The following report describes a calculus for representing propositions as sentences, that is, as syntactically defined sequences of signs, and for working with those sentences in light of their semantically defined contents as logical propositions.  In their computational representation the expressions of the calculus parse into a class of graph‑theoretic data structures whose underlying graphs are called painted cacti.

Painted cacti are a specialization of what graph‑theorists refer to as cacti, which are in turn a generalization of what they call trees.  The data structures corresponding to painted cacti have especially nice properties, not only useful in computational terms but interesting from a theoretical standpoint.  The remainder of the present Overview is devoted to motivating the development of the indicated family of formal languages, going under the generic name of Cactus Language.

Resource

For readers interested and intrepid enough to read ahead, here’s an outline of my work in progress on the OEIS Wiki, which I’ll be revising and serializing to the present blog.

Part 1

Cactus Language • Syntax

Part 2

Generalities About Formal Grammars

Part 3

References

Document History

cc: Academia.edu • BlueSky • Laws of Form • Ma^thstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science