Related papers: Plausibility and probability in deductive reasonin…
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.
A number of writers(Joseph Halpern and Fahiem Bacchus among them) have offered semantics for formal languages in which inferences concerning probabilities can be made. Our concern is different. This paper provides a formalization of…
Qualitative probabilistic reasoning in a Bayesian network often reveals tradeoffs: relationships that are ambiguous due to competing qualitative influences. We present two techniques that combine qualitative and numeric probabilistic…
The systematic biases seen in people's probability judgments are typically taken as evidence that people do not reason about probability using the rules of probability theory, but instead use heuristics which sometimes yield reasonable…
We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the…
In this work we first illustrate the subjective theory of de Finetti. We recall the notion of coherence for both the betting scheme and the penalty criterion, by considering the unconditional and conditional cases. We show the equivalence…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A…
We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using…
Recent advancements in machine learning have emphasized the need for transparency in model predictions, particularly as interpretability diminishes when using increasingly complex architectures. In this paper, we propose leveraging…
This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…
The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
The quantification of uncertainties of computer simulations due to input parameter uncertainties is paramount to assess a model's credibility. For computationally expensive simulations, this is often feasible only via surrogate models that…
Dealing with uncertain, contradicting, and ambiguous information is still a central issue in Artificial Intelligence (AI). As a result, many formalisms have been proposed or adapted so as to consider non-monotonicity, with only a limited…
We give an algorithm A which assigns probabilities to logical sentences. For any simple infinite sequence of sentences whose truth-values appear indistinguishable from a biased coin that outputs "true" with probability p, we have that the…
In recent years, there has been an increased need for the use of active systems - systems required to act automatically based on events, or changes in the environment. Such systems span many areas, from active databases to applications that…
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…
In recent years there has been a spate of papers describing systems for probabilisitic reasoning which do not use numerical probabilities. In some cases the simple set of values used by these systems make it impossible to predict how a…
This paper presents an advance in the direction of working with probabilities in a paracomplete setting using Logics of Formal Undeterminedness (LFUs). The undeterminedness is interpreted here as missing evidence. A theorem of total…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…