Grammar 1

Grammar 1 is something of a misnomer.  It is nowhere near exemplifying any kind of a standard form and it’s put forth only as a starting point for the initiation of more respectable grammars.  Such as it is, it uses the terminal alphabet coming with the territory of the cactus language it specifies in other words, it employs no intermediate symbols, and it embodies the covering set as listed in the following display.

The last two rules of Grammar 1 dictate the following typings.

5. The concept of a sentence in covers any concatenation of sentences in that is, any finite number of freely chosen sentences available to be concatenated one after another.
6. The concept of a sentence in covers any surcatenation of sentences in that is, any string opening with a continuing with a sentence, possibly empty, following with a finite number of phrases of the form and closing with a

The above appears to be just about the most concise description of the cactus language one can imagine but there are a couple of problems commonly felt to afflict its style of presentation and to make it less than completely acceptable.  Briefly stated, the problems turn on the following properties of the formulation.

• The invocation of the kleene star operation is not reduced to a manifestly finitary form.
• The type indicative of a sentence is allowed to cover not only itself but also the empty string.

We’ll discuss those issues at first in general, and especially in regard to how the two features interact with one another, and then we’ll return to address in further detail the questions they engender on their individual bases.

Resources

• Cactus Language • Syntax
• 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