Bayesian inference for the information gain model

One of the most popular paradigms to use for studying human reasoning involves the Wason card selection task. In this task, the participant is presented with four cards and a conditional rule (e.g., “If there is an A on one side of the card, there is always a 2 on the other side”). Participants are asked which cards should be turned to verify whether or not the rule holds. In this simple task, participants consistently provide answers that are incorrect according to formal logic. To account for these errors, several models have been proposed, one of the most prominent being the information gain model (Oaksford & Chater, Psychological Review, 101, 608–631, 1994). This model is based on the assumption that people independently select cards based on the expected information gain of turning a particular card. In this article, we present two estimation methods to fit the information gain model: a maximum likelihood procedure (programmed in R) and a Bayesian procedure (programmed in WinBUGS). We compare the two procedures and illustrate the flexibility of the Bayesian hierarchical procedure by applying it to data from a meta-analysis of the Wason task (Oaksford & Chater, Psychological Review, 101, 608–631, 1994). We also show that the goodness of fit of the information gain model can be assessed by inspecting the posterior predictives of the model. These Bayesian procedures make it easy to apply the information gain model to empirical data. Supplemental materials may be downloaded along with this article from www.springerlink.com

Jean-Paul Brodeur, the man and his thought

This issue of the Canadian Journal of Criminology and Criminal Justice contains a number of contributions to mark the scholarship of Professor Jean-Paul Brodeur, of the Ecole de criminologie at the Universite de Montreal, Canada, and the Western world of academic criminology, lost one of its brightest stars when Jean-Paul passed away in 2010. Jean-Paul was also Associate Editor of the Canadian Journal of Criminology for many years. In this brief introduction, we provide some information on Jean-Paul, his career in criminology, and the contributions which follow.Arts, Education & Law Group, School of Criminology and Criminal JusticeNo Full Tex

The Scholarship of Jean-Paul Brodeur

This issue of the Canadian Journal of Criminology and Criminal Justice contains a number of contributions to mark the scholarship of Professor Jean-Paul Brodeur, of the Ecole de criminologie at the Universite de Montreal, Canada, and the Western world of academic criminology, lost one of its brightest stars when Jean-Paul passed away in 2010. Jean-Paul was also Associate Editor of the Canadian Journal of Criminology for many years. In this brief introduction, we provide some information on Jean-Paul, his career in criminology, and the contributions which follow.Arts, Education & Law Group, School of Criminology and Criminal JusticeNo Full Tex

Logic in University Mathematics Education

International audienc

How diagrams can support syllogistic reasoning: an experimental study

This paper explores the question of what makes diagrammatic representa- tions effective for human logical reasoning, focusing on how Euler diagrams support syllogistic reasoning. It is widely held that diagrammatic representations aid intuitive understanding of logical reasoning. In the psychological literature, however, it is still controversial whether and how Euler diagrams can aid untrained people to success- fully conduct logical reasoning such as set-theoretic and syllogistic reasoning. To challenge the negative view, we build on the findings of modern diagrammatic logic and introduce an Euler-style diagrammatic representation system that is designed to avoid problems inherent to a traditional version of Euler diagrams. It is hypothesized that Euler diagrams are effective not only in interpreting sentential premises but also in reasoning about semantic structures implicit in given sentences. To test the hypothesis, we compared Euler diagrams with other types of diagrams having different syntactic or semantic properties. Experiment compared the difference in performance between syllogistic reasoning with Euler diagrams and Venn diagrams. Additional analysis examined the case of a linear variant of Euler diagrams, in which set-relationships are represented by one-dimensional lines. The experimental results provide evidence supporting our hypothesis. It is argued that the efficacy of diagrams in supporting syllo- gistic reasoning crucially depends on the way they represent the relational information contained in categorical sentences