Formation of transitivity in conditional matching to sample by pigeons.

Four pigeons learned a zero-delay matching-to-sample game. Each bird had to peck ten times on a center key to see a sample color. Then three side keys lit up. Pecking the key that matched the sample earned food.

After many correct matches, new pairs appeared. The birds had never seen these pairs together. Yet all four birds instantly picked the correct match. The untrained choices proved transitive relations had formed.

Every pigeon showed emergent transitivity. They acted as if they knew A = B and B = C, so A must equal C. No extra training was needed. The result shows stimulus equivalence can live in a bird brain.

THOMAS et al. (1963) first taught pigeons to pass delayed matching tests. Their work gave the basic method that Brown et al. (1994) later used to probe higher-order relations. It is a straight line from simple matching to full equivalence.

Reichow et al. (2011) asked humans to do the same kind of transitive task. People also showed mixed success until the stimuli were made arbitrary, just like the colors for the pigeons. Same phenomenon, different species.

Zhirnova et al. (2025) pushed the idea further with children. After kids learned to name relations in both directions, analogical performances popped out with no direct analogy training. The bird data foreshadowed this leap.

You now have a non-human model for equivalence. Use it to check your teaching order: conditional discrimination first, then probe for untrained relations. If a pigeon can derive transitivity, your learners probably can too. Start with simple matching, watch for emergent skills, and move on only when the relations solidify.