# Category Archives: Topology

## Differential Logic • Discussion 3

Re: R.J. Lipton • P<NP Instead of boolean circuit complexity I would look at logical graph complexity, where those logical graphs are constructed from minimal negation operators. Physics once had a frame problem (complexity of dynamic updating) long before AI … Continue reading

## Differential Logic • 10

It’s been a while, so let’s review … Tables A1 and A2 showed two ways of organizing the sixteen boolean functions or propositional forms on two variables, as expressed in several notations.  For ease of reference, here are fresh copies … Continue reading

## Differential Logic • Discussion 2

Re: Peirce List • Edwina Taborsky I first encountered Peirce’s Collected Papers sometime during my freshman year in one of the quieter corners of the Michigan State Math Library where I used to hide out to study and shortly after … Continue reading

## Differential Logic • 9

Propositional Forms on Two Variables Table A2 arranges the propositional forms on two variables according to another plan, sorting propositions with similar shapes into seven subclasses.  Thereby hangs many a tale, to be told in time. Table A2.  Propositional Forms … Continue reading

## Differential Logic • Discussion 1

Re: Structural Modeling • Joseph Simpson Thanks, Joe, glad you liked the table, I’ve got a million of ’em!  I’ll be setting another mess of tables directly as we continue studying the effects of differential operators on families of propositional … Continue reading

## Differential Logic • 8

Propositional Forms on Two Variables To broaden our experience with simple examples, let’s examine the sixteen functions of concrete type and abstract type   Our inquiry into the differential aspects of logical conjunction will pay dividends as we study the … Continue reading

## Differential Logic • 7

Differential Expansions of Propositions Panoptic View • Enlargement Maps The enlargement or shift operator exhibits a wealth of interesting and useful properties in its own right, so it pays to examine a few of the more salient features playing out … Continue reading

## Differential Logic • 6

Differential Expansions of Propositions Panoptic View • Difference Maps In the previous section we computed what is variously described as the difference map, the difference proposition, or the local proposition of the proposition at the point where and In the universe … Continue reading

## Differential Logic • 5

Differential Expansions of Propositions Worm’s Eye View Let’s run through the initial example again, keeping an eye on the meanings of the formulas which develop along the way.  We begin with a proposition or a boolean function whose venn diagram … Continue reading

## Differential Logic • 4

Differential Expansions of Propositions Bird’s Eye View An efficient calculus for the realm of logic represented by boolean functions and elementary propositions makes it feasible to compute the finite differences and the differentials of those functions and propositions. For example, … Continue reading