Algebraic Learning and Neural Network Models for Transitive and Non-transitive Responding

Transitive inference is a kind of deductive reasoning. Given the premises “Anna is taller than Paul” and “Paul is taller than Mary”, adults and older children easily conclude that “Anna is taller than Mary”. However, a related transitive responding ability has also been demonstrated in younger children and some animals with non-verbal tasks. For this, the premise statements are converted into an operant discrimination task. The subjects are offered the stimulus pairs A+ B-, B+ C-, C+ D-, D+ Ewhere + signifies that the choice of the relevant stimulus is rewarded and- indicates that its choice is penalised. When the subjects responded correctly to these premises, unreinforced tests with the conclusion stimulus pair BD were conducted. If they preferentially chose B, they were said to respond transitively. Algebraic conditioning models have been shown to be capable of reproducing such transitive behaviour. We describe a particularly simple algebraic model based on instrumental conditioning and then develop a ...

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