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#PaintedAndRootedCacti

#DifferentialPropositionalCalculus • 5.3
• https://inquiryintoinquiry.com/2020/02/29/differential-propositional-calculus-5/

At the top of Figure 8 is the #VennDiagram for the #LinearProposition of rank 3, which may be expressed by any one of the following 3 forms:

\[\texttt{(}p\texttt{,(}q\texttt{,}r\texttt{))}, \quad \texttt{((}p\texttt{,}q\texttt{),}r\texttt{)}, \quad p+q+r.\]

\(\text{Figure 8.1. Rank 3 Linear}\, f : \mathbb{B}^3 \to \mathbb{B}\)
• https://inquiryintoinquiry.files.wordpress.com/2020/02/venn-diagram-e280a2-p-q-r-e280a2-p-q-r.jpg

#Logic #LogicalGraphs
#PaintedAndRootedCacti
#MinimalNegationOperators

This is a venn diagram for a particular boolean function on 3 boolean variables p, q, r.

The venn diagram consists of a rectangular area representing the universe of discourse and 3 overlapping circular areas representing 3 subsets of that universe. The circular areas are labeled p, q, r respectively to indicate the subsets where the corresponding boolean variables are equal to 1, in other words, true.

The function of interest in this case is called the rank 3 linear function on 3 variables and it evaluates to 1 on just 4 subsets, namely, the following:

(1) p and q and r are all true.
(2) p alone is true, but neither q or r.
(3) q alone is true, but neither p or r
(4) r alone is true, but neither p or q.

The venn diagram indicates those 4 subsets with a conventional shading, in this case, a shade of blue, leaving the remaining regions white.

#DifferentialPropositionalCalculus • 2
https://inquiryintoinquiry.com/2020/02/22/differential-propositional-calculus-2/

#CactusCalculus —

Table 6 introduces a #Syntax for #PropositionalCalculus based on 2 families of #MultigradeLogicalConnectives.

Table 6. #Syntax and #Semantics of a Calculus for #PropositionalLogic
https://inquiryintoinquiry.files.wordpress.com/2020/02/syntax-and-semantics-of-a-calculus-for-propositional-logic.png

Related Subjects —
#Peirce #Semiotics #BooleanFunctions
#Logic #LogicalGraphs #DifferentialLogic
#GraphTheory #CactusGraphs #CactusLanguage
#MinimalNegationOperators #PaintedAndRootedCacti

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