相关论文: Grades of Discrimination: Indiscernibility, symmet…

We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…

Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. (These definitions are based on definitions…

We study the fair allocation of indivisible items under relevance constraints, where each agent has a set of relevant items and can only receive items that are relevant to them. While the relevance constraint has been studied in recent…

Impossibility results show that important fairness measures (independence, separation, sufficiency) cannot be satisfied at the same time under reasonable assumptions. This paper explores whether we can satisfy and/or improve these fairness…

We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…

Symmetry is often treated in philosophy of physics as an interpretive problem. A particularly lively dispute concerns local symmetries: do they indicate surplus structure that ought to be expunged, or are they merely a harmless redundancy?…

We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…

We discuss the nature and a general formulation of the relativity principle and we show that it can be justified starting from a strictly operational point of view. We give some remark on the connection with the spacetime symmetry groups.…

Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a coded expression of our experience then its effectiveness is quite reasonable. Its…

We propose a class of semimetrics for preference relations any one of which is an alternative to the classical Kemeny-Snell-Bogart metric. (We take a fairly general viewpoint about what constitutes a preference relation, allowing for any…

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

It is introduced the concept of Superiority Degree one competitive decision over another. On the basis of this concept the mathematics theoretic structure is developed, which is part of pairs comparisons branch in modern decision making…

Equivalence principles played a central role in the development of general relativity. Furthermore, they have provided operative procedures for testing the validity of general relativity, or constraining competing theories of gravitation.…

The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…

With AI systems widely applied to assist humans in decision-making processes such as talent hiring, school admission, and loan approval; there is an increasing need to ensure that the decisions made are fair. One major challenge for…

We consider a class of systems of difference equations defined on an elementary quadrilateral of the ${\mathbb{Z}}^2$ lattice, define their eliminable and dynamical variables, and demonstrate their use. Using the existence of infinite…

We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…

Algorithmic fairness has conventionally adopted the mathematically convenient perspective of racial color-blindness (i.e., difference unaware treatment). However, we contend that in a range of important settings, group difference awareness…

We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…