| Abstract: Since 1982, many papers have showed results on learning skills using the Stimulus Equivalence paradigm, based on the mathematical Set Theory, using the properties of reflexivity, symmetry and transitivity applied over elements and sets to explain the "emergence"of new relations (not directly taught). Those papers usually refer to words like node, arc, and distance that cannot be explained within the Set Theory. This paper suggests Graph Theory to substitute the Set Theory as the major mathematical support of the equivalence concepts, based on empirical observations from those papers and selects some basic concepts and operations to justify that and to show that it improves the efficiency of learning. Under this new approach, those words have a specific meaning and provide more mathematical properties and attributes such as weight and length of an arc. On the other hand, since a Graph is a complex structure composed of sets (set of arcs, set of nodes, set of Psi relations), it can hold more mathematical properties without excluding the three Set properties mentioned and used to test the emergence of new equivalent classes stimuli during the matching-to-sample (MTS) testing phase. MTS is considered a Graph operator that builds up the resulting graph, after each iteration, that contains the equivalent stimuli in an acyclic connected net. The way MTS works on the graphs shows a unique path between any two equivalent class stimuli, and those paths can be tested with the transitivity and symmetry properties. A teaching strategy can be directed to build balanced tree-like graphs. An experiment uses four classes A, B, C and D, each containing three abstract symbols as elements, and shows the two possibilities of training structures, while another experiment with five classes (A to E), shows the results over the three possible arrangements under Graph Theory. Although MTS is a Graph Operator of Union, there are different strategies to use it to build bigger and more stable graphs. |