COMPUTATIONAL ARGUMENTATION
Argumentative Reasoning in ASPIC⁺ under Incomplete Information
This research addresses the critical challenge of reasoning under incomplete information within the ASPIC+ argumentation framework. It provides a comprehensive analysis of stability and relevance, fundamental concepts for determining the resilience of acceptance statuses in dynamic, real-world applications like criminal investigation. The study establishes new complexity results and introduces the first exact, scalable algorithms based on Answer Set Programming (ASP) for these problems.
Executive Impact: Clarity in Complex Decisions
Understanding the computational limits and practical solutions for argumentative reasoning under incomplete information is vital for enterprise AI. This research provides a robust framework for building more reliable and responsive decision support systems, particularly in domains requiring high assurance like legal tech and critical infrastructure analysis.
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ASPIC+ Stability Complexity (coNP)
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ASPIC+ Relevance Complexity (ΣP)
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Avg Stability Runtime (L=5000, no prefs)
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Avg Relevance Runtime (Real-world, no prefs)
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
P-Complexity of Justification Status
The research establishes that determining the justification status of a literal within a complete ASPIC+ framework is decidable in polynomial time (P). This foundational result underpins the broader complexity analysis for stability and relevance, demonstrating that the immediate assessment of a claim's status is computationally efficient.
CoNP-Completeness for ASPIC+ Stability
The paper proves that deciding stability in incomplete ASPIC+ is coNP-complete. This means that while verifying a literal is not stable might be hard, confirming it *is* stable can be done efficiently given the right information. This finding is crucial for designing systems that can confidently assess when no further information can change a conclusion's acceptance status.
ΣP2-Completeness for ASPIC+ Relevance
Deciding relevance in incomplete ASPIC+ is shown to be ΣP2-complete, indicating a significantly higher computational complexity than stability. This reflects the inherent difficulty in identifying minimal sets of unknown information that could alter a conclusion's acceptance. Enterprises leveraging such systems must account for this complexity when prioritizing inquiry efforts.
Practical ASP Algorithms for Incomplete ASPIC+
The work introduces the first exact, scalable algorithms for stability and relevance, built upon the declarative paradigm of Answer Set Programming (ASP). These algorithms avoid exponential argument construction by rephrasing grounded semantics in terms of rule sets, enabling efficient computation even for complex scenarios. The incremental CEGAR approach for relevance further optimizes the search for critical information.
Bridging Structured and Abstract Argumentation
A significant conceptual contribution is the demonstration that notions of stability and relevance in incomplete ASPIC+ cannot be directly reduced to their counterparts in Incomplete Abstract Argumentation Frameworks (IAFs). This highlights the unique dynamics of structured argumentation and validates the necessity for dedicated research at this granular level for practical applications.
coNP-complete
For ASPIC+ Stability
The paper establishes that deciding stability in incomplete ASPIC+ is coNP-complete, even when accounting for rule preferences via the last-link ordering principle. This refines previous findings and provides a precise computational boundary for this critical aspect of argumentation under uncertainty.
ΣP2-complete
For ASPIC+ Relevance
A key theoretical contribution is the finding that determining relevance in incomplete ASPIC+ is significantly more complex, proving it to be ΣP2-complete. This high complexity underscores the challenge of identifying minimal information needed to stabilize a conclusion.
Enterprise Process Flow
Problem Definition
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Grounded Semantics Rephrasing
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ASP Encodings for Justification & Stability
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Iterative CEGAR for Relevance
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Empirical Evaluation
The proposed methodology leverages Answer Set Programming (ASP) to provide the first exact algorithms for determining stability and relevance. This iterative approach, particularly for relevance, employs Counterexample-Guided Abstraction Refinement (CEGAR) to efficiently navigate the complex search space of incomplete theories.
| Feature | Exact ASP Approach | Inexact Approach (Prior Work) |
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| Preferences Handling |
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| Aspect | ASPIC+ (Structured) | IAFs (Abstract) |
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| Information Updates |
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| Stability/Relevance Mapping |
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