Peirce's non reduction and relational completeness claims in the context of first-order predicate logic

Herzberger (1981) gave a systematic analysis of Peirce's relational theses, and included work on "bonding algebra." We approach the topic from a different expository angle, and discuss its basics with a less weighty toolbox. Setting forth the fundamentals in Sections I and II, we then mention in Section III the availability of an embedding of our basic set-up in a type of "fine structure" for relational statements of higher adicity. This embedding consists in using monadic, dyadic, and triadic "atoms" (which we call "Relation Types") to construct "molecules" of arbitrary adicity via bonding. These molecules can then be incorporated into an easy-to-read version of Beta graphs that can readily be made to embrace first-order predicate logic. Possibilities for cross-disciplinary applications are noted.