In 1904, CSP gave a "grammar free" definition of a relation in terms of firstness, secondness and thirdness. By "grammar free", I mean that it was not based on predicate logic and was closer to the existential diagrammatic logics he proposed. It is consistent with the iconicity of chemical notation.
"Firstness is the mode of being of that which is such as it is, positively and without reference to anything else.
Secondness is the mode of being of that which is such as it is, with respect to a second but regardless of any third.
Thirdness is the mode of being of that which is such as it is, in bringing a second and third in relation to each other." - Letter to Lady Welby, 1904 Oct 12, (CP 8.328)
Thirdness is the mode of being of that which is such as it is, in bringing a second and third in relation to each other." - Letter to Lady Welby, 1904 Oct 12, (CP 8.328)