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.

The thinking doctor: clinical decision making in contemporary medicine

Diagnostic errors are responsible for a significant number of adverse events. Logical reasoning and good decision-making skills are key factors in reducing such errors, but little emphasis has traditionally been placed on how these thought processes occur, and how errors could be minimised. In this article, we explore key cognitive ideas that underpin clinical decision making and suggest that by employing some simple strategies, physicians might be better able to understand how they make decisions and how the process might be optimised.

From inconsistency handling to non-canonical requirements management: A logical perspective

As a class of defects in software requirements specification, inconsistency has been widely studied in both requirements engineering and software engineering. It has been increasingly recognized that maintaining consistency alone often results in some other types of non-canonical requirements, including incompleteness of a requirements specification, vague requirements statements, and redundant requirements statements. It is therefore desirable for inconsistency handling to take into account the related non-canonical requirements in requirements engineering. To address this issue, we propose an intuitive generalization of logical techniques for handling inconsistency to those that are suitable for managing non-canonical requirements, which deals with incompleteness and redundancy, in addition to inconsistency. We first argue that measuring non-canonical requirements plays a crucial role in handling them effectively. We then present a measure-driven logic framework for managing non-canonical requirements. The framework consists of five main parts, identifying non-canonical requirements, measuring them, generating candidate proposals for handling them, choosing commonly acceptable proposals, and revising them according to the chosen proposals. This generalization can be considered as an attempt to handle non-canonical requirements along with logic-based inconsistency handling in requirements engineering.

Logic feels so good-I like it! Evidence for intuitive detection of logicality in syllogistic reasoning

When people evaluate syllogisms, their judgments of validity are often biased by the believability of the conclusions of the problems. Thus, it has been suggested that syllogistic reasoning performance is based on an interplay between a conscious and effortful evaluation of logicality and an intuitive appreciation of the believability of the conclusions (e.g., Evans, Newstead, Allen, & Pollard, 1994). However, logic effects in syllogistic reasoning emerge even when participants are unlikely to carry out a full logical analysis of the problems (e.g., Shynkaruk & Thompson, 2006). There is also evidence that people can implicitly detect the conflict between their beliefs and the validity of the problems, even if they are unable to consciously produce a logical response (e.g., De Neys, Moyens, & Vansteenwegen, 2010). In 4 experiments we demonstrate that people intuitively detect the logicality of syllogisms, and this effect emerges independently of participants' conscious mindset and their cognitive capacity. This logic effect is also unrelated to the superficial structure of the problems. Additionally, we provide evidence that the logicality of the syllogisms is detected through slight changes in participants' affective states. In fact, subliminal affective priming had an effect on participants' subjective evaluations of the problems. Finally, when participants misattributed their emotional reactions to background music, this significantly reduced the logic effect.

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.

Logic Brightens My Day: Evidence for Implicit Sensitivity to Logical Validity.

A key assumption of dual process theory is that reasoning is an explicit, effortful, deliberative process. The present study offers evidence for an implicit, possibly intuitive component of reasoning. Participants were shown sentences embedded in logically valid or invalid arguments. Participants were not asked to reason but instead rated the sentences for liking (Experiment 1) and physical brightness (Experiments 2-3). Sentences that followed logically from preceding sentences were judged to be more likable and brighter. Two other factors thought to be linked to implicit processing-sentence believability and facial expression-had similar effects on liking and brightness ratings. The authors conclude that sensitivity to logical structure was implicit, occurring potentially automatically and outside of awareness. They discuss the results within a fluency misattribution framework and make reference to the literature on discourse comprehension. 

Mathematical prerequisites for learning statistics in Psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates.

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology - calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylie's (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge , likely to hamper the learning of statistics.