Transitive inference

The linear and circular arrangements of tunnels used by Roberts and Phelps (1994) to study the use of a spatial code by rats given transitive inference problems. 

It should be noted that the control conditions of Roberts and Phelps eliminated both temporal serial order cues and spatial cues, since problems were presented concurrently and their spatial positions were either randomized (Experiment 1) or placed in a circle (Experiment 2). When both sources of ordering were removed, animals showed indifference between stimuli B and D. Could rats use just serial order as a cue Davis (1992) trained rats with no spatial cues present but presented his training pairs in serial order. When tested, rats showed significant transitive inference. This finding, when combined with that of Roberts and Phelps, suggests that rats can use either spatial order or temporal order as a cue for the overall order of training stimuli. What is unknown from these observations is whether the final representations differ or are the same. That is, could a rat use temporal order to form a spatial representation of linearity or use spatial position to form a temporal representation of linearity Such questions await further research. 

Given the unquestionable importance of spatial representation to animals, it is possible that they use such representations to deal with problems in other cognitive domains. Some evidence in support of the idea that animals might use linear spatial models to keep track of time and number and to perform transitive inference was discussed, but these possibilities remain highly speculative. 

The evidence that the children were actually making transitive inferences about space in these tasks was indirect, but the idea was bolstered by some other work (Bryant Trabasso, 1971), done in a completely different context, on transitive inferences. We made the controversial claim that we had shown that pre-school children can make transitive inferences about quantity provided that they could remember the premises that they had to put together to make the inference. 

The experiments that we have described show that some spatial arrangements help and others hinder children s solution to various mathematical problems. Young children are adept at using simple, all-or-none spatial relations, and the principles of gestalt psychology provide a good account of the way that they do so. Add to this their evident ability to combine relationships in deductive and transitive inferences and you have already a formidable set of mechanisms for learning about the environment. 

It seems very likely that many other aspects of human reasoning, besides transitive inference, also depend on the integration of semantic knowledge and working-memory operations with representations derived from those that support visuospatial perception. We hope the model we have described here may provide an example of how the connections between perception and thought may be given explicit realization in a neural architecture. 

Bryant, P. E., and Trabasso, T. (1971). Transitive inferences and memory in young children. Nature, 232, 456-458. 

Coulmas, F. (1989). The writing systems of the world. Oxford Basil Blackwell. Couvillon, P. A., and Bitterman, M. E. (1992). A conventional conditioning analysis of transitive inference in pigeons. Journal of Experimental Psychology Animal Behavior Processes, 18, 308-310. 

Davis, H. (1992). Transitive inference in rats Rattus norvegicus). Journal of Comparative Psychology, 106, 342-349. 

Fersen, L. von, Wynne, C. D. L., Delius, J. D., and Staddon, J. E. R. (1991). Transitive inference formation in pigeons. Journal of Experimental Psychology Animal Behavior Processes, 17, 334-341. 

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