相关论文: Consistency, non triviality and redundancy in math…

In this paper, we examine the long-run behavior of regularized, no-regret learning in finite games. A well-known result in the field states that the empirical frequencies of no-regret play converge to the game's set of coarse correlated…

This paper gives a broad account of the various sequent-based proof formalisms in the proof-theoretic literature. We consider formalisms for various modal and tense logics, intuitionistic logic, conditional logics, and bunched logics. After…

Recently people started to understand that applications of the mathematical formalism of quantum theory are not reduced to physics. Nowadays, this formalism is widely used outside of quantum physics, in particular, in cognition, psychology,…

System design is often taught through domain-specific solutions specific to particular domains, such as databases, operating systems, or computer architecture, each with its own methods and vocabulary. While this diversity is a strength, it…

In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…

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…

In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…

In the present paper we study stability of recurrence equations (which in particular case contain a dynamics of rational functions) generated by contractive functions defined on an arbitrary non-Archimedean algebra. Moreover,…

Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a…

The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. We will give a brief overview about important and…

Data consistency is very desirable because strong semantic properties make it easier to write correct programs that perform as users expect. However, there are good reasons why consistency may have to be weakened to achieve other business…

Redundancy of experimental data is the basic statistic from which the complexity of a natural phenomenon and the proper number of experiments needed for its exploration can be estimated. The redundancy is expressed by the entropy of…

The fact that redundant information does not update a rational belief implies that rational beliefs are updated using Bayes rule. In the framework of Hild (1998a), this is true under mild conditions for discrete, continuous, and arbitrary…

This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…

This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…

Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…

Reliability has long been treated as an engineering practice supported by testing, statistics and standards, yet its status as a scientific discipline remains unsettled. From a philosophical perspective, scientific truth is characterized by…

Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…

The concept of association rules is well--known in data mining. But often redundancy and subsumption are not considered, and standard approaches produce thousands or even millions of resulting association rules. Without further information…

We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…