Argument Graph Construction

Based on Dung's foundational model, this approach treats arguments as abstract nodes in a directed graph, ignoring internal structure to focus solely on attack relations. An argument is acceptable if it belongs to an admissible set—a conflict-free collection that defends all its members against attackers. Key semantics include:

• Grounded semantics: The most skeptical, uniquely determined set of accepted arguments
• Preferred semantics: Maximally inclusive admissible sets, allowing for multiple valid interpretations
• Stable semantics: Admissible sets that attack every argument not in the set This abstraction is particularly useful for modeling defeasible legal reasoning, where conclusions can be overturned by exceptions.

Extends abstract frameworks by introducing a second edge type: support relations. In legal reasoning, a precedent can support a claim, while a contrary statute attacks it. This creates a bipolar graph where:

• Attack edges represent rebuttal, undercutting, or contradiction
• Support edges represent evidential backing, legal authority, or logical entailment
• Coalition formation algorithms identify clusters of mutually supporting arguments
• Supported attacks model how a supporting argument can be defeated by attacking its foundation This structure mirrors the Toulmin model, where warrants and backing provide support for claims.

Not all arguments carry equal weight in legal discourse. Preference-based frameworks assign a partial or total ordering to arguments, reflecting:

• Hierarchical authority: Supreme Court precedents outweigh district court rulings
• Lex specialis: Specific statutes override general provisions
• Temporal recency: More recent decisions may supersede older ones
• Jurisdictional relevance: Binding vs. persuasive authority distinctions When a weaker argument attacks a stronger one, the attack may be defeated or reversed, allowing the system to model the nuanced priority structures inherent in common law reasoning and statutory interpretation.

Introduced by Bench-Capon, this framework acknowledges that legal disputes often hinge on competing social values or principles. Arguments are associated with the values they promote, and audiences are defined by their value preferences. This enables:

• Teleological reasoning: Choosing between arguments based on which societal purpose they advance
• Multi-audience modeling: Explaining why different judges might reach different conclusions from identical facts
• Constitutional balancing: Weighing fundamental rights like privacy vs. free speech
• Purposive statutory interpretation: Resolving ambiguity by considering legislative intent and protected values This approach is essential for modeling normative conflict resolution in constitutional and human rights law.

Unlike abstract frameworks, ASPIC+ models the internal logical structure of arguments. Each argument is a tree where:

• The root is the conclusion or claim
• Leaves are premises drawn from a knowledge base of facts and rules
• Inference steps apply strict or defeasible rules
• Strict rules represent deductive, incontrovertible logic
• Defeasible rules represent presumptive reasoning that can be countered ASPIC+ can instantiate arguments from rule-based legal expert systems while maintaining compatibility with Dung-style abstract semantics. It directly supports reasoning chain reconstruction by making each inferential step explicit and auditable.

Building a legal argument graph from raw text involves a multi-stage NLP pipeline:

• Claim Detection: Identify assertive propositions using sequence labeling models fine-tuned on legal corpora
• Argument Component Classification: Categorize spans as premises, conclusions, or legal rules
• Relation Extraction: Classify directed edges as support or attack using transformer-based models with legal pretraining
• Coreference Resolution: Link mentions of the same statute, party, or precedent across the document
• Cross-Document Linking: Connect arguments in a complaint to counter-arguments in a motion using argument coreference resolution
• Graph Validation: Apply argument coherence scoring to detect logical inconsistencies This pipeline transforms unstructured legal text into a queryable, navigable reasoning structure.