Configurations of planar non-overlapping closed curves

Composition of closed, non-intersecting planar curves, called *boundaries*, constructs a formal diagrammatic language, independent of an interpretation as logic. The alphabet is a singleton set of symbols consisting of the *empty boundary*, { ○ }, which is called a *mark*.

A word consists of replicates of marks composed in a nonconventional manner. Since boundaries have both an inside and an outside, replicate symbols can be juxtaposed in two ways: on the inside of the original boundary and on the outside of the original boundary.

Rather than one "concatenation" operator, there are two: SHARING is composition on the outside, while BOUNDING is composition on the inside. The formal language consists of the set of composable boundary forms.