− | The first extension is the ''reflective extension of logical graphs'', or what may be described as the ''cactus language'', after its principal graph-theoretic data structure. It is generated by generalizing the negation operator <math>\texttt{(_)}\!</math> in a particular manner, treating <math>\texttt{(_)}\!</math> as the ''[[minimal negation operator]]'' of order 1, and adding another such operator for each integer parameter greater than 1. | + | The first extension is the ''reflective extension of logical graphs'', or what may be described as the ''cactus language'', after its principal graph-theoretic data structure. It is generated by generalizing the negation operator <math>\texttt{(} \_ \texttt{)}\!</math> in a particular manner, treating <math>\texttt{(} \_ \texttt{)}\!</math> as the ''[[minimal negation operator]]'' of order 1 and adding another such operator for each order greater than 1. Taken in series, the minimal negation operators are symbolized by parenthesized argument lists of the following shapes: <math>\texttt{(} \_ \texttt{)},\!</math> <math>\texttt{(} \_ \texttt{,} \_ \texttt{)},\!</math> <math>\texttt{(} \_ \texttt{,} \_ \texttt{,} \_ \texttt{)},\!</math> and so on, where the number of argument slots is the order of the reflective negation operator in question. |