Entre relações de ordem e de equivalência: uma visão matemática para a psicologia

Abstract

This work explores the role of Equivalence Relations, Equivalence Classes, and Order Relations, emphasizing their mathematical and psychological applications. Equivalence Relations are sets formed by elements that share reflexive, symmetric, and transitive relations, grouping them according to specific similarities. In contrast, Order Relations organize the elements of a set into hierarchies or logical sequences based on the properties of reflexivity, antisymmetry, and transitivity. The research analyzes these mathematical structures and highlights their relevance in data analysis and understanding behavioral phenomena. The concepts are connected to Murray Sidman’s investigations into stimulus equivalences, particularly his contributions to understanding the relationships between auditory and visual stimuli in reading and learning. Practical applications are discussed, with an emphasis on education, where such concepts provide tools to enhance the acquisition of reading and language skills. By uniting the concepts of equivalence and order, the study suggests that these complementary approaches offer a solid foundation for analyzing and organizing complex data, contributing to advances in both mathematical and psychological contexts.