Yes, no, maybe, I don’t know: Complexity and application of abstract argumentation with incomplete knowledge

argumentation, as originally defined by Dung, is a model that allows the description of certain information about arguments and relationships between them: in an abstract argumentation framework (AF), the agent knows for sure whether a given argument or attack exists. It means that the absence of an attack between two arguments can be interpreted as “we know that the first argument does not attack the second one”. But the question of uncertainty in abstract argumentation has received much attention in the last years. In this paper, we survey approaches that allow to express information like “There may (or may not) be an attack between these arguments”. We describe the main models that incorporate qualitative uncertainty (or ignorance) in abstract argumentation, as well as some applications of these models. We also highlight some open questions that deserve some attention in the future.

Application of a Mobile Robot for Picking Berries Under Qualitative Uncertainty of Conditions

Over the last decade, the development of computer technology has progressed significantly, which allowed to automate many production processes through the use of intelligent control systems. The possibility of creating modern control systems that allow solving complex multi-factor tasks in conditions of uncertainty has significantly expanded the scope of application of robotics. The article considers an approach to solving one of the tasks of controlling an intelligent mobile robot for agricultural purposes – selecting the order of application of the robot for picking berries. The procedure for decision-making by an intelligent control system for a mobile robot under the qualitative uncertainty of berry picking conditions has been developed. This procedure can be implemented by developing software. The approach proposed by the authors to solving such problems can be used not only for control the intelligent mobile robot for picking berries, but also for other purposes. The article presents the results of applying the developed method for solving the task of control the agricultural mobile robot for picking strawberry in the climatic conditions of Central Russia.

Effects of communicating uncertainty descriptions in hazard identification, risk characterization, and risk protection

Uncertainty is a crucial issue for any risk assessment. Consequently, it also poses crucial challenges for risk communications. Many guidebooks advise reporting uncertainties in risk assessments, expecting that the audience will appreciate this disclosure. However, the empirical evidence about the effects of uncertainty reporting is sparse and inconclusive. Therefore, based on examples of potential health risks of electromagnetic fields (EMF), three experiments were conducted analysing the effects of communicating uncertainties separately for hazard identification, risk characterisation and risk protection. The setups aimed to explore how reporting and how explaining of uncertainty affects dependent variables such as risk perception, perceived competence of the risk assessors, and trust in risk management. Each of the three experiments used a 2x2 design with a first factor presenting uncertainty descriptions (as used in public controversies on EMF related health effects) or describing a certainty conditions; and a second factor explaining the causes of uncertainties (by pointing at knowledge gaps) or not explaining them. The study results indicate that qualitative uncertainty descriptions regarding hazard identification reduce the confidence in the professional competencies of the assessors. In contrast, a quantitative uncertainty description in risk characterisation–regarding the magnitude of the risk–does not affect any of the dependent variables. Concerning risk protection, trust in exposure limit values is not affected by qualitative uncertainty information. However, the qualitative description of uncertainty regarding the adequacy of protection amplifies fears. Furthermore, explaining this uncertainty results in lower text understandability.

Uncertain About Uncertainty: How Qualitative Expressions of Forecaster Confidence Impact Decision-Making With Uncertainty Visualizations

When forecasting events, multiple types of uncertainty are often inherently present in the modeling process. Various uncertainty typologies exist, and each type of uncertainty has different implications a scientist might want to convey. In this work, we focus on one type of distinction between direct quantitative uncertainty and indirect qualitative uncertainty. Direct quantitative uncertainty describes uncertainty about facts, numbers, and hypotheses that can be communicated in absolute quantitative forms such as probability distributions or confidence intervals. Indirect qualitative uncertainty describes the quality of knowledge concerning how effectively facts, numbers, or hypotheses represent reality, such as evidence confidence scales proposed by the Intergovernmental Panel on Climate Change. A large body of research demonstrates that both experts and novices have difficulty reasoning with quantitative uncertainty, and visualizations of uncertainty can help with such traditionally challenging concepts. However, the question of if, and how, people may reason with multiple types of uncertainty associated with a forecast remains largely unexplored. In this series of studies, we seek to understand if individuals can integrate indirect uncertainty about how “good” a model is (operationalized as a qualitative expression of forecaster confidence) with quantified uncertainty in a prediction (operationalized as a quantile dotplot visualization of a predicted distribution). Our first study results suggest that participants utilize both direct quantitative uncertainty and indirect qualitative uncertainty when conveyed as quantile dotplots and forecaster confidence. In manipulations where forecasters were less sure about their prediction, participants made more conservative judgments. In our second study, we varied the amount of quantified uncertainty (in the form of the SD of the visualized distributions) to examine how participants’ decisions changed under different combinations of quantified uncertainty (variance) and qualitative uncertainty (low, medium, and high forecaster confidence). The second study results suggest that participants updated their judgments in the direction predicted by both qualitative confidence information (e.g., becoming more conservative when the forecaster confidence is low) and quantitative uncertainty (e.g., becoming more conservative when the variance is increased). Based on the findings from both experiments, we recommend that forecasters present qualitative expressions of model confidence whenever possible alongside quantified uncertainty.

Possibilistic Games with Incomplete Information

Bayesian games offer a suitable framework for games where the utility degrees are additive in essence. This approach does nevertheless not apply to ordinal games, where the utility degrees do not capture more than a ranking, nor to situations of decision under qualitative uncertainty. This paper proposes a representation framework for ordinal games under possibilistic incomplete information (π-games) and extends the fundamental notion of Nash equilibrium (NE) to this framework. We show that deciding whether a NE exists is a difficult problem (NP-hard) and propose a Mixed Integer Linear Programming (MILP) encoding. Experiments on variants of the GAMUT problems confirm the feasibility of this approach.

A COMPACT QUALITATIVE UNCERTAINTY PRINCIPLE FOR SOME NONUNIMODULAR GROUPS

Let $G$ be a separable locally compact group with type $I$ left regular representation, $\widehat{G}$ its dual, $A(G)$ its Fourier algebra and $f\in A(G)$ with compact support. If $G=\mathbb{R}$ and the Fourier transform of $f$ is compactly supported, then, by a classical Paley–Wiener theorem, $f=0$. There are extensions of this theorem for abelian and some unimodular groups. In this paper, we prove that if $G$ has no (nonempty) open compact subsets, $\hat{f}$, the regularised Fourier cotransform of $f$, is compactly supported and $\text{Im}\,\hat{f}$ is finite dimensional, then $f=0$. In connection with this result, we characterise locally compact abelian groups whose identity components are noncompact.