Symbol Emergence and The Solutions to Any Task

TL;DR

The paper argues that artificial general intelligence can be achieved by agents that consistently construct Intensional Solutions, which capture the commonalities needed to satisfy goals across tasks using minimal, necessary constraints. It formalizes an arbitrary task with binary variables $\mathcal{X}$, state sets $\mathcal{Z}$, and goal/initial-state definitions $\mathcal{G}=\{z: C(z)\}$ and $\mathcal{S}=\{s: V(s)\}$, then contrasts Intensional versus Extensional Solutions within a physically implementable language $\mathcal{L}$, linking the former to Ockham's Razor and to AIXI-like predictive modelling via solution archives. The interpretant role of the Intensional Solution grounds natural language as an emergent symbol system that encodes and decodes goal-directed meaning, with normativity arising from shared compulsions and cooperative interaction among agents. The work discusses ostensive learning, objective-function drives, and practical demonstrations, including learning Intensional Solutions for simple tasks, and notes the potential for one-class classification as an advantage of the approach.

Abstract

The following defines intent, an arbitrary task and its solutions, and then argues that an agent which always constructs what is called an Intensional Solution would qualify as artificial general intelligence. We then explain how natural language may emerge and be acquired by such an agent, conferring the ability to model the intent of other individuals labouring under similar compulsions, because an abstract symbol system and the solution to a task are one and the same.