The University of Edinburgh -
Division of Informatics
Forrest Hill & 80 South Bridge

PhD Thesis #8803

Title:Computational Modelling of Transitive Inference: a Micro Analysis of a Simple Form of Reasoning.
Date: 1988
Abstract:The goal of this research is to provide an account of transitive inference which has both psychological and computational justification, and to relate it to the broader context of inference and information gaining systems in general. perhaps the most well known transitive inference task is called the "N-term series problem" which has been used, for example, to assess cognitive development in young children. It is argued that this task taps basic cognitive skills which are likely to form the building blocks of more complex forms of reasoning. In a typical five-term series task, subjects are given the information A > B, B > C, C > D and D > E, where the letters donate arbitrary stimuli and ">" denotes an ordinal comparison, such as "longer than". Subjects are then able to infer the relationship between "remote" pairs such as B and D. A typical phenomenon associated with this, and related tasks, is called the ordinal distance effect - the time taken to make comparisons between remote pairs is, typically, faster than the responses to the original training pairs, suggesting that much inference has taken place during the initial learning process. Recent evidence from monkeys has been shown to be fully representative of this class of experiment. Furthermore, the monkey studies are the only ones to provide a sufficiently rich database to permit a microanalysis based on computational modelling. This thesis contains such an analysis, and it is shown how many aspects of the subjects' behaviour can be accounted for with a surprisingly simple rule-based model, in which subjects' strategies are represented by highly constrained rule stacks. The model can account for the major phenomena associated with the five-term series task, and can model individual subject variation within a principled framework. Finally, an algorithm is proposed for acquiring appropriate rule stacks, given a random sequence of training examples such as received by experimental subject

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