Dynamics of Knowledge in DeLP through Argument Theory Change

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 `a 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.

💡 Research Summary

The paper investigates how to dynamically modify defeasible logic programs (de.l.p.s), the knowledge bases used by the Defeasible Logic Programming (DeLP) interpreter, so that a newly introduced argument becomes warranted after the revision. The authors bridge belief revision theory—particularly the AGM model of expansion, contraction, and revision—with Argument Theory Change (ATC), a framework that adapts belief revision concepts to abstract argumentation systems. By concretizing ATC within the rule‑based, non‑monotonic setting of DeLP, they define prioritized argument revision operators that guarantee the success condition (the new argument is accepted) while adhering to a minimal‑change principle.

The paper first reviews the motivation for handling inconsistent knowledge bases, citing domains such as law, medicine, and task scheduling where contradictory information is unavoidable. Traditional belief revision seeks to restore consistency, but the authors argue that in many real‑world scenarios it is preferable to keep inconsistencies and instead ensure that the new information is “warranted” according to the argumentation semantics.

DeLP’s core components—facts, strict rules, and defeasible rules—are used to build arguments. Arguments attack each other, and a dialectical tree (or argumentation tree) captures the recursive defeat/rebuttal process. An argument is warranted if its root survives all attacks in the tree. When a new argument is inserted, it may be defeated by existing arguments; the revision task is to modify the underlying de.l.p. so that the new argument wins.

To achieve this, the authors propose three minimal‑change criteria: (1) Rule‑Deletion Minimality, which seeks to delete as few defeasible rules as possible; (2) Priority‑Shift Minimality, which limits changes to the priority ordering among rules; and (3) Structural Minimality, which tries to preserve the overall shape of the dialectical tree. Since these criteria can conflict, a cost‑function based selection mechanism is introduced to choose the most appropriate compromise for a given situation.

The central algorithm is presented in a Prolog‑like syntax. It proceeds as follows: (i) identify the support set of rules that underlie the new argument; (ii) locate all counter‑arguments that defeat it in the current dialectical tree; (iii) collect the rules constituting those counter‑arguments into candidate deletion sets; (iv) evaluate each candidate against the minimal‑change criteria using the cost function; (v) apply the optimal set of deletions or priority adjustments, thereby producing a revised de.l.p. in which the new argument is warranted. The algorithm employs backtracking and heuristic pruning to keep the search tractable.

The paper illustrates the approach with several realistic scenarios. In a legal example, the authors model the introduction of a new media law as an argument and show how conflicting articles from older statutes can be selectively weakened or removed, respecting constitutional supremacy. In a scheduling example, a high‑priority new task is inserted; the algorithm adjusts task‑allocation rules so that the new task is assigned without causing excessive disruption to existing assignments. These case studies demonstrate that ATC can operate on complex, rule‑based knowledge bases rather than on atomic sentences, offering a richer notion of revision.

Finally, the authors acknowledge that a full axiomatic characterization of ATC for DeLP is beyond the scope of the paper; they refer readers to earlier work for a more formal treatment. Nonetheless, the presented algorithm provides a concrete, implementable method for argument‑level revision in defeasible logic programming. The contribution lies in (a) extending belief revision to non‑monotonic, argument‑centric settings, (b) defining concrete minimal‑change strategies tailored to dialectical semantics, and (c) delivering a prototype implementation that can be integrated into existing DeLP systems. The work opens avenues for further research on formal postulates, optimization techniques, and broader applications in domains where inconsistency is intrinsic but controlled evolution of knowledge is essential.