Abstract Argumentation-based CBR

• AA-CBR is a unified reasoning paradigm that represents cases as arguments, enabling effective decision making under uncertainty.
• It constructs and evaluates epistemic, recommending, and decision arguments to handle inconsistencies via defeat mechanisms.
• The framework quantitatively ranks decisions by integrating rule-based, case-based, and multi-criteria strategies for robust inference.

Abstract Argumentation-based Case-Based Reasoning (AA-CBR) models the process of using a repository of past cases to reason about new problems within the formal setting of abstract argumentation, in which cases or assets of knowledge are represented as arguments that may attack or support one another. AA-CBR unifies inference from inconsistent information and decision making under uncertainty, integrating multiple reasoning styles—including rule-based, multi-criteria, and case-based strategies—by constructing and evaluating arguments against a backdrop of possibly non-coherent, conflicting knowledge and goals. The output is both a set of justified conclusions (from the argumentation debate) and an explicit, ranked set of decisions or predictions, grounded in a dialectical comparison of competing lines of reasoning.

1. Unified Argumentation-Driven Reasoning Paradigm

AA-CBR, as introduced in "A unified setting for inference and decision: An argumentation-based approach" (Amgoud, 2012), formulates a general theory $T = (D, K, G^+, G^-)$ where $D$ is a set of candidate decisions, $K$ is a potentially inconsistent knowledge base, $G^+$ and $G^-$ denote weighted positive and negative goals. Arguments are of three types:

• Epistemic arguments: founded upon subsets of $K$ supporting beliefs.
• Recommending arguments: deductively infer decisions from strict or defeasible rules.
• Decision arguments: abductively show how decisions satisfy/violate goals.

This framework operationalizes both inference (selecting justified conclusions from inconsistency) and decision (ordering options by acceptability of supporting arguments) as manifestations of the same underlying argumentative process. Argument construction involves chaining strict ($\rightarrow$) and defeasible ($\Rightarrow$) rules, while extensions (i.e. justified sets) are computed with semantics such as grounded or preferred, using dialectical defeat relations.

2. Managing Inconsistency through Argumentation Semantics

A defining feature is the ability to reason in the presence of inconsistency. Arguments are constructed from consistent subsets of $K$ by applying strict and defeasible rules. The closure operator $\operatorname{Cls}(F)$ ensures that the subset $F$ is consistent if no formula and its negation coexist. When conflicting arguments arise (e.g., opposing conclusions), their rivalry is resolved by defeat mechanisms:

• Rebuttal: direct contradiction.
• Undercut and assumption-attacking: challenge the justification or assumptions of an argument.

Only "acceptable" arguments—those that withstand all justified attacks—are retained to make inferences; this guarantees the output $\operatorname{Output}(AF)$ retains internal consistency, even if input knowledge was incoherent. This defeat-driven curation is central to robust decision making under real-world, uncertain or contradictory information.

3. Decision Making under Uncertainty and Multiple Criteria

Each argument (especially decision and recommending arguments) carries quantitative attributes:

• Certainty degree: $\operatorname{Cert}(A)$ represents the minimal certainty of beliefs supporting argument $A$.
• Importance degree: $\operatorname{Imp}(A)$ quantifies the priority of goals satisfied or violated.

For decision arguments, the strength ("force") is given by the tuple $(\operatorname{Cert}, \operatorname{Imp})$, and decisions are compared via a conjunctive criterion:

$$A \succ B \quad \text{iff} \quad \min(\operatorname{Cert}(A), \operatorname{Imp}(A)) > \min(\operatorname{Cert}(B), \operatorname{Imp}(B))$$

This scheme naturally extends to multiple criteria, as $G^+$ and $G^-$ encode vectors of weighted goals. The decision-ranking process aggregates certainty and importance, enabling prioritization of decisions that satisfy high-importance goals, even when some evidence is less certain.

4. Argumentation-Based Case Comparison and Adaptation

AA-CBR generalizes classical CBR by representing the retrieval and adaptation steps argumentatively. A new problem is addressed by constructing decision arguments from past cases—where a prior decision $d$ led to the satisfaction of goals, abductively supporting $d$ now. Unlike fixed similarity metrics, AA-CBR formalizes both construction and dialectical evaluation, allowing explicit treatment of conflict and priority in adaptation.

This approach is particularly advantageous when cases are non-uniform, contradictory, or must be justified against explicit goals and beliefs. By ranking decisions according to the accumulated "force" from supporting arguments, the system outputs justified recommendations in the face of case conflict.

5. Integration of Rule-Based, Case-Based, and Multi-Source Evidence

AA-CBR's architecture permits the integration of rule-based decision making and case-based adaptation. Strict and defeasible rules connect evidence from $K$ to decisions, forming recommending arguments; these are compared (often given precedence) with decision arguments induced from case histories. The model supports:

• Decision under uncertainty.
• Multiple criteria evaluation.
• Rule-based recommendations.
• Case-based (abductive) reasoning.

Epistemic arguments derive beliefs, recommending arguments reason from general rules, and decision arguments operate through goal evaluation—each with quantitative appraisal. This heterogeneity enhances versatility and generalization across domains, permitting sophisticated, conflict-resilient recommendations and predictions.

6. Coherence Guarantees and Real-World Interoperability

Unlike classical decision-theoretical models, the AA-CBR framework does not assume coherence of environmental information. It is designed to handle knowledge bases rife with inconsistencies, using its defeat-driven filtering to ensure that only robust, surviving arguments inform final decisions. This allows operation in environments where conflicting sensor data, expert opinions, or rules collide, and ensures that outputs are consistent and justifiable.

By decoupling output decision consistency from input coherence, AA-CBR is suited to domains such as legal reasoning, medical diagnostics, and autonomous agent decision making where incoherence is pervasive.

7. Summary of Impact and Theoretical Innovation

The unified AA-CBR framework advances the modeling of human-like reasoning by explicitly linking inference from inconsistent information, goal-based decision making, and case adaptation within an argumentation semantic. It quantifies argument strength and enables principled decision comparison, integrates rule-based and case-based approaches, and fundamentally supports reasoning under uncertainty and incoherence. This architecture has proven systematic, computationally tractable, and context-adaptable, establishing the theoretical basis for robust, transparent, and justifiable case-based reasoning in artificial intelligence systems.