Assumption-Based Argumentation (ABA)

• Assumption-Based Argumentation (ABA) is a structured formalism that models defeasible assumptions, deductive consequences, and explicit attack relations.
• Advanced ABA variants incorporate non-flat structures, preference handling, and quantitative measures to enhance argument evaluation and decision-making.
• ABA frameworks support practical applications in logic programming, explainability, learning, and ethical reasoning through tools like ASP encodings and GNNs.

Assumption-Based Argumentation (ABA) is a comprehensively developed formalism for structured argumentation that models reasoning with defeasible assumptions, their deductive consequences, and inter-argument attacks controlled by explicit contraries. ABA plays a central role in theoretical AI, logic programming, computational argumentation, preference reasoning, explanation, and non-monotonic machine learning. Its semantics, generalizations, and computational properties have been deeply studied, with ABA frameworks enabling fine-grained modelling of debate, default reasoning, learning, and explainability across a broad spectrum of applications.

1. Formal Structure of ABA Frameworks

An Assumption-Based Argumentation (ABA) framework is classically defined as a tuple

$$\mathcal{F} = \langle L, R, A, \overline{\cdot} \rangle$$

where:

• $L$ is a (ground) language of atoms or their first-order/propositional schemata.
• $R$ is a finite set of inference rules of the form

$$s_0 \leftarrow s_1, \dots, s_m \quad (m \geq 0,\, s_i \in L)$$

with facts as rules with empty bodies ($m = 0$).

• $A \subseteq L$ is a non-empty set of assumptions; flat ABA restricts $A \cap \mathrm{head}(R) = \emptyset$, i.e., assumptions are not derivable.
• $\overline{\cdot} : A \to L$ is a total contrary mapping, assigning to each $a \in A$ a unique $\overline{a} \in L$.

An argument for a claim $s \in L$ is a finite derivation tree with root $s$, leaves being facts or assumptions, and internal nodes justified by rules in $R$. For flat ABA, attacks are defined strictly at the assumption level: argument $\alpha$ attacks $\beta$ if the claim of $\alpha$ equals the contrary of some assumption supporting $\beta$.

Extension-based ABA semantics are inherited from Dung's abstract frameworks, with sets of arguments forming conflict-free, admissible, preferred, complete, stable, or grounded extensions subject to the attack relation. ABA's structured nature provides concrete justifications and explicit defeat dynamics.

2. Advanced ABA Variants: Non-Flat Frameworks, Preferences, and Quantitative Extensions

Non-flat ABA allows assumptions to be derivable (i.e., may occur as heads of rules), increasing modeling power (e.g., to express support among assumptions). The semantic definition of support, attack, closure, and extension now relies on tree-based derivability and closure operators:

• $D = (L, R, A, \overline{\cdot})$ with non-flat $R$.
• For $S \subseteq A$, the closure $\mathrm{cl}_D(S) = \mathrm{Th}_D(S) \cap A$ and $S$ is closed if $\mathrm{cl}_D(S) = S$. Attacks, supports, and defense must account for the inherent nontrivial closure structure.

Preference handling (ABA⁺) incorporates a preorder $\leq$ on assumptions, directly modifying the attack relation. The ABA⁺ attack (denoted $\xrightarrow{<}$) ensures that attacks from less preferred sets are reversed or blocked depending on relative priority, incorporating both normal and reverse attacks. A new family of $<$-semantics (preferred, stable, complete, grounded, ideal) naturally arises, satisfying a range of preference-handling postulates, including conflict preservation, maximal element inclusion, and various rationality postulates under mild (weak contraposition) logical constraints (Čyras et al., 2016, Cyras et al., 2016).

Weighted ABA (wABA) introduces numerical weights on atoms/assumptions via a semiring structure, propagates these to attack strengths, and redefines extension semantics with a bounded inconsistency "budget." A wABA framework is a sextuple $(L,R,A,\overline{\cdot}, \mathcal{S}, w)$, and extensions are computed as in flat ABA after potentially discarding attacks whose cumulative weight remains below a threshold (Baldi et al., 22 Jun 2025).

Gradual semantics for ABA build on set-based bipolar argumentation abstractions. Each assumption is assigned a dialectical strength as a fixed point of influence from attacks and supports, generalized from quantitative bipolar frameworks (QBAFs), and extended to (possibly non-flat) ABA via modular aggregation and influence functions, yielding monotonicity, balance, and convergence properties (Rapberger et al., 14 Jul 2025).

3. Computation and Reasoning in ABA: ASP, GNNs, and Algorithmic Advances

Reasoning in ABA (credulous/skeptical acceptance of atoms under various extension-based semantics) is computationally intractable in general (NP-complete for stable semantics, $\Sigma_2^P$-complete for preferred/complete in non-flat frameworks).

Answer Set Programming (ASP) Encodings: There is a strong correspondence between stable extensions of flat ABA frameworks and answer sets of logic programs. This enables an efficient reduction of ABA reasoning to ASP, with major implementations leveraging Clingo:

• Encoding rules, assumption selection, contraries, and integrity constraints for examples and closure.
• All key entailment and learning queries reduce to cautious consequence computation in ASP (Angelis et al., 2023, Angelis et al., 19 Aug 2024).
• For beyond-NP tasks (skeptical preferred, preferential reasoning), incremental ASP-based CEGAR (Counterexample-Guided Abstraction Refinement) yields effective $\Sigma_2^P$/$\Pi_2^P$-complete procedures by alternately guessing candidate sets and refining via counterexamples (Lehtonen et al., 2021).

Graph Neural Networks (GNNs): Recent work has leveraged heterogeneous GNN architectures (ABAGCN, ABAGAT) for scalable approximate credulous acceptance prediction in large ABA frameworks. Here, ABAFs are encoded as dependency graphs with node/edge types distinguishing assumptions, claims, rules, and attack/support/derive relations. Residual message-passing or attention architectures trained on large benchmarks outperform previous AF-based baselines, achieving F1 scores up to 0.74 and supporting polynomial-time reconstruction of (approximate) stable extensions in very large frameworks (Gehlot et al., 12 Nov 2025).

Instantiation to Bipolar Argumentation Frameworks (BAFs): General (non-flat) ABA frameworks can be semantically preserved via translation into (deductive support-enhanced) bipolar AFs, with closure and defense conditions lifted to support-induced closure over arguments. This translation induces a tight correspondence between ABA and BAF extensions for key semantics (Ulbricht et al., 2023, Lehtonen et al., 17 Apr 2024).

• Efficient algorithms prune redundant arguments (derivation redundancy, expendability, assumption redundancy) and enable polynomial-time instantiations in atomic/additive fragments, with instantiation-based reasoning outperforming direct approaches in hard non-flat settings.

Web-based Tools and Human-in-the-Loop Applications: Modern implementations (e.g., aba-web) provide user interfaces for inputting, visualizing, and computing ABA frameworks in Python, with back-ends supporting multiple semantics. Algorithmic enhancements such as pickle-based graph copying and dispute tree caching yield competitive empirical performance compared to Prolog-based solvers (Kenrick, 2016).

4. Learning ABA Frameworks: Rule Induction, Generalization, and Defeasible Knowledge

Automated learning of ABA frameworks aims to construct intensional rules (schemata) capturing the defeasible structure consistent with background knowledge and labeled positive/negative examples.

Core learning problem: Given background $\mathcal{F} = (L,R,A,\overline{\cdot})$ and positive/negative examples $\mathcal{E}^+,\mathcal{E}^-$, infer an extension $\mathcal{F}'$ with $R' \supseteq R,\, A' \supseteq A$, and all positive (resp. negative) examples entailed (resp. not entailed) under cautious or brave reasoning.

Rule transformation operators:

• Rote learning: Add ground facts to explain uncovered positives.
• Folding: Generalize facts by inverse resolution, compacting ground rules into schemata.
• Assumption introduction: Replace over-general rules with defeasible variants by introducing new assumptions (with fresh contraries), thus supporting exception handling.
• Fact subsumption: Remove superfluous ground rules re-covered by generalizations.

Learning strategies:

• Interleaved RoLe (Rote Learning) and GEN (Generalization) steps, guided by cautious consequence test in ASP or via answer set minimization (e.g., in ASP-ABAlearn), ensure intensional, minimal rule sets.
• Fully automated workflows are realized via ASP encodings supporting integrative cycle checks and generalization operators (Angelis et al., 2023, Angelis et al., 19 Aug 2024).
• Experimental evaluations demonstrate that ABA learning can outperform ILP tools that directly learn logic programs or rules, especially when handling exceptions and defeat.

Handling exception mechanisms: ABA learning natively accommodates undercutting (contrary of assumption) and body-literal defeat, enabling more concise models than rebuttal-based approaches found in logic program induction (Proietti et al., 2023).

5. Explainability, Justification, and Applications

ABA provides fine-grained justification structures for both individual claims and entire answer sets:

• Attack Trees: Labelled dispute trees explicate why a particular literal or argument is justified (survives all attacks) or not, with each node mapping to an admissible fragment for the corresponding extension (Schulz et al., 2014).
• ABA-based answer set justifications: Provide “flattened” logic-program justifications, expressing the support and attack relations in logic programming terms, and rigorously aligned with answer set semantics.

Probabilistic Modeling: ProbLog’s distribution semantics can be recast as probabilistic abstract argumentation over an ABA-derived argument graph, allowing ABA-based query explanations in probabilistic logic programming (Toni et al., 2023).

Value-driven and ethical agents: ABA has been successfully applied to formalizing, justifying, and explaining machine-ethical agents' decisions, mapping agent’s principles and scenario-dependent duties into argumentation frameworks, with attack and defeat yielding transparent, minimally sufficient explanations for both accepted and rejected actions (Liao et al., 2018).

Aggregation and Multi-Agent Argumentation: Bipolar ABA formalisms support the aggregation of diverse agent opinions via quota, oligarchic, or dictatorship rules, with social-choice-theoretic results precisely characterizing which preservation properties can be guaranteed under what conditions (Lauren et al., 2021).

6. Recent Challenges and Future Directions

Complexity and Reasoning Beyond Flatness: Sophisticated fragments (atomic/additive) allow for tractable instantiation and reasoning, but generic non-flat ABA often induces exponential argument sets. Efficient modularization, redundancy elimination, and robust semantics (e.g., strong/weak admissibility, $\Gamma$-closure) are active areas of investigation (Berthold et al., 15 Aug 2025, Lehtonen et al., 17 Apr 2024).

Preference Elicitation and Inverse Problems: Algorithms exist to enumerate all possible preorderings on assumptions that would render a chosen extension preferred/grounded, directly supporting value alignment and explainability in systems with implicit or designable preferences (Mahesar et al., 2020).

Learning in Noisy or Incomplete Domains: Ongoing work addresses extensions beyond flat ABA, richer ontologies, learning with noise, and soundness/completeness guarantees for intensional induction under syntactic and semantic language bias (Angelis et al., 2023, Angelis et al., 19 Aug 2024).

Approximate Reasoning and ML Integration: GNN-based approximations for credulous acceptance offer order-of-magnitude scalability increases, raising questions about hybrid symbolic–subsymbolic methods and their integration into symbolic argumentation (Gehlot et al., 12 Nov 2025).

Ethical Reasoning and Weighted Semantics: wABA provides a formal foundation for reasoning with quantified ethical dilemmas, hardness budgets, and prioritization, advancing explainability and practical deployment in AI ethics (Baldi et al., 22 Jun 2025).

Gradual Semantics and Strength Measures: Gradual acceptability metrics, grounded in bipolar set-based abstraction, offer a fine-grained alternative to classic extension-based accept/reject dichotomies, enabling nuanced, continuous trust measures for arguments and assumptions in dynamic or ambiguous settings (Rapberger et al., 14 Jul 2025).

Continued progress in semantics, tractable computation, rule acquisition, and explainability ensures that ABA remains a foundational formalism for structured, defeasible, and interpretable AI reasoning.