[CG] Re: Cactus Language • Preliminaries

Cactus Language • Preliminaries 5 • https://inquiryintoinquiry.com/2025/04/13/cactus-language-preliminaries-5/ The easiest way to define the language ‡C‡(‡P‡) is to indicate the general run of operations required to construct the greater share of its sentences from the designated few which require a special election. To do that we introduce a family of operations called “syntactic connectives” on the strings of ‡A‡*. If the strings on which they operate are already sentences of ‡C‡(‡P‡) then the operations amount to “sentential connectives”. If the syntactic sentences, viewed as abstract strings of uninterpreted signs, are provided with a semantics where they denote propositions, in other words, indicator functions on a universe of discourse, then the operations amount to “propositional connectives”. Rather than presenting the most concise description of cactus languages right from the beginning, it aids comprehension to develop a picture of their forms in gradual stages, starting with the most natural ways of viewing their elements, if somewhat at a distance, and working through the most easily grasped impressions of their structures, if not always the sharpest acquaintances with their details. We begin by defining two sets of basic operations on strings of ‡A‡*. Concatenation — • The “concatenation” of one string s₁ is the string s₁ • The “concatenation” of two strings s₁, s₂ is the string s₁ ∙ s₂ • The “concatenation” of n strings (sₖ)ₖ₌₁…ₙ is the string s₁ ∙ … ∙ sₙ Surcatenation — • The “surcatenation” of one string s₁ is the string “(” ∙ s₁ ∙ “)” • The “surcatenation” of two strings s₁, s₂ is the string “(” ∙ s₁ ∙ “,” ∙ s₂ ∙ “)” • The “surcatenation” of n strings (sₖ)ₖ₌₁…ₙ is the string “(” ∙ s₁ ∙ “,” ∙ … ∙ “,” ∙ sₙ ∙ “)” Resources — Cactus Language • Preliminaries • https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1#Cactus_Language_.E2.… Survey of Animated Logical Graphs • https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs… Survey of Theme One Program • https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/ Regards, Jon cc: https://www.academia.edu/community/lavx71 cc: https://www.researchgate.net/post/Cactus_Language_Preliminaries