Changes

By way of equipping this inquiry with a bit of concrete material, I begin with a consideration of ''higher order propositional expressions'', in particular, those that stem from the propositions on 1 and 2 variables.

By way of equipping this inquiry with a bit of concrete material, I begin with a consideration of ''higher order propositional expressions'', in particular, those that stem from the propositions on 1 and 2 variables.

'''Note on notation.'''  The discussion that follows uses [[minimal negation operations]], expressed as bracketed tuples of the form $\texttt{(} e_1 \texttt{,} \ldots \texttt{,} e_k \texttt{)},$ and logical conjunctions, expressed as concatenated tuples of the form $e_1 ~\ldots~ e_k$, as the sole expression-forming operations of a calculus for [[boolean-valued functions]] or "propositions".  The expressions of this calculus parse into data structures whose underlying graphs are called ''cacti'' by graph theorists.  Hence the name ''[[cactus language]]'' for this dialect of propositional calculus.

'''Note on notation.'''  The discussion that follows uses [[minimal negation operations]], expressed as bracketed tuples of the form <math>\texttt{(} e_1 \texttt{,} \ldots \texttt{,} e_k \texttt{)},</math> and logical conjunctions, expressed as concatenated tuples of the form <math>e_1 ~\ldots~ e_k,</math> as the sole expression-forming operations of a calculus for [[boolean-valued functions]] or "propositions".  The expressions of this calculus parse into data structures whose underlying graphs are called ''cacti'' by graph theorists.  Hence the name ''[[cactus language]]'' for this dialect of propositional calculus.

====Higher Order Propositions and Logical Operators (''n'' = 1)====

====Higher Order Propositions and Logical Operators (''n'' = 1)====