Cactus Language • Preliminaries 11

Posted on May 16, 2025 by Jon Awbrey

Given the idea of a Parce on \mathfrak{P} as a member of the cactus language \mathfrak{C}(\mathfrak{P}) a number of frequently occurring sublanguages and commonly invoked operations on their expressions can now be given succinct definition.

A bare Parce, a bit loosely referred to as a bare cactus expression, is a Parce on the empty palette \mathfrak{P} = \varnothing.  A bare Parce is a sentence in the bare cactus language, variously notated as follows.

\mathfrak{C}^0 = \mathfrak{C} (\varnothing) = \mathrm{Parce}^0 = \mathrm{Parce}(\varnothing)

That set of strings, regarded as a formal language in its own right, is a sublanguage of every cactus language \mathfrak{C}(\mathfrak{P}).  A bare cactus expression is commonly encountered in practice when one has occasion to start with an arbitrary Parce and then finds reason to delete or erase all its paints.

Resources

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

This entry was posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization and tagged , , , , , , , , , , , , , , , , . Bookmark the permalink.

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