Differential Logic • 2.1
• https://inquiryintoinquiry.com/2026/02/06/differential-logic-2-b/
Cactus Language for Propositional Logic —
The development of differential logic is facilitated by having a moderately efficient calculus in place at the level of boolean-valued functions and elementary logical propositions. One very efficient calculus on both conceptual and computational grounds is based on just two types of logical connectives, both of variable k-ary scope. The syntactic formulas of that calculus map into a family of graph-theoretic structures called “painted and rooted cacti” which lend visual representation to the functional structures of propositions and smooth the path to efficient computation.
The first kind of connective is a parenthesized sequence of propositional expressions, written (e₁, e₂, …, eₖ₋₁, eₖ) to mean exactly one of the propositions e₁, e₂, …, eₖ₋₁, eₖ is false, in short, their “minimal negation” is true. An expression of that form is associated with a cactus structure called a “lobe” and is “painted” with the colors e₁, e₂, …, eₖ₋₁, eₖ as shown below.
Lobe Connective
• https://inquiryintoinquiry.files.wordpress.com/2020/04/cactus-graph-ej-lobe-connective.jpg
Resources —
Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/
Minimal Negation Operator
• https://oeis.org/wiki/Minimal_negation_operator
Survey of Differential Logic
• https://inquiryintoinquiry.com/2025/05/03/survey-of-differential-logic-8/
Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2025/05/02/survey-of-animated-logical-graphs-8/
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