The link between logic, mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain-general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief-laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief-neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real-life referents) develops later than the ability to reason about belief-inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8.

A longitudinal analysis of estimation, counting skills, and mathematical ability across the first school year

In response to claims that the quality (and in particular linearity) of children's mental representation of number acts as a constraint on number development, we carried out a longitudinal assessment of the relationships between number line estimation, counting, and mathematical abilities. Ninety-nine 5-year-olds were tested on 4 occasions at 3 monthly intervals. Correlations between the 3 types of ability were evident, but while the quality of children's estimations changed over time and performance on the mathematical tasks improved over the same period, changes in one were not associated with changes in the other. In contrast to the earlier claims that the linearity of number representation is potentially a unique contributor to children's mathematical development, the data suggest that this variable is not significantly privileged in its impact over and above simple procedural number skills. We propose that both early arithmetic success and estimating skill are bound closely to developments in counting ability.

A defeasible reasoning model of inductive concept learning from examples and communication

This paper introduces a logical model of inductive generalization, and specifically of the machine learning task of inductive concept learning (ICL). We argue that some inductive processes, like ICL, can be seen as a form of defeasible reasoning. We define a consequence relation characterizing which hypotheses can be induced from given sets of examples, and study its properties, showing they correspond to a rather well-behaved non-monotonic logic. We will also show that with the addition of a preference relation on inductive theories we can characterize the inductive bias of ICL algorithms. The second part of the paper shows how this logical characterization of inductive generalization can be integrated with another form of non-monotonic reasoning (argumentation), to define a model of multiagent ICL. This integration allows two or more agents to learn, in a consistent way, both from induction and from arguments used in the communication between them. We show that the inductive theories achieved by multiagent induction plus argumentation are sound, i.e. they are precisely the same as the inductive theories built by a single agent with all data. © 2012 Elsevier B.V.

Integrating textual analysis and evidential reasoning for decision making in Engineering design

Decision making is an important element throughout the life-cycle of large-scale projects. Decisions are critical as they have a direct impact upon the success/outcome of a project and are affected by many factors including the certainty and precision of information. In this paper we present an evidential reasoning framework which applies Dempster-Shafer Theory and its variant Dezert-Smarandache Theory to aid decision makers in making decisions where the knowledge available may be imprecise, conflicting and uncertain. This conceptual framework is novel as natural language based information extraction techniques are utilized in the extraction and estimation of beliefs from diverse textual information sources, rather than assuming these estimations as already given. Furthermore we describe an algorithm to define a set of maximal consistent subsets before fusion occurs in the reasoning framework. This is important as inconsistencies between subsets may produce results which are incorrect/adverse in the decision making process. The proposed framework can be applied to problems involving material selection and a Use Case based in the Engineering domain is presented to illustrate the approach. © 2013 Elsevier B.V. All rights reserved.

Common-sense reasoning for human action recognition

This paper presents a novel method that leverages reasoning capabilities in a computer vision system dedicated to human action recognition. The proposed methodology is decomposed into two stages. First, a machine learning based algorithm - known as bag of words - gives a first estimate of action classification from video sequences, by performing an image feature analysis. Those results are afterward passed to a common-sense reasoning system, which analyses, selects and corrects the initial estimation yielded by the machine learning algorithm. This second stage resorts to the knowledge implicit in the rationality that motivates human behaviour. Experiments are performed in realistic conditions, where poor recognition rates by the machine learning techniques are significantly improved by the second stage in which common-sense knowledge and reasoning capabilities have been leveraged. This demonstrates the value of integrating common-sense capabilities into a computer vision pipeline. © 2012 Elsevier B.V. All rights reserved.

Online Multiperson Tracking With Occlusion Reasoning and Unsupervised Track Motion Model

We address the problem of multi-target tracking in realistic crowded conditions by introducing a novel dual-stage online tracking algorithm. The problem of data-association between tracks and detections, based on appearance, is often complicated by partial occlusion. In the first stage, we address the issue of occlusion with a novel method of robust data-association, that can be used to compute the appearance similarity between tracks and detections without the need for explicit knowledge of the occluded regions. In the second stage, broken tracks are linked based on motion and appearance, using an online-learned linking model. The online-learned motion-model for track linking uses the confident tracks from the first stage tracker as training examples. The new approach has been tested on the town centre dataset and has performance comparable with the present state-of-the-art

Reasoning on the basis of fantasy content:two studies with high-functioning autistic adolescents

Reasoning about problems with empirically false content can be hard, as the inferences that people draw are heavily influenced by their background knowledge. However, presenting empirically false premises in a fantasy context helps children and adolescents to disregard their beliefs, and to reason on the basis of the premises. The aim of the present experiments was to see if high-functioning adolescents with autism are able to utilize fantasy context to the same extent as typically developing adolescents when they reason about empirically false premises. The results indicate that problems with engaging in pretence in autism persist into adolescence, and this hinders the ability of autistic individuals to disregard their beliefs when empirical knowledge is irrelevant.

Mathematical Modelling of a Reciprocating Piston Expander

Modern internal combustion (IC) engines reject around two thirds of the energy provided by the fuel as low-grade waste heat. Capturing a portion of this waste heat energy and transforming it into a more useful form of energy could result in a significant reduction in fuel consumption. By using the low-grade heat, an organic Rankine cycle (ORC) can produce mechanical work from a pressurised organic fluid with the use of an expander.
Ideal gas assumptions are shown to produce significant errors in expander performance predictions when using an organic fluid. This paper details the mathematical modelling technique used to accurately model the thermodynamic processes for both ideal and non-ideal fluids within the reciprocating expander. A comparison between the two methods illustrates the extent of the errors when modelling a reciprocating piston expander. Use of the ideal gas assumptions are shown to produce an error of 55% in the prediction of power produced by the expander when operating on refrigerant R134a.

An extended framework for evidential reasoning systems

Based on the Dempster-Shafer (D-S) theory of evidence and G. Yen's (1989), extension of the theory, the authors propose approaches to representing heuristic knowledge by evidential mapping and pooling the mass distribution in a complex frame by partitioning that frame using Shafter's partition technique. The authors have generalized Yen's model from Bayesian probability theory to the D-S theory of evidence. Based on such a generalized model, an extended framework for evidential reasoning systems is briefly specified in which a semi-graph method is used to describe the heuristic knowledge. The advantage of such a method is that it can avoid the complexity of graphs without losing the explicitness of graphs. The extended framework can be widely used to build expert systems

An Improvement of Subject Reacquisition by Reasoning and Revision

CCTV systems are broadly deployed in the present world. Despite this, the impact on anti-social and criminal behaviour has been minimal. Subject reacquisition is a fundamental task to ensure in-time reaction for intelligent surveillance. However, traditional reacquisition based on face recognition is not scalable, hence in this paper we use reasoning techniques to reduce the computational effort which deploys the time-of-flight information between interested zones such as airport security corridors. Also, to improve accuracy of reacquisition, we introduce the idea of revision as a method of post-processing.We demonstrate the significance and usefulness of our framework with an experiment which shows much less computational effort and better accuracy.

Episodic Reasoning for Vision-Based Human Action Recognition

Smart Spaces, Ambient Intelligence, and Ambient Assisted Living are environmental paradigms that strongly depend on their capability to recognize human actions. While most solutions rest on sensor value interpretations and video analysis applications, few have realized the importance of incorporating common-sense capabilities to support the recognition process. Unfortunately, human action recognition cannot be successfully accomplished by only analyzing body postures. On the contrary, this task should be supported by profound knowledge of human agency nature and its tight connection to the reasons and motivations that explain it. The combination of this knowledge and the knowledge about how the world works is essential for recognizing and understanding human actions without committing common-senseless mistakes. This work demonstrates the impact that episodic reasoning has in improving the accuracy of a computer vision system for human action recognition. This work also presents formalization, implementation, and evaluation details of the knowledge model that supports the episodic reasoning.