Re: Cactus Language • Mechanics 4

The following Table summaries the mechanics of the parsing rules given in the previous post.

A substructure of a painted and rooted cactus is defined recursively as follows.  Starting from the root node of the cactus each of its attachments is a substructure of   If a substructure is a blank or a paint then it constitutes a minimal substructure, meaning no further substructures of arise from it.  If a substructure is a lobe then each of its appendants is also a substructure of and needs to be examined for further substructures.

The concept of substructure can be used to define the varieties of deletion and erasure operations which respect the structure of the abstract graph.  In that application a blank symbol “ ” is treated as a primer, in other words, a clear paint or neutral tint, in effect letting   In that frame of discussion it is useful to make the following distinction.

• To delete a substructure is to replace it with an empty node, in effect, to reduce the whole structure to a trivial point.
• To erase a substructure is to replace it with a blank symbol, in effect, to paint it out of the picture or overwrite it.

A bare PARC, loosely referred to as a bare cactus, is a painted and rooted cactus on the empty palette   A bare cactus can be described in various ways, depending on how the form arises in practice.

• Leaning on the definition of a bare PARCE, a bare PARC can be described as the type of parse graph which arises from parsing a bare cactus expression, in other words, from parsing a sentence of the bare cactus language

• To express it more in its own terms, a bare PARC can be defined by tracing the recursive definition of a generic PARC, but then by detaching an independent form of description from the source of that analogy.  The method is sufficiently sketched as follows.
• A bare PARC is a PARC whose attachments are limited to blanks and bare lobes.
• A bare lobe is a lobe whose appendants are limited to bare PARCs.

• In practice a bare cactus is usually encountered in the process of analyzing or handling an arbitrary PARC, the circumstances of which frequently call for deleting or erasing its paints.  Among other things, that generally makes it easier to observe the unadorned properties of its underlying graphical structure.

Resources

• Cactus Language • Mechanics
• Survey of Animated Logical Graphs
• Survey of Theme One Program

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