Operator Variables in Logical Graphs • 10

Re: Operator Variables in Logical Graphs • 9

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.

Alternatively, if we think in terms of the corresponding cactus graphs, writing for an unmarked node and for a terminal edge, we get the following Table.

Evidently, the rule is that denotes the value denoted by if and only if exactly one of the variables has the value denoted by otherwise denotes the value denoted by   Examining the whole series of reflective forms shows this to be the general rule.

• In the Entitative Interpretation where = false and = true,
  translates as “not just one of the is true”.

• In the Existential Interpretation where = true and = false,
  translates as “just one of the is not true”.

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