Related papers: An axiomatic approach to diversity
With the rapid development of recommender systems, accuracy is no longer the only golden criterion for evaluating whether the recommendation results are satisfying or not. In recent years, diversity has gained tremendous attention in…
This paper takes an axiomatic and calculational view of diversity (or "N-version programming"), where multiple implementations of the same specification are executed in parallel to increase dependability. The central notion is…
This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…
As the world's democratic institutions are challenged by dissatisfied citizens, political scientists and also computer scientists have proposed and analyzed various (innovative) methods to select representative bodies, a crucial task in…
Diversity measurement underpins the study of biological systems, but measures used vary across disciplines. Despite their common use and broad utility, no unified framework has emerged for measuring, comparing and partitioning diversity.…
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
This paper introduces a qualitative measure of ambiguity and analyses its relationship with other measures of uncertainty. Probability measures relative likelihoods, while ambiguity measures vagueness surrounding those judgments. Ambiguity…
When selecting applicants for scholarships, universities, or jobs, practitioners often aim for a diverse cohort of qualified recipients. However, differing articulations, constructs, and notions of diversity prevents decision-makers from…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
We study, in an abstract axiomatic setting, the notion of sectional category of a morphism. From this, we unify and generalize known results about this invariant in different settings as well as we deduce new applications.
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good…
We derive axiomatically the probability function that should be used to make decisions given any form of underlying uncertainty.
Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…
The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a…
We contemplate the notion of ambiguity in mathematical discourse. We consider a general method of resolving ambiguity and semantic options for sustaining a resolution. The general discussion is applied to the case of `fraction' which is…
We develop new aspects of the the of numerosity theory; more exactly, we emphasize its relation with the ordinal numbers, cardinal numbers, hyperreal numbers and surreal numbers. In particular, we combine the notion of numerosity with the…