Interactions among emergent relations during equivalence class formation

The interactions among symmetry, transitivity, and equivalence tests during the formation of 3-member equivalence classes were studied with 14 college students. After training AB and BC, a test with BA, CB, AC, and CA was conducted concurrently. Failure led to serial testing with probes for CA equivalence, BA symmetry, CA equivalence, CB symmetry, CA equivalence, AC transitivity, and CA equivalence. For five subjects, equivalence tests were passed immediately once BA and CB symmetry as well as AC transitivity had been induced. Thus, symmetry and transitivity were precursors for successful performance on equivalence tests. The conjoint function of symmetry and transitivity was assessed with the equivalence probes. As the equivalence probes were passed immediately, the presence of symmetry alone and transitivity alone were sufficient for their conjoint function without additional intervention. For different subjects, transitivity alone and symmetry were induced either directly with BA, CB, or AC probes or indirectly with equivalence probes. Equivalence probes can also induce various combinations of symmetry and transitivity. Thus, different subjects formed classes in various patterns at different rates.