Differential Logic and Dynamic Systems • Overview
• https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

❝Stand and unfold yourself.❞
— Hamlet • Francisco • 1.1.2

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 quantitative measures and differential equations to model the evolution of a system’s state through time. Symbolic models use logical methods to describe systems and their agents in qualitative terms, deriving logical consequences of a system’s description or an agent’s state of information. Logic-based systems have tended to be static in character, largely because we have lacked a proper logical analogue of differential calculus. The work laid out in this report is intended to address that lack.

This article develops a differential extension of propositional calculus and applies it to the analysis of dynamic systems whose states are described in qualitative logical terms. The work pursued here is coordinated with a parallel application focusing on neural network systems but the dependencies are arranged to make the present article the main and the more self-contained work, to serve as a conceptual frame and a technical background for the network project.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange
#MinimalNegationOperators #NeuralNetworkSystems #Semiotics