General document | Literature Review on Mental Models and Linear Separability

Abstract

The mental models theory suggests that people make reasoning errors because they construct partial – and inaccurate – mental models. It predicts that where people are required to consider false information, they are more prone to making errors than when they are only required to consider true information. Findings consistent with this theory have been demonstrated across a number of studies, particularly the work of Johnson-Laird. However, researchers at DSTO suggested that these findings are better explained by a linear separability effect. That is, problems are easier to solve when they are linearly separable than when they are nonlinearly separable. That is, the simplicity and precision with which correct and incorrect answers can be separated determines the extent to which they will be solved correctly. This literature review examines research on mental models and linear separability published between 2000 and 2012, to establish if this explanation has been proposed by other researchers. Results indicate that no other researchers have proposed this, or similar, explanations, hence the linear separability hypothesis has the potential to make a novel contribution to the literature 

Executive Summary

Researchers such as Johnson-Laird have consistently demonstrated that people have difficulty solving complex reasoning problems, such as:

Only one statement about a hand of cards is true:

1. There is a King or Ace or both.

2. There is a Queen or Ace or both.

While the majority of people will respond that the Ace is more likely to occur, this is logically incorrect. As only one statement about the hand of cards is true, the Ace can never occur, hence the King is more likely. Johnson-Laird suggests that the reason people make such mistakes is that they construct partial mental models to assist in reasoning. However, these models are flawed as they do not represent false information, e.g. that if Statement 1 is true in the problem above, then Statement 2 must be false, and vice versa.

Defence Science and Technology Organisation (DSTO) researchers have suggested that the concept of linear separability is more accurate at explaining Johnson-Laird’s findings. Categories are linearly separable when a single line (for categories with two dimensions, such as height/weight, colour/shape) can be drawn that differentiates between categories. Categories are nonlinearly separable when they cannot be differentiated using a single line.

In a preliminary study conducted in 2003-2004, DSTO researchers demonstrated that the linear separability explanation for Johnson-Laird’s findings was plausible and supported by the data. In order to examine this more fully, research was commenced in 2011 under the auspices of Land Operations Division’s Enabling Research project.

One key component of this work was a review of relevant literature on mental models and linear separability published between 2000 and 2012 to identify related studies and ensure that no similar or competing research had been conducted. Results indicated that while a number of similar studies have been conducted, the Enabling Research Project still represents a novel contribution to the body of research.