Cactus Language • Discussion

[Jon Awbrey]

Cactus Language • Discussion 1
• https://inquiryintoinquiry.com/2025/05/07/cactus-language-discussion-1/

All,

Answering some questions from a reader ...

Re: Cactus Language • Preliminaries 9
• https://inquiryintoinquiry.com/2025/04/25/cactus-language-preliminaries-9/

Re: Cybernetics • Joe Bury
• https://groups.google.com/g/cybcom/c/kqwcuOMDtJo/m/aclbc7llDwAJ

JB:
❝What does subcatenation and surcatenation mean?
Their definitions are not found in a dictionary.
I get the formulas you wrote but I don't understand the meaning.❞

Thanks for the question, Joe,

The current presentation of Cactus Language is rather abstract and formal
because that's what we need for a fully computational parsing algorithm,
and there's quite a bit more to do on that score as we go, but I have
written more intuitive introductions to the same material various
times before — You might try one of the following for starters.

Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-b/

Keeping it short and simple as possible —

Under the Existential Interpretation —

• The syntactic connective of Concatenation is interpreted as the
Logical Conjunction, which says all of its operands are true.

• The syntactic connective of Surcatenation is interpreted as the
Minimal Negation Operation, which says exactly one of its operands
is false.

Under the Entitative Interpretation —

• The syntactic connective of Concatenation is interpreted as the
Logical Disjunction, which says some of its operands are true.

• The syntactic connective of Surcatenation is interpreted as the
Dual of Minimal Negation, which says not just one of its operands
is true.

Regards,

Jon

[Jon Awbrey]

Cactus Language • Discussion 2
• https://inquiryintoinquiry.com/2025/05/13/cactus-language-discussion-2/

A reader has questions —

Re: Alex Shkotin
• https://inquiryintoinquiry.com/2025/04/25/cactus-language-preliminaries-9/#comment-89423

Thanks for the questions, Alex,

As I mentioned in the first discussion post, the current presentation

of Cactus Language is rather abstract and formal because that's what

we need to implement a fully computational parser for the family of
languages we have in mind. That is all well and good but it does
leave us hanging when it comes to motivation and remembering why
we are bothering with such a mass of formal detail.

When I find myself getting lost in syntactic abstractions it's a good idea
to stop and remind myself what led me to explore the computational powers
of cactus graphs in the first place. In my case it began with C.S. Peirce's
and Spencer Brown's systems of logical graphs. Two developments of that
work which take up the story much nearer to scratch can be found on the
following pages.

Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-b/

Short answers to Alex's questions —

• One blank in brackets i.e. “( )” is a sentence.

• Two blanks in brackets i.e. “( )” is a sentence.
(Blanks can be concatenated any number of times.)

• All three of the following strings are sentences.
(,,)
( , , )
((),(),())

Finally, I think cactus languages are context‑free as I think
the last best grammars I constructed for them are context‑free,
but that is one of those hazy memories I'll need to check out
on the current pass through the material.

Resources —

Cactus Language • Preliminaries
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1#Cactus_Language_.E2.80.A2_Preliminaries

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2025/05/02/survey-of-animated-logical-graphs-8/

Survey of Theme One Program
• https://inquiryintoinquiry.com/2025/05/06/survey-of-theme-one-program-7/

Regards,

Jon