Techniques for Measuring the Inferential Strength of Forgetting Policies
Patrick Doherty, Andrzej Szalas
TL;DR
This work introduces quantitative loss measures for the inferential weakening caused by forgetting in knowledge bases, formalizing strong and weak forgetting and showing how to compare policies using model-counting and probabilistic perspectives. It then implements these measures in ProbLog, providing transformations and algorithms to compute exact or approximate losses for propositional and first-order theories. The contributions include formal loss definitions, a ProbLog-based computation framework, and a practical methodology with illustrative examples, highlighting when certain forgetting choices preserve more inferential strength. The results have broad relevance to belief-base engineering, abstraction, and knowledge compilation, offering a principled, tool-supported means to optimize forgetting policies under varying practical priorities.
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.