[CG] Re: Operator Variables in Logical Graphs

Operator Variables in Logical Graphs • 10 • https://inquiryintoinquiry.com/2024/04/18/operator-variables-in-logical-gra… Re: Operator Variables in Logical Graphs • 9 • https://inquiryintoinquiry.com/2024/04/17/operator-variables-in-logical-gra… All, Let's examine the Formal Operation Table for the third in our series of reflective forms to see if we can elicit the general pattern. Table 14. Formal Operation Table (a,b,c) Variant 1 • https://inquiryintoinquiry.com/wp-content/uploads/2021/04/formal-operation-… Alternatively, if we think in terms of the corresponding cactus graphs, writing “o” for an unmarked node and “|” for a terminal edge, we get the following Table. Table 15. Formal Operation Table (a,b,c) Variant 2 • https://inquiryintoinquiry.com/wp-content/uploads/2021/04/formal-operation-… Evidently, the rule is that “(a , b , c)” denotes the value denoted by “o” if and only if exactly one of the variables a, b, c has the value denoted by “|”, otherwise “(a , b , c)” denotes the value denoted by “|”. Examining the whole series of reflective forms shows this to be the general rule. • In the Entitative Interpretation (En), where o = false and | = true, “(x₁ , … , xₙ)” translates as “not just one of the xₖ is true”. • In the Existential Interpretation (Ex), where o = true and | = false, “(x₁ , … , xₙ)” translates as “just one of the xₖ is not true”. Regards, Jon cc: https://www.academia.edu/community/5AA9dN cc: https://mathstodon.xyz/@Inquiry/112225263055943815