[CG] Re: Cactus Language • Preliminaries

Cactus Language • Preliminaries 4 • https://inquiryintoinquiry.com/2025/04/11/cactus-language-preliminaries-4/ The informal mechanisms illustrated in the preceding discussion equip us with a description of “cactus language” adequate to providing conceptual and computational representations for the minimal formal logical system variously known as “propositional logic” or “sentential calculus”. The “painted cactus language” ‡C‡ is actually a parameterized family of languages, consisting of one language ‡C‡(‡P‡) for each set ‡P‡ of “paints”. The alphabet ‡A‡ = ‡M‡ ∪ ‡P‡ is the disjoint union of the following two sets of symbols. ‡M‡ is the alphabet of “markers”, the set of “punctuation marks”, or the collection of “syntactic constants” common to all the languages ‡C‡(‡P‡). Various ways of representing the elements of ‡M‡ are shown in the following display. Cactus Language Display 2 • https://inquiryintoinquiry.files.wordpress.com/2025/04/cactus-language-disp… • ‡M‡ = { ‡m‡₁ , ‡m‡₂ , ‡m‡₃ , ‡m‡₄ } = { “ ” , “(” , “,” , “)” } = { blank , links , comma , right } ‡P‡ is the “palette”, the alphabet of “paints”, or the collection of “syntactic variables” peculiar to the language ‡C‡(‡P‡). The set of signs in ‡P‡ may be enumerated as follows. • ‡P‡ = {‡p‡ₖ : k ∈ K}. 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