Essential Question: ‘Equal or Equivalent Entities?’ About Two Things as Same, Similar, or Different

We discuss definitions of entities, equality, and equivalence as used by a transdisciplinary diversity of research fields including mathematics, statistics, computational linguistics, computer programming, knowledge engineering, and music theory. Declaring definitions for these concepts in the situational context of each domain specific field supports the essential question ‘Equal or equivalent entities?’ about two things as same, similar, related, or different for that field. Pattern recognition performed by artificial intelligence applications can be described as the automated process of answering this fundamental question about the similarity or difference between two things.