Computational Complexity and Algorithmic Approaches for Non-Flat Assumption-based Argumentation

Conceptos Básicos

Addressing the computational challenges of non-flat assumption-based argumentation through theoretical analysis and the development of efficient algorithmic approaches.

Resumen

The paper investigates computational aspects of non-flat assumption-based argumentation (ABA), which is a more general case than the commonly studied flat ABA. The authors make the following key contributions:

They establish a theoretical result based on compilability theory, showing that it is impossible to instantiate a non-flat ABA framework into a polynomial-sized argumentation framework or bipolar argumentation framework while preserving the semantics.

To address the exponential size of the instantiated frameworks, the authors identify three notions of redundancy in argument generation - derivation redundancy, expendable arguments, and assumption redundancy. They show that eliminating these redundancies preserves the semantics.

The authors also identify two fragments of non-flat ABA, called atomic and additive ABA, which admit a polynomial-sized instantiation and thus lower computational complexity.

The paper proposes two algorithmic approaches for reasoning in non-flat ABA:

ABABAF: An approach that efficiently instantiates a bipolar argumentation framework using the redundancy notions and then performs SAT-based reasoning on the constructed framework.
ABASP: A direct approach that performs reasoning on the non-flat ABA framework using iterative ASP calls, without constructing the arguments.

The empirical evaluation shows that the ABABAF approach outperforms the ABASP approach on many instances, especially for the problems on the second level of the polynomial hierarchy, in contrast to the current dominance of non-instantiation approaches for other structured argumentation formalisms.

Estadísticas

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Citas

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Ideas clave extraídas de

Instantiations and Computational Aspects of Non-Flat Assumption-based Argumentation

by Tuomo Lehton... a las arxiv.org 04-18-2024

https://arxiv.org/pdf/2404.11431.pdf

Consultas más profundas

How can the proposed algorithms be extended to handle other reasoning tasks, such as skeptical acceptance, in non-flat ABA

To extend the proposed algorithms to handle other reasoning tasks like skeptical acceptance in non-flat ABA, we can modify the ASP encodings and algorithms to accommodate the specific requirements of skeptical reasoning.
For skeptical acceptance, we would need to adjust the ASP encodings to capture the notion of skepticism, where arguments are accepted only if they cannot be defeated by any other argument. This would involve introducing constraints that ensure that the extension defends against all possible attacks, rather than just being conflict-free and closed.
Additionally, the algorithms would need to be adapted to consider the skeptical acceptance criteria, checking for the absence of defeating arguments rather than just the presence of defending arguments. This would involve refining the abstraction process and the verification steps to focus on the skeptical criteria.
By incorporating these adjustments into the ASP encodings and algorithms, we can effectively handle skeptical acceptance in non-flat ABA, providing a comprehensive solution for a wider range of reasoning tasks.

How can the instantiation-based approach be leveraged to provide explanations for the derived conclusions in non-flat ABA, similar to the work on flat ABA

The instantiation-based approach can be leveraged to provide explanations for derived conclusions in non-flat ABA by utilizing the structure of the instantiated BAF. Similar to the work on flat ABA, where explanations are derived from the argument graph, in non-flat ABA, we can extract explanations from the instantiated BAF.
By analyzing the relationships between arguments in the BAF, we can identify the paths that lead to a specific conclusion, highlighting the supporting and attacking arguments along the way. These paths can be used to construct coherent and structured explanations for how a particular conclusion was reached based on the underlying assumptions and rules.
Furthermore, by considering the redundancies identified in the instantiation process, we can streamline the explanations by focusing on the essential arguments that contribute to the derivation of a conclusion. This can lead to more concise and informative explanations that are easier to understand and interpret.
Overall, leveraging the instantiation-based approach in non-flat ABA for providing explanations can enhance the transparency and interpretability of the reasoning process, aiding users in understanding the rationale behind the derived conclusions.

What other fragments of non-flat ABA, beyond atomic and additive, could exhibit lower computational complexity and be amenable to efficient algorithmic solutions

Beyond atomic and additive fragments, other fragments of non-flat ABA that could exhibit lower computational complexity and be amenable to efficient algorithmic solutions include the following:

Hierarchical ABA: Introducing a hierarchical structure to the assumptions and rules in ABA frameworks could lead to a fragment where reasoning tasks become more tractable. By organizing assumptions and rules in a hierarchical manner, with dependencies and relationships clearly defined, the complexity of reasoning could be reduced.

Temporal ABA: Considering temporal aspects in ABA frameworks, where assumptions and rules have temporal constraints or dependencies, could lead to a fragment with specific properties that make reasoning more efficient. By incorporating temporal reasoning into the framework, certain reasoning tasks may become simpler and more manageable.

Probabilistic ABA: Extending non-flat ABA to incorporate probabilistic elements, where the certainty or likelihood of assumptions and conclusions is quantified, could result in a fragment with different computational characteristics. By introducing probabilistic reasoning into the framework, certain reasoning tasks may exhibit lower complexity and lend themselves to efficient algorithmic solutions.

Exploring these and other fragments of non-flat ABA could provide valuable insights into the computational properties of different types of assumption-based argumentation and offer new avenues for developing specialized algorithms and approaches for reasoning in diverse contexts.