Young children's statistical reasoning : a tale of two contexts

This thesis explored the knowledge and reasoning of young children in solving novel statistical problems, and the influence of problem context and design on their solutions. It found that young children's statistical competencies are underestimated, and that problem design and context facilitated children's application of a wide range of knowledge and reasoning skills, none of which had been taught. A qualitative design-based research method, informed by the Models and Modeling perspective (Lesh & Doerr, 2003) underpinned the study. Data modelling activities incorporating picture story books were used to contextualise the problems. Children applied real-world understanding to problem solving, including attribute identification, categorisation and classification skills. Intuitive and metarepresentational knowledge together with inductive and probabilistic reasoning was used to make sense of data, and beginning awareness of statistical variation and informal inference was visible.

Deviant consumer behaviour : a qualitative exploration

Deviant behaviour is an ongoing problem in the consumer marketplace (Daunt and Harris, 2012). To investigate this issue, a number of authors have focused on empirically assessing consumer perceptions of right and wrong behaviours, such as the Muncy-Vitell (1992) consumer ethics scale. While studies like this have provided extensive empirical insights, qualitative insight into why consumers make these behaviour classifications remains underexplored. The aim of this paper is to extend on that literature by exploring the reasoning behind behavioural classifications. Using interviews, seven factors were identified in consumer definitions of acceptable, questionable, and unacceptable consumer behaviours including; official classification, prevalence, ease of justification, perceived fairness, consequences, risk, and values. These results also provide actionable insights for marketers in that multi-level deterrence strategies must be employed to more effectively deter consumer deviance, as opposed to traditional deterrence strategies based on cost-benefit analyses.

Qualitative theorem proving in linear constraints

We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of the proof is not an issue. Indeed what we need is the existence of the proof and not its mechanization. In this paper, we treat the linear case and illustrate the power of this paradigm by giving extremely simple proofs of two central theorems in the complexity and geometry of linear programming.

Representing and Reasoning About Change in Geologic Interpretation

Geologic interpretation is the task of inferring a sequence of events to explain how a given geologic region could have been formed. This report describes the design and implementation of one part of a geologic interpretation problem solver -- a system which uses a simulation technique called imagining to check the validity of a candidate sequence of events. Imagining uses a combination of qualitative and quantitative simulations to reason about the changes which occured to the geologic region. The spatial changes which occur are simulated by constructing a sequence of diagrams. The quantitative simulation needs numeric parameters which are determined by using the qualitative simulation to establish the cumulative changes to an object and by using a description of the current geologic region to make quantitative measurements. The diversity of reasoning skills used in imagining has necessitated the development of multiple representations, each specialized for a different task. Representations to facilitate doing temporal, spatial and numeric reasoning are described in detail. We have also found it useful to explicitly represent processes. Both the qualitative and quantitative simulations use a discrete 'layer cake' model of geologic processes, but each uses a separate representation, specialized to support the type of simulation. These multiple representations have enabled us to develop a powerful, yet modular, system for reasoning about change.

Causal and Teleological Reasoning in Circuit Recognition

This thesis presents a theory of human-like reasoning in the general domain of designed physical systems, and in particular, electronic circuits. One aspect of the theory, causal analysis, describes how the behavior of individual components can be combined to explain the behavior of composite systems. Another aspect of the theory, teleological analysis, describes how the notion that the system has a purpose can be used to aid this causal analysis. The theory is implemented as a computer program, which, given a circuit topology, can construct by qualitative causal analysis a mechanism graph describing the functional topology of the system. This functional topology is then parsed by a grammar for common circuit functions. Ambiguities are introduced into the analysis by the approximate qualitative nature of the analysis. For example, there are often several possible mechanisms which might describe the circuit's function. These are disambiguated by teleological analysis. The requirement that each component be assigned an appropriate purpose in the functional topology imposes a severe constraint which eliminates all the ambiguities. Since both analyses are based on heuristics, the chosen mechanism is a rationalization of how the circuit functions, and does not guarantee that the circuit actually does function. This type of coarse understanding of circuits is useful for analysis, design and troubleshooting.

Combining Functional and Structural Reasoning for Safety Analysis of Electrical Designs

C.J.Price, D.R.Pugh, N.A.Snooke, J.E.Hunt, M.S.Wilson, Combining Functional and Structural Reasoning for Safety Analysis of Electrical Designs, Knowledge Engineering Review, vol 12:3, pp.271-287, 1997.

Model-Based Reasoning: A Principled Approach for Software Engineering

Lee M.H., Model-Based Reasoning: A Principled Approach for Software Engineering, Software - Concepts and Tools,19(4), pp179-189, 2000.

Qualitative Modelling of Linear Networks in Engineering Applications

Lee M.H., Qualitative Modelling of Linear Networks in Engineering Applications, in Proc. ECAI?2000, 14th European Conf. on Artificial Intelligence, Berlin, August 19th - 25th 2000, pp161-5.

On Models, Modelling and the Distinctive Nature of Model-Based Reasoning

M.H. Lee, On Models, Modelling and the Distinctive Nature of Model-Based Reasoning, AI Communications, 12 (3), pp127-137.1999.

Characterising Model-Based Reasoning

Lee M.H., Characterising Model-Based Reasoning, Proc. 10th Int. Workshop on Principles of Diagnosis, (DX'99), Loch Awe, Scotland, 1999, pp140-146.

Inductive reasoning in the justification of the result of adding two even numbers

In this paper we present an analysis of the inductive reasoning of twelve secondary students in a mathematical problem-solving context. Students were proposed to justify what is the result of adding two even numbers. Starting from the theoretical framework, which is based on Pólya’s stages of inductive reasoning, and our empirical work, we created a category system that allowed us to make a qualitative data analysis. We show in this paper some of the results obtained in a previous study.

Intelligent design assistant (IDA): a case base reasoning system for material and design

This paper describes the approach to the modelling of experiential knowledge in an industrial application of Case-Based Reasoning (CBR). The CBR involves retrieval techniques in conjunction with a relational database. The database is especially designed as a repository of experiential knowledge, and includes qualitative search indices. The system is intended to help design engineers and material engineers in the submarine cable industry. It consists of three parts: a materials database; a database of experiential knowledge; and a CBR system used to retrieve similar past designs based upon component and material qualitative descriptions. The system is currently undergoing user testing at the Alcatel Submarine Networks site in Greenwich.

On the Qualitative Comparison of Decisions Having Positive and Negative Features

Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly distinguished. That is what is done, for example, in Cumulative Prospect Theory. However, contrary to the latter framework that presupposes genuine numerical assessments, human agents often decide on the basis of an ordinal ranking of the pros and the cons, and by focusing on the most salient arguments. In other terms, the decision process is qualitative as well as bipolar. In this article, based on a bipolar extension of possibility theory, we define and axiomatically characterize several decision rules tailored for the joint handling of positive and negative arguments in an ordinal setting. The simplest rules can be viewed as extensions of the maximin and maximax criteria to the bipolar case, and consequently suffer from poor decisive power. More decisive rules that refine the former are also proposed. These refinements agree both with principles of efficiency and with the spirit of order-of-magnitude reasoning, that prevails in qualitative decision theory. The most refined decision rule uses leximin rankings of the pros and the cons, and the ideas of counting arguments of equal strength and cancelling pros by cons. It is shown to come down to a special case of Cumulative Prospect Theory, and to subsume the “Take the Best” heuristic studied by cognitive psychologists.

In and out of home care decisions: The influence of confirmation bias in developing decision supportive reasoning

The aims of this study were to identify the themes Social Workers regard as important in supporting decisions to remove children from, or return them to, the care of their parents. To further elicit underlying hypotheses that are discernible in interpretation of evidence. A case study, comprising a two-part vignette with a questionnaire, recorded demographic information, child welfare attitudes and risk assessments, using scales derived from standardised instruments, was completed by 202 Social Workers in Northern Ireland. There were two manipulated variables, mother’s attitude to removal and child’s attitude to reunification2 years later. In this paper we use data derived from respondents’ qualitative comments explaining their reasoning for in and out of home care decisions. Some 60.9% of respondent’s chose the parental care option at part one, with 94% choosing to have the child remain in foster care at part two. The manipulated variables were found to have no significant statistical effect. However, three underlying hypotheses were found to underpin decisions; (a)child rescue, (b) kinship defence and (c) a hedged position on calculation of risk subject to further assessment. Reasoning strategies utilised by social workers to support their decision making suggest that they tend to selectively interpret information either positively or negatively to support pre-existing underlying hypotheses. This finding is in keeping with the literature on ‘confirmation bias.’ The research further draws attention to the need to incorporate open questions in quantitative studies, to help guard against surface reading of data, which often does not ‘speak for itself.’