinite groups. First, for finitely generated just infinite groups we show that the word problem is uniformly decidable for presentations with recursively enumerable sets of…

A notion of arithmetic similarity between number fields is defined by requiring equality of some arithmetic statistics over all but finitely many rational primes. The exceptional set is empty in all previously studied cases, but existing…

A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they…

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…

The incompressibility method is a counting argument in the framework of algorithmic complexity that permits discovering properties that are satisfied by most objects of a class. This paper gives a preliminary insight into Kolmogorov's…

We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…

Arrow's Impossibility Theorem states that any constitution which satisfies Transitivity, Independence of Irrelevant Alternatives (IIA) and Unanimity is a dictatorship. Wilson derived properties of constitutions satisfying Transitivity and…

Orbifold equivalence is a notion of symmetry that does not rely on group actions. Among other applications, it leads to surprising connections between hitherto unrelated singularities. While the concept can be defined in a very general…

We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such…

In a crowd forecasting system, aggregation is an algorithm that returns aggregated probabilities for each question based on the probabilities provided per question by each individual in the crowd. Various aggregation methods have been…

When aggregating Subjective Expected Utility preferences, the Pareto principle leads to an impossibility result unless the individuals have a common belief. This paper examines the source of this impossibility in more detail by considering…

Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…

An extension of an abstract argumentation framework, called collective argumentation, is introduced in which the attack relation is defined directly among sets of arguments. The extension turns out to be suitable, in particular, for…

The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…

The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation iff they must remain occurrences of the same…

We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result for simplicial algebras over these theories, showing…

We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive…

There is an innate human tendency, one might call it the "league table mentality," to construct rankings. Schools, hospitals, sports teams, movies, and myriad other objects are ranked even though their inherent multi-dimensionality would…