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

TL;DR

The paper investigates how PLN and NARS handle uncertainty in inference by comparing their first-order deduction, induction, and abduction under high term-probability uncertainty. By analyzing and simulating the core truth-value formulas, it shows that the power measure $s \times c$ in PLN and $f \times c$ in NARS often yield very similar values in many practical scenarios, despite different underlying mechanisms; this convergence is most evident when term probabilities are uncertain, though PLN’s normalization and NARS’ experience parameter can still introduce differences. The work provides both qualitative heuristic arguments and concrete numeric examples demonstrating when the two frameworks align and when they diverge, especially highlighting that the alignment largely breaks down when term probabilities are confidently known. The findings suggest that the product of strength/frequency and confidence is a robust, cross-framework indicator of inference power under uncertainty, offering insight into designing AI systems that must reason with limited probabilistic knowledge. This could inform the development of hybrid or comparative reasoning modules and motivates further quantitative simulations and domain-specific evaluations to assess practical impacts across tasks requiring uncertain inference.

Abstract

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.