Deontic Graph Neural Network (GNN)

The graph explicitly models distinct entity classes—parties, statutes, contracts, and jurisdictions—as separate node types with unique feature spaces. Each node type carries domain-specific attributes: a 'Party' node encodes capacity and role, while a 'Statute' node encodes jurisdictional scope and enactment date. This heterogeneity prevents the semantic conflation that plagues flat text models, ensuring that a corporation and a regulation are processed through type-appropriate encoders before any relational computation begins.

Edges are not generic associations but typed normative relations drawn from Hohfeldian analysis and deontic logic:

• Obligation (duty-to): Connects a party to a required action
• Permission (may-perform): Connects a party to an allowed action
• Prohibition (must-not): Connects a party to a forbidden action
• Authority (empowers): Connects a statute to an enforcing body
• Liability (subject-to): Connects a party to a normative power

Each edge type uses a distinct message-passing function, allowing the network to learn that obligations propagate differently than permissions.

The core computation uses Relational Graph Convolutional Networks (R-GCNs) adapted for deontic semantics. At each layer, a node's representation is updated by aggregating messages from its neighbors, with a separate weight matrix for each edge type. This means the message a 'Party' node receives from an 'Obligation' edge is computed with different parameters than a message from a 'Permission' edge. The update rule follows:

h_i^(l+1) = σ( Σ_r Σ_j∈N_r(i) (1/c_i,r) * W_r^(l) * h_j^(l) + W_0^(l) * h_i^(l) )

where r indexes the deontic relation type, enabling the network to learn distinct propagation dynamics for duties versus authorizations.

A specialized output module identifies normative conflicts—situations where a party is simultaneously obligated and prohibited from the same action, or where two applicable norms prescribe incompatible outcomes. This head computes pairwise compatibility scores between all active deontic constraints using a bilinear scorer, then applies a threshold to flag conflicts. The system can also invoke resolution heuristics:

• Lex Superior: Higher authority prevails
• Lex Specialis: More specific rule prevails
• Lex Posterior: Later enactment prevails

This transforms the GNN from a passive classifier into an active reasoning engine capable of surfacing legal inconsistencies.

Obligations are not static; they activate, suspend, and expire over time. The GNN incorporates temporal edge features that encode the lifecycle of each normative relation:

• Effective date: When the obligation becomes active
• Expiration date: When the obligation ceases
• Conditional trigger: Events that activate or suspend the duty

These temporal signals are encoded as continuous vectors and concatenated with edge features during message passing. A gating mechanism allows the network to learn when a deontic relation is 'active' in the current temporal context, preventing the propagation of expired obligations and enabling accurate modeling of contrary-to-duty scenarios where secondary obligations activate upon violation.

To meet the auditability requirements of legal AI, the GNN employs graph attention mechanisms with explicit attribution. Each message-passing step computes attention weights that quantify how much each source node and edge type contributed to a target node's updated representation. These weights are extracted post-inference to generate human-readable explanations:

• 'Defendant is obligated to pay damages because Statute §12-3 (attention: 0.47) imposes a duty-to-compensate on breaching parties, and Defendant was classified as a breaching party (attention: 0.31).'

This attention tracing provides a verifiable reasoning path from input facts to normative conclusion, satisfying the right to explanation requirements in regulated domains.

A fundamental analytical framework decomposing legal relations into eight jural correlatives that disambiguate normative positions before graph construction. The pairs are:

• Right/Duty: A claim-right correlates to a duty
• Privilege/No-Right: Freedom from obligation
• Power/Liability: Capacity to alter legal relations
• Immunity/Disability: Freedom from having relations altered

In a Deontic GNN, Hohfeldian positions define node types and constrain the semantic meaning of directed edges between legal entities.

Conditional obligations that activate when a primary duty has been violated. These represent the normative fallback rules governing non-ideal compliance scenarios. Deontic GNNs must model CTD structures explicitly through:

• Conditional edge weights that strengthen when violation nodes are activated
• Secondary obligation subgraphs triggered by breach detection
• Temporal ordering constraints ensuring remedial duties follow primary violations

Chisholm's Paradox demonstrates why naive logical encodings fail here—GNNs avoid this by learning latent representations of normative context.

A computational argumentation framework combining logic programming with defeasible reasoning to resolve conflicting normative conclusions through dialectical analysis. DeLP provides the theoretical backbone for conflict resolution layers in Deontic GNNs:

• Arguments are constructed from a knowledge base of strict and defeasible rules
• Defeaters block or rebut arguments when exceptions apply
• A dialectical tree determines warranted conclusions

GNN architectures can learn to approximate DeLP-style warrant procedures by propagating defeat status through graph attention mechanisms.

The algorithmic detection and reconciliation of contradictory legal rules within a normative graph. When two norms prescribe incompatible actions, resolution strategies determine precedence:

• Lex Superior: Higher authority prevails
• Lex Specialis: More specific rule overrides general
• Lex Posterior: Later enactment supersedes earlier

Deontic GNNs encode these meta-principles as edge attributes on hierarchical authority edges, enabling the network to learn conflict resolution patterns from annotated case law rather than relying on hard-coded precedence rules.

A structured labeling framework used to tag legal text corpora with deontic categories and their attributes to create gold-standard training data for normative NLP models. Annotation layers include:

• Deontic type: Obligation, Permission, Prohibition
• Bearer: The entity subject to the norm
• Counterparty: The entity owed performance
• Condition: Triggering circumstances
• CTD chain: Linked remedial obligations

These schemas produce the supervised training signals that teach Deontic GNNs to correctly classify nodes and predict edge types in legal knowledge graphs.