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

2024-12-27

AI Summary

This study investigates behavioral differences and conclusion consistency between Probabilistic Logic Networks (PLN) and the Non-Axiomatic Reasoning System (NARS) in deductive, inductive, and abductive reasoning under high lexical probability uncertainty. Using heuristic analysis and numerical computation, we compare their core inference strength metrics: PLN’s *strength × confidence* versus NARS’s *frequency × confidence*. Results demonstrate that, despite fundamentally distinct underlying mechanisms—probabilistic calculus versus frequency-driven updating—both systems exhibit strong numerical convergence in inference strength across multiple practical reasoning tasks under high uncertainty. This finding provides the first empirical evidence of implicit convergence in cognitive “efficacy” across heterogeneous uncertain reasoning frameworks. It establishes a theoretical foundation for unifying uncertainty modeling in Artificial General Intelligence (AGI) and introduces a novel cross-framework evaluation paradigm grounded in comparative inference strength.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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 ($s imes c$) in PLN against the product of frequency and confidence ($f imes c$) 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.

Problem

• Uncertainty Reasoning
• Probabilistic Logic Networks
• Non-Axiomatic Reasoning System

Innovation

• Probabilistic Logic
• Comparative Analysis
• Inference Power