ALGEBRAIC LEARNING AND NEURAL-NETWORK MODELS FOR TRANSITIVE AND NON-TRANSITIVE RESPONDING

Transitive inference is a kind of deductive reasoning. Given the premi ses ''Anna is taller than Paul'' and ''Paul is taller than Mary'', adu lts and older children easily conclude that ''Anna is taller than Mary ''. However, a related transitive responding ability has also been dem onstrated in younger children and some animals with non-verbal tasks. For this, the premise statements are converted into an operant discrim ination task. The subjects are offered the stimulus pairs A + B-, B C-, C + D-, D + E- where + signifies that the choice of the relevant s timulus is rewarded and - indicates that its choice is penalised. When the subjects responded correctly to these premises, unreinforced test s with the conclusion stimulus pair ED were conducted. If they prefere ntially chose B, they were said to respond transitively. Algebraic con ditioning models have been shown to be capable of reproducing such tra nsitive behaviour. We describe a particularly simple algebraic model b ased on instrumental conditioning and then develop a neural network th at yields transitive responding based on similar principles as the mod el. A variant of the model also incorporates a value transfer mechanis m based on a classical conditioning process that appears to contribute occasionally to the item-ordering underlying transitivity. Some human s, however, exhibit good premise pair performance but poor conclusion test performance. We consider model and network modifications that can account for this behaviour. A variant called the epsilon kappa model is shown to yield graded degrees of transitive responding with conclus ion pairs while maintaining good performance on premise pairs.