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

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.