Differential Logic and Dynamic Systems • Overview

• Overview • Part 1 • Part 2 • Part 3 • Part 4 • Part 5 • Appendices • References • Document History •

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.

Differential Logic and Dynamic Systems • Overview

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