arXiv:2412.19524cs.AI2024-12

在不确定性强时,两种推理系统得出的结论强度接近。

PLN and NARS Often Yield Similar strength $\times$ confidence Given Highly Uncertain Term Probabilities

  • 对比分析PLN与NARS在高不确定性下的推理机制
  • 发现两者推导出的结论'力度'数值非常相似
  • 适合关注不确定推理框架的AGI研究者阅读

我们对概率逻辑网络(PLN)和非公理化推理系统(NARS)这两种面向通用人工智能(AGI)的不确定推理框架中的演绎、归纳和类比公式进行了比较分析。二者的一个关键区别在于:在单个推理规则层面,PLN直接利用项概率和关系概率,而NARS仅使用关系频率,且没有项概率的直接对应。因此,本文聚焦于项概率高度不确定的情形,探讨这种不确定性如何影响两个系统的推理结论。通过启发式分析和基础数值计算,我们比较了PLN中强度×置信度(s×c)与NARS中频率×置信度(f×c)——我们称之为“陈述力度”的量值,在高项概率不确定性情况下的表现。结果发现,在许多实际场景中,尽管两种系统以不同方式得出结论,但它们的推理力度数值非常接近。

原文摘要 · Abstract (English)

We provide a comparative analysis of the deduction, induction, and abduction formulas used in Probabilistic Logic Networks (PLN) and the Non-Axiomatic Reasoning System (NARS), two uncertain reasoning frameworks aimed at AGI. One difference between the two systems is that, at the level of individual inference rules, PLN directly leverages both term and relationship probabilities, whereas NARS only leverages relationship frequencies and has no simple analogue of term probabilities. Thus we focus here on scenarios where there is high uncertainty about term probabilities, and explore how this uncertainty influences the comparative inferential conclusions of the two systems. We compare the product of strength and confidence ($s\times c$) in PLN against the product of frequency and confidence ($f\times c$) in NARS (quantities we refer to as measuring the "power" of an uncertain statement) in cases of high term probability uncertainty, using heuristic analyses and elementary numerical computations. We find that in many practical situations with high term probability uncertainty, PLN and NARS formulas give very similar results for the power of an inference conclusion, even though they sometimes come to these similar numbers in quite different ways.

不确定推理AGIPLNNARS

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