相关论文: Nonstandard numbers for qualitative decision makin…

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk…

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…

With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…

In this paper some initial work towards a new approach to qualitative reasoning under uncertainty is presented. This method is not only applicable to qualitative probabilistic reasoning, as is the case with other methods, but also allows…

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…

In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterparts - to prove this statement, a nonstandard…

This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…

This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…

Normal numbers were introduced by Borel and later proven to be a weak notion of algorithmic randomness. We introduce here a natural relativization of normality based on generalized number representation systems. We explore the concepts of…

This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…

We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a…

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…

There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…

Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…

The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function,…

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…

Comprehensible explanations of probabilistic reasoning are a prerequisite for wider acceptance of Bayesian methods in expert systems and decision support systems. A study of human reasoning under uncertainty suggests two different…

It is standard in computational social choice to analyse welfare considerations under the assumptions of normalized utilities. In this note, we summarize some common reasons for this approach. We then mention another justification which is…

Optimization is offered as an objective approach to resolving complex, real-world decisions involving uncertainty and conflicting interests. It drives business strategies as well as public policies and, increasingly, lies at the heart of…