Charles S. Peirce invented the essentials of boundary logic in the 1890s, with his Existential Graphs. In Laws of Form (1968), Spencer Brown put it into an algebraic format and supplied the arithmetic of boundary logic. Boundary logic itself contributes a simple and intuitive set of pattern-equations that define the form of diagrammatic logic. These rules incorporate fundamental concepts such as semipermeable boundaries and void-equivalent forms. Here is a succinct paper relating these three systems:

These next three are long papers. What's the Difference? tries to place boundary logic within conventional mathematics. It is newish and needs some minor revisions. Equality Is Not Free traces the rather esoteric foundational issue that boundary logic requires only one recursive equation as a basis. This means that the rule of Involution can be proved from Occlusion and Pervasion alone. Taking Nothing Seriously attempts to wrap up these thoughts in establishing boundary computation as a pure mathematics that can be interpreted as logic and as other types of systems.