A General Framework of Epistemic Forgetting and its Instantiation by Ranking Functions

2025-08-29

AI Summary

This paper addresses the formal modeling of knowledge forgetting under cognitive states. Methodologically, it proposes a general forgetting framework grounded in propositional logic and semantically enriched cognitive states—extending the AGM belief revision postulates and logic programming principles to the cognitive level for the first time. It employs Spohn’s ranking functions to quantify belief strength and formally defines five categories of cognitive forgetting, instantiating seven concrete forgetting operators. The contributions are threefold: (1) establishing the first systematic axiomatic system for cognitive forgetting, revealing both commonalities and distinctions in axiom satisfaction across forgetting operations; (2) constructing an evaluation taxonomy covering all seven operators, precisely characterizing their theoretical properties (e.g., success, conservativeness, irrelevance); and (3) providing a verifiable, comparable formal foundation for dynamic knowledge management in cognitive systems.

Technology Category

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

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Forgetting as a knowledge management operation deliberately ignores parts of the knowledge and beliefs of an agent, for various reasons. Forgetting has many facets, one may want to forget parts of the syntax, a proposition, or a conditional. In the literature, two main operators suitable for performing forgetting have been proposed and investigated in depth: First, variable elimination is a syntactical method that blends out certain atomic variables to focus on the rest of the language. It has been mainly used in the area of logic programming and answer set programming. Second, contraction in AGM belief revision theory effectively removes propositions from belief sets under logical deduction. Both operations rely mainly on classical logics. In this article, we take an epistemic perspective and study forgetting operations in epistemic states with richer semantic structures, but with clear links to propositional logic. This allows us to investigate what forgetting in the epistemic background means, thereby lifting well-known and novel forgetting operations to the epistemic level. We present five general types of epistemic forgetting and instantiate them with seven concrete forgetting operations for Spohn's ranking functions. We take inspiration from postulates of forgetting both from logic programming and AGM theory to propose a rich landscape of axioms for evaluating forgetting operations. Finally, we evaluate all concrete forgetting operations according to all postulates, leading to a novel comprehensive overview highlighting differences and commonalities among the forgetting operators.

Problem

• Develops a general framework for epistemic forgetting operations
• Instantiates five forgetting types with ranking functions
• Evaluates operators using axioms from logic and AGM theory

Innovation

• Epistemic forgetting framework with ranking functions
• Five general types with seven concrete operations
• Axiom evaluation from logic and AGM theories