Research map / Learning theory and algorithms / Combinatorial and search optimization
Non-flat ABA Is an Instance of Bipolar Argumentation
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Shows that general non-flat ABA frameworks can be instantiated as bipolar argumentation frameworks using novel deductive-support BAF semantics, extended with premise-augmented BAFs to cover admissible-based semantics, and analyses their complexity.
Problem
No translation existed from general (non-flat) ABA frameworks into any abstract argumentation formalism, since flat ABA can only be mapped to Dung-style AFs.
Approach
Instantiate each ABA argument as a BAF node, use attacks for contraries and support edges from an argument to generic assumption arguments in its closure; define BAF semantics via closure-based defense, and augment with premise functions (premise-augmented BAFs) so exhaustive admissible sets capture admissible ABA semantics.
Key results
- Complete, grounded and stable semantics of non-flat ABAFs are captured by instantiated BAFs (asms of complete/grounded/stable BAF extensions yield ABA extensions and vice versa).
- Premise-augmented BAFs capture admissible, preferred, complete, grounded and stable ABA semantics via exhaustive sets.
- Complexity of BAFs and pBAFs is one level lower in the polynomial hierarchy than non-flat ABA for each reasoning problem considered (e.g., preferred skeptical Pi2P-complete vs Pi3P-complete for ABA).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Translate non-flat ABA into BAFs with deductive-support semantics | Non-flat ABA · Complete-, grounded-, and stable-semantics reasoning | semantics correspondence | Helped |
| Add premise information and require exhaustive extensions (pBAF) | BAF translation of non-flat ABA · Admissible-, complete-, preferred-, grounded-, and stable-semantics reasoning | semantics correspondence | Helped |
| Add premises and exhaustiveness to BAFs | Skeptical acceptance under admissible semantics · Non-flat ABA reasoning | complexity | Mixed |
| Use BAFs or pBAFs rather than non-flat ABA | Reasoning problems in non-flat ABA · Verification, credulous acceptance, and skeptical acceptance | complexity | Helped |
| Use BAFs instead of pBAFs | Skeptical acceptance under admissible semantics · Non-flat ABA reasoning | complexity | Mixed |
Surprising findings
- Plain BAFs under the proposed semantics cannot capture admissible ABA semantics; the instantiation needs premise augmentation to fix this.
- Preferred extensions are not necessarily complete and complete extensions may not exist in BAFs, so no translation into Dung AFs is possible.
Limitations
- Instantiated BAFs are infinite in general, though they can be reduced to finite ones by argument identity.
- Plain BAFs do not capture admissible or preferred ABA semantics; premise augmentation is required.
- Only basic properties of the new BAF semantics are studied (no fundamental lemma or existence results).
Experimental setup
Metrics: computational complexity classes (Ver, Cred, Skept)
Baselines: Non-flat ABA semantics (Dung-style AF instantiation for flat ABA) Deductive support BAF semantics (prior work on ABA-BAF relation)
Builds on: Assumption-based Argumentation Bipolar argumentation frameworks Claim-augmented argumentation frameworks Dung abstract argumentation
Closest papers by meaning
- Redefining ABA+ Semantics via Abstract Set-to-Set Attacks (AAAI 2024 · similarity 0.93)
- Under-Approximating Semantics in Clustered Assumption-Based Argumentation (AAAI 2026 · similarity 0.89)
- Defeasible Normative Reasoning: A Proof-Theoretic Integration of Logical Argumentation (AAAI 2024 · similarity 0.87)
- Bilateral Gradual Semantics for Weighted Argumentation (AAAI 2024 · similarity 0.87)
- Dung’s Argumentation Framework: Unveiling the Expressive Power with Inconsistent Databases (AAAI 2025 · similarity 0.86)
- Complexity of Credulous and Skeptical Acceptance in Epistemic Argumentation Framework (AAAI 2024 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.