Quantitative and methodological aspects of stimulus equivalence.

O'mara (1991) wrote a methods paper. The author built a math tool with graph theory. The tool counts every way you can link stimuli in equivalence training.

The paper also fixes an old mistake. Earlier work said negative choices show past reinforcement. H shows that idea can be wrong.

The graph tool gives the exact count of training paths. You plug in your set size and it lists every link you could teach.

The fix matters because many labs still read the old error. Assuming negative picks always trace to history can lead to bad probes.

Fetterman et al. (1989) came first. They showed kids only form transitive classes when each link earned reinforcement. O'mara (1991) later gave the math that maps all those links.

Ninness et al. (2006) extended the idea to math graphs. Adults learned to match new formulas to charts after brief equivalence training. The graph tool in O'mara (1991) can predict the training paths Chris used.

Boldrin et al. (2022) tested two-choice matching. Equivalence passed even with only one foil, as long as the foil changed across trials. H’s count of possible links stays the same no matter how many choices you show, so the two papers fit together.

You can use the graph tool to plan your own equivalence set. Draw nodes for each stimulus, draw arrows for trained links, and the tool tells you how many paths you must probe. That saves trials and keeps you from missing a test. The warning about negative choices also helps you write cleaner probes—don’t assume a “no” means bad history; it may just be an untested link.