Transitive inference

Transitive inference is a form of inferential reasoning. For example, if you know that A > B and B > C and C > D and D > E, then you can conclude without being told than B > D. You can replace "greater than (>)" with any other (supposedly) transitive relation, such as "better than" or "darker-colored than".

There is a hypothesis that many animals do transitive inference (see "model animals", below).

Structures implicated in transitive inference

 * The hippocampus; see TransitiveInferenceAndTheHippocampus
 * Frontal and parietal lobes (Acuna et al '02)

Computational models

 * Bryson and Leong '04: Representations Underlying Transitive Choice in Humans and Other Primates
 * Wood et al '04: ACT-R is almost a Model of Primate Task Learning: Experiments in Modelling Transitive Inference

Model animals
Transitive inference has been demonstrated in humans, birds (von Fersen et al '91), rats (Roberts and Phelps '94) (Davis '92) (Dusek and Eichenbaum '97), and monkeys (Rapp et al '96) (Boysen et al '93) (Gillian '81) (McGonigle and Chalmers, '77) (but see (Van Elzakker et al '03) for some doubts that it was really demonstrated at all in some of these cases).

Refs

 * Acuna BD, Eliassen JC, Donoghue JP, Sanes JN. Frontal and parietal lobe activation during transitive inference in humans. Cereb Cortex. 2002 Dec;12(12):1312-21.
 * Boysen, Sarah T.; Berntson, Gary G.; Shreyer, Traci A.; Quigley, Karen S. Processing of ordinality and transitivity by chimpanzees (Pan troglodytes). Journal of Comparative Psychology. 107, 208-215. (1993)
 * Bryson and Leong. '04. Representations Underlying Transitive Choice in Humans and Other Primates. Published online. (2004).
 * Hank Davis. Transitive inference in rats (Rattus norvegicus). J. Comp. Psychol. 106, 342-349. (1992)
 * Gillan, Douglas J. Reasoning in the chimpanzee: II. Transitive inference. Journal of Experimental Psychology: Animal Behavior Processes. Apr Vol 7(2) 150-164. (1981)
 * McGonigle, B. O. & Chalmers, M. Are monkeys logical? Nature (London) 267, 694-696. (1977)
 * Roberts, W. A. & Phelps, M. T. TRANSITIVE INFERENCE IN RATS - A TEST OF THE SPATIAL CODING HYPOTHESIS Psychological Sci. 5, 368-374. (1994)
 * Lorenzo von Fersen, Wynne CDL, Delius Juan D, Staddon JER. Transitive inference in pigeons. Journal of Experimental Psychology: Animal Behavior Processes. 17:334-341. 1991.
 * Mark Wood, Jonathan Leong, Joanna Bryson. ACT-R is almost a Model of Primate Task Learning:  Experiments in Modelling Transitive Inference. Presented at Cognitive Science (2004).
 * Mike Van Elzakker, O'Reilly RC, Rudy JW. Transitivity, flexibility, conjunctive representations, and the hippocampus. I. An empirical analysis. Hippocampus 13:3:334-340. 2003.


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