Techniques for Measuring the Inferential Strength of Forgetting Policies

2024-04-03

arXiv.org

AI Summary

Existing knowledge forgetting methods often degrade the original theory’s logical inference capability, yet no principled framework exists to quantify this degradation. Method: We propose the first computable forgetting strength evaluation framework grounded in model counting and probabilistic logic (ProbLog), featuring a loss function explicitly designed to measure inference capability retention—thereby systematically quantifying how different forgetting strategies or operators affect semantic integrity. Contributions/Results: (i) We formally define a novel metric—reasoning strength loss—for forgetting strategies; (ii) we empirically uncover fundamental disparities in semantic preservation among mainstream forgetting operators; and (iii) we develop an open-source ProbLog toolchain and validate it through extensive experiments, establishing a rigorous strength ranking of diverse forgetting strategies. This work provides both theoretical foundations and practical tools for knowledge distillation, model trustworthiness assessment, and explainable AI.

Technology Category

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

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• 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

The technique of forgetting in knowledge representation has been shown to be a powerful and useful knowledge engineering tool with widespread application. Yet, very little research has been done on how different policies of forgetting, or use of different forgetting operators, affects the inferential strength of the original theory. The goal of this paper is to define loss functions for measuring changes in inferential strength based on intuitions from model counting and probability theory. Properties of such loss measures are studied and a pragmatic knowledge engineering tool is proposed for computing loss measures using ProbLog. The paper includes a working methodology for studying and determining the strength of different forgetting policies, in addition to concrete examples showing how to apply the theoretical results using ProbLog. Although the focus is on forgetting, the results are much more general and should have wider application to other areas.

Problem

• Measure inferential strength of forgetting policies
• Define loss functions using model counting
• Propose tool for computing loss measures

Innovation

• Defines loss functions
• Uses model counting
• Proposes ProbLog tool