Reasoning under uncertainty within the context of probability education: A case study of preservice mathematics teachers

Interpreting phenomena under uncertainty stands as a substantial cognitive activity in our daily life. Furthermore, in probability education research, there is a need for developing a unified model that involves several probabilistic conceptions. From this aspect, a central inquiry has been raised through this study: how do preservice mathematics teachers (PSMTs) reason under uncertainty? A multiple case study design was operated in which a purposive sample of PSMTs was selected to justify their reasoning in two probabilistic contexts while their responses were coded by NVivo, and corresponding categories were developed. As a result, PSMTs’ probabilistic reasoning was classified into mathematical (M), subjective (S), and outcome-oriented (O). Besides, several biases emerged along with these modes of reasoning. While M thinkers shared equiprobability and insensitivity to prior probability, the prediction bias and the belief of Allah’s willingness were yielded among S thinkers. Also, the causal conception spread among O thinkers.

Nonmonotonic Reasoning, Expectations Orderings, and Conceptual Spaces

In Gärdenfors and Makinson (Artif Intell 65(2):197–245, 1994) and Gärdenfors (Knowledge representation and reasoning under uncertainty, Springer-Verlag, 1992) it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties.

The Probabilistic Turn in Semantics and Pragmatics

This article provides an overview of graded and probabilistic approaches in semantics and pragmatics. These approaches share a common set of core research goals: ( a) a concern with phenomena that are best described as graded, including a vast lexicon of words whose meaning adapts flexibly to the contexts in which they are used, as well as reasoning under uncertainty about interlocutors, their goals, and their strategies; ( b) the need to show that representations are learnable, that a listener can learn semantic representations and pragmatic reasoning from data; ( c) an emphasis on empirical evaluation against experimental data or corpus data at scale; and ( d) scaling up to the full size of the lexicon. The methods used are sometimes explicitly probabilistic and sometimes not. Previously, there were assumed to be clear boundaries among probabilistic frameworks, classifiers in machine learning, and distributional approaches, but these boundaries have been blurred. Frameworks in semantics and pragmatics use all three of these, sometimes in combination, to address the four core research questions above. Expected final online publication date for the Annual Review of Linguistics, Volume 8 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Structured argumentation dynamics

This paper develops a logical theory that unifies all three standard types of argumentative attack in AI, namely rebutting, undercutting and undermining attacks. We build on default justification logic that already represents undercutting and rebutting attacks, and we add undermining attacks. Intuitively, undermining does not target default inference, as undercutting, or default conclusion, as rebutting, but rather attacks an argument’s premise as a starting point for default reasoning. In default justification logic, reasoning starts from a set of premises, which is then extended by conclusions that hold by default. We argue that modeling undermining defeaters in the view of default theories requires changing the set of premises upon receiving new information. To model changes to premises, we give a dynamic aspect to default justification logic by using the techniques from the logic of belief revision. More specifically, undermining is modeled with belief revision operations that include contracting a set of premises, that is, removing some information from it. The novel combination of default reasoning and belief revision in justification logic enriches both approaches to reasoning under uncertainty. By the end of the paper, we show some important aspects of defeasible argumentation in which our logic compares favorably to structured argumentation frameworks.

Technical Perspective

The paper entitled "Probabilistic Data with Continuous Distributions" overviews recent work on the foundations of infinite probabilistic databases [3, 2]. Prior work on probabilistic databases (PDBs) focused almost exclusively on the finite case: A finite PDB represents a discrete probability distribution over a finite set of possible worlds [4]. In contrast, an infinite PDB models a continuous probability distribution over an infinite set of possible worlds. In both cases, each world is a finite relational database instance. Continuous distributions are essential and commonplace tools for reasoning under uncertainty in practice. Accommodating them in the framework of probabilistic databases brings us closer to applications that naturally rely on both continuous distributions and relational databases.

A Tutorial on Fire Domino Effect Modeling Using Bayesian Networks

High complexity and growing interdependencies of chemical and process facilities have made them increasingly vulnerable to domino effects. Domino effects, particularly fire dominoes, are spatial-temporal phenomena where not only the location of involved units, but also their temporal entailment in the accident chain matter. Spatial-temporal dependencies and uncertainties prevailing during domino effects, arising mainly from possible synergistic effects and randomness of potential events, restrict the use of conventional risk assessment techniques such as fault tree and event tree. Bayesian networks—a type of probabilistic network for reasoning under uncertainty—have proven to be a reliable and robust technique for the modeling and risk assessment of domino effects. In the present study, applications of Bayesian networks to modeling and safety assessment of domino effects in petroleum tank terminals has been demonstrated via some examples. The tutorial starts by illustrating the inefficacy of event tree analysis in domino effect modeling and then discusses the capabilities of Bayesian network and its derivatives such as dynamic Bayesian network and influence diagram. It is also discussed how noisy OR can be used to significantly reduce the complexity and number of conditional probabilities required for model establishment.

The Precision-Bias Distinction for Evaluating Visual Decision Aids for Risk Perception

Risk communication is critically important, for both patients and providers. However, people struggle to understand risks because there are inherent biases and limitations to reasoning under uncertainty. A common strategy to enhance risk communication is the use of decision aids, such as charts or graphs, that depict the risk visually. A problem with prior research on visual decision aids is that it used a metric of performance that confounds 2 underlying constructs: precision and bias. Precision refers to a person’s sensitivity to the information, whereas bias refers to a general tendency to overestimate (or underestimate) the level of risk. A visual aid is effective for communicating risk only if it enhances precision or, once precision is suitably high, reduces bias. This article proposes a methodology for evaluating the effectiveness of visual decision aids. Empirical data further illustrate how the new methodology is a significant advancement over more traditional research designs.

WOLED: A tool for Online Learning Weighted Answer Set Rules for Temporal Reasoning Under Uncertainty

Complex Event Recognition (CER) systems detect event occurrences in streaming time-stamped input using predefined event patterns. Logic-based approaches are of special interest in CER, since, via Statistical Relational AI, they combine uncertainty-resilient reasoning with time and change, with machine learning, thus alleviating the cost of manual event pattern authoring. We present WOLED, a system based on Answer Set Programming (ASP), capable of probabilistic reasoning with complex event patterns in the form of weighted rules in the Event Calculus, whose structure and weights are learnt online. We compare our ASP-based implementation with a Markov Logic-based one and with a crisp version of the algorithm that learns unweighted rules, on CER datasets for activity recognition, maritime surveillance and fleet management. Our results demonstrate the superiority of our novel implementation, both in terms of efficiency and predictive performance.