Cactus Language • Preliminaries 14

A notation of the form S :> T is introduced to indicate a category of grammatical relationships whose sense is suggested by any of the following readings.

\begin{array}{l}  S ~\mathrm{covers}~ T  \\[2pt]  S ~\mathrm{governs}~ T  \\[2pt]  S ~\mathrm{rules}~ T  \\[2pt]  S ~\mathrm{subsumes}~ T  \\[2pt]  S ~\mathrm{types~over}~ T  \end{array}

The form S :> T plays a number of roles in the description of formal languages by means of formal grammars, flexible enough to be read in the following variety of senses.

Individual
The named or quoted string T is being typed as a sentence S of the language \mathfrak{L}.
Extensional
Each member of the set T also belongs to the set S of sentences in the language \mathfrak{L}.
Intensional
The quality of being T entails the quality S of being a sentence in the language \mathfrak{L}.

Resources

cc: Academia.edu • BlueSky • Laws of FormMathstodonResearch Gate
cc: Conceptual GraphsCyberneticsStructural ModelingSystems 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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