# Category Archives: Dynamical Systems

## Differential Propositional Calculus • 4

Special Classes of Propositions Before moving on, let’s unpack some of the assumptions, conventions, and implications involved in the array of concepts and notations introduced above. A universe of discourse based on the logical features is a set plus the … Continue reading

## Differential Propositional Calculus • 3

Formal Development The preceding discussion outlined the ideas leading to the differential extension of propositional logic.  The next task is to lay out the concepts and terminology needed to describe various orders of differential propositional calculi. Elementary Notions Logical description … Continue reading

## Differential Propositional Calculus • 2

Cactus Calculus Table 6 outlines a syntax for propositional calculus based on two types of logical connectives, both of variable -ary scope. A bracketed list of propositional expressions in the form indicates exactly one of the propositions is false. A … Continue reading

## Differential Propositional Calculus • 1

A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target … Continue reading

## Differential Propositional Calculus • Overview

The most fundamental concept in cybernetics is that of “difference”, either that two things are recognisably different or that one thing has changed with time. W. Ross Ashby • An Introduction to Cybernetics Here’s the outline of a sketch I … Continue reading

## Differential Logic and Dynamic Systems • Overview

In modeling intelligent systems, whether we are trying to understand a natural system or engineer an artificial system, there has long been a tension or trade-off between dynamic paradigms and symbolic paradigms.  Dynamic models take their cue from physics, using … Continue reading

## Abductive Inference, Concept Formation, Hypothesis Formation • 1

In pragmatic semiotics, concept formation like hypothesis formation falls under the heading of abductive inference.  A lot has been said and there’s a lot more to say about that, but things are too much in flux right now to allow … Continue reading

## Differential Logic, Dynamic Systems, Tangent Functors • Discussion 8

Re: Systems Science • Len Troncale It’s been a while since I started this thread, with many sidetrips and tangents, so let me go back to the top and expand on the motivations I expressed there, addressing a few issues … Continue reading

## Differential Logic, Dynamic Systems, Tangent Functors • Discussion 7

Re: Systems Science • JS Let’s stand back from the picture and see how the dimensions of syntax, semantics, and pragmatics look from a pragmatic semiotic or sign relational perspective. is an object domain, a set of elements under view … Continue reading

## Differential Logic, Dynamic Systems, Tangent Functors • Discussion 6

Re: Systems Science • JS A few of my readers are racing well ahead of me, exploring a range of different roads, but I’ll be making a dogged effort to stick to my math-bio-graphical narrative this time around, and try … Continue reading