# Category Archives: Propositional Equation Reasoning Systems

## Animated Logical Graphs • 25

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: Or, thinking in terms of the corresponding cactus graphs, writing for a blank node and for … Continue reading

## Animated Logical Graphs • 24

Re: Ontolog Forum • Joseph Simpson Boolean functions and different ways of contemplating their complexity are definitely the right ballpark, or at least the right planet, for field-testing logical graphs. I don’t know much about the Boolean Sensitivity Conjecture but … Continue reading

## Animated Logical Graphs • 23

The following Table will suffice to show how the “streamer-cross” forms C.S. Peirce used in his essay on “Qualitative Logic” and Spencer Brown used in his Laws of Form, as they are extended through successive steps of controlled reflection, translate into … Continue reading

## Animated Logical Graphs • 22

The step of controlled reflection we just took can be repeated at will, as suggested by the following series of forms: Written inline, we have the series and so on, whose general form is   With this move we have … Continue reading

## Animated Logical Graphs • 21

A funny thing just happened.  Let’s see if we can tell where.  We started with the algebraic expression in which the operand suggests the contemplated absence or presence of any arithmetic expression or its value, then we contemplated the absence … Continue reading

## Animated Logical Graphs • 20

Another tactic I tried by way of porting operator variables into logical graphs and laws of form was to hollow out a leg of Spencer-Brown’s crosses, gnomons, markers, whatever you wish to call them, as shown below: The initial idea … Continue reading

## Animated Logical Graphs • 19

We have encountered the question of how to extend our formal calculus to take account of operator variables. In the days when I scribbled these things on the backs of computer punchcards, the first thing I tried was drawing big … Continue reading