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, 17:51, 2 November 2008→Formal extension : Cactus calculus: sub "\_" for " \ldots"
Let us now extend the CSP–GSB calculus in the following way:
Let us now extend the CSP–GSB calculus in the following way:
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>(\ldots),</math> in a particular direction, treating "<math>(\ldots)</math>" as the ''controlled'', ''moderated'', or ''reflective'' negation operator of order 1, and adding another such operator for each integer parameter greater than 1. Taken in series, these operators are symbolized by bracketed argument lists of the following shapes: <math>(\ldots),</math> <math>(\ldots, \ldots),</math> <math>(\ldots, \ldots, \ldots),</math> and so on, where the number of argument slots is the order of the reflective negation operator in question.
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>(\_)\!</math> in a particular manner, treating <math>(\_)\!</math> as the ''[[minimal negation operator]]'' of order 1, and adding another such operator for each integer parameter greater than 1. Taken in series, the minimal negation operators are symbolized by parenthesized argument lists of the following shapes: <math>(\_),\!</math> <math>(\_, \_),\!</math> <math>(\_, \_, \_),\!</math> and so on, where the number of argument slots is the order of the reflective negation operator in question.
The formal rule of evaluation for a <math>k\!</math>''-lobe'' or <math>k\!</math>-operator may be summarized as follows:
The formal rule of evaluation for a <math>k\!</math>''-lobe'' or <math>k\!</math>-operator may be summarized as follows:
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==Case analysis-synthesis theorem==
==Case analysis-synthesis theorem==
