[Paper Review] Dynamics of Knowledge in DeLP through Argument Theory Change

Martín O. Moguillansky, Nicolás D. Rotstein+3 more|arXiv (Cornell University)|Nov 29, 2011

Multi-Agent Systems and Negotiation26 references3 citations

TL;DR

This paper proposes a formal framework for dynamically revising defeasible logic programs (de.l.p.s) in the Defeasible Logic Programming (DeLP) system using Argument Theory Change (ATC). It introduces a prioritized revision operator that ensures newly inserted arguments are warranted by minimally altering the knowledge base through selection and incision functions, with a Prolog-like algorithm enabling practical implementation while preserving argument structure and rational change principles.

ABSTRACT

This article is devoted to the study of methods to change defeasible logic programs (de.l.p.s) which are the knowledge bases used by the Defeasible Logic Programming (DeLP) interpreter. DeLP is an argumentation formalism that allows to reason over potentially inconsistent de.l.p.s. Argument Theory Change (ATC) studies certain aspects of belief revision in order to make them suitable for abstract argumentation systems. In this article, abstract arguments are rendered concrete by using the particular rule-based defeasible logic adopted by DeLP. The objective of our proposal is to define prioritized argument revision operators à la ATC for de.l.p.s, in such a way that the newly inserted argument ends up undefeated after the revision, thus warranting its conclusion. In order to ensure this warrant, the de.l.p. has to be changed in concordance with a minimal change principle. To this end, we discuss different minimal change criteria that could be adopted. Finally, an algorithm is presented, implementing the argument revision operations.

Motivation & Objective

• To address the dynamics of knowledge in DeLP by enabling rational revision of defeasible logic programs when new arguments are introduced.
• To ensure that newly inserted arguments are warranted in the argumentation framework, even when conflicting with existing knowledge.
• To formalize minimal change principles in the context of argumentation, focusing on preserving prior knowledge and minimizing structural disruption to dialectical trees.
• To adapt abstract Argument Theory Change (ATC) to the concrete, rule-based structure of DeLP, enabling practical implementation in argumentation systems.

Proposed method

• Reifies abstract ATC into DeLP by mapping argumentation-level changes to modifications in defeasible logic programs.
• Defines selection functions that identify candidate sets of argumentation lines to be altered, based on minimal change criteria such as minimizing removed beliefs or altering lines closest to leaves.
• Introduces the concept of incision-aware alteration sets to control collateral damage, ensuring only necessary lines in dialectical trees are modified.
• Reformulates classical belief revision postulates—core-retainment and success—within the argumentation framework to guide rational revision.
• Develops a Prolog-like algorithm for implementing the revision operator, with optimizations based on structural properties of dialectical trees.
• Uses the DeLP marking procedure to evaluate dialectical trees and determine argument warrant after revision.

Experimental results

Research questions

• RQ1 How can argument revision be formalized in DeLP such that a newly inserted argument becomes warranted in the argumentation framework?
• RQ2 What criteria for minimal change are most appropriate when revising a defeasible logic program to accommodate a new argument?
• RQ3 How can the impact of revision be localized to avoid unnecessary disruption to existing argument structures?
• RQ4 What formal properties ensure that the revision operator preserves rationality, such as success and core-retainment?
• RQ5 How can the revision process be efficiently implemented in practice, given the complexity of argumentation trees?

Key findings

• The proposed revision operator successfully ensures that the claim of a newly inserted argument is warranted after revision, satisfying the success postulate.
• The framework preserves prior knowledge by enforcing the core-retainment principle, ensuring beliefs not involved in conflicts remain intact.
• Multiple minimal change criteria—such as minimizing removed beliefs or altering argumentation lines closest to the leaves—are formally justified and compared.
• The incision-aware alteration set concept effectively reduces collateral damage by focusing changes on only the necessary parts of the dialectical tree.
• A detailed Prolog-like algorithm is provided, with optimizations that can avoid exhaustive search for the optimal alteration set under certain conditions.
• The formalization demonstrates that rational belief revision principles can be adapted to argumentation systems while maintaining correctness and structural coherence.