Permission Graph

The foundational edge type in a permission graph is the deontic permission modality, formally distinct from obligation or prohibition. In deontic logic, permission is defined as the absence of a prohibition: an action P is permitted for actor A if and only if there is no norm stating that A must not do P. This is often modeled using the modal operator 'P'.

• Explicit Permission: A statute affirmatively grants the right (e.g., 'The Commissioner may issue guidance').
• Implicit Permission: An action is not addressed by any obligation or prohibition, making it legally permissible by default in most legal systems.
• Bilateral Permission: An actor is permitted to both perform and refrain from performing an action, representing true discretion.

Every edge in a permission graph is a directed, labeled relationship from a source actor node to a target action node or another actor node. The directionality encodes the flow of authorization.

• Actor-to-Action: [EPA Administrator] --(may issue)--> [Guidance Document] represents a direct grant of authority.
• Actor-to-Actor: [Principal] --(may delegate to)--> [Agent] models the transfer or sharing of discretionary power.
• Conditional Edges: Edges can carry attributes representing preconditions that must be satisfied before the permission becomes active, such as 'upon a finding of good cause' or 'after public notice and comment.'
• Edge Weighting: In quantitative models, edges can be weighted to represent the scope of discretion, from narrow (specific enumerated actions) to broad (general regulatory authority).

Permission graphs must algorithmically resolve conflicts with other deontic modalities in the same legal corpus. A well-formed graph enforces deontic consistency rules to prevent logical contradictions.

• Permission vs. Obligation: If an action is both permitted and obligatory, the obligation takes precedence. The permission edge is retained but marked as superseded or redundant.
• Permission vs. Prohibition: A prohibition always defeats a permission. The graph must detect and flag normative conflicts where a permission edge and a prohibition edge connect the same actor to the same action.
• Lex Specialis Priority: Specific permissions override general ones. A statute granting a specific agency the right to waive a requirement takes precedence over a general prohibition on waivers.
• Temporal Precedence: Newer enactments override older ones. The graph must version edges by effective date to resolve temporal conflicts.

Permission graphs model organizational and legal hierarchies through inheritance of permissions. Subordinate actors may inherit the permissions of their principals, subject to constraints.

• Vertical Inheritance: A regional director may inherit the enforcement permissions of the agency head, unless explicitly limited by regulation.
• Delegation Chains: The graph traces multi-hop delegation paths: [Secretary] --(may delegate to)--> [Deputy Secretary] --(may sub-delegate to)--> [Assistant Secretary].
• Scope Limitation: Inherited permissions can be narrowed but not expanded. A delegate cannot grant themselves more authority than the delegator possessed.
• Revocation Propagation: If a principal's permission is revoked, the graph must propagate the revocation to all downstream inherited permissions, requiring cascading invalidation logic.

Permissions are rarely absolute. The graph encodes conditional predicates as metadata on edges, representing the factual triggers that activate or deactivate a permission.

• Precondition Gates: IF [emergency declaration is active] THEN [FEMA Director] --(may deploy resources)--> [Disaster Zone].
• Temporal Bounds: Permissions can have effective dates, sunset clauses, and renewal conditions that constrain their temporal validity.
• Jurisdictional Constraints: A permission may be limited to a specific geographic area, industry sector, or class of regulated entities.
• Procedural Prerequisites: Many permissions require procedural steps before exercise, such as notice-and-comment rulemaking, environmental impact assessment, or congressional notification.

Permission graphs support specific query patterns essential for computational legal reasoning and compliance checking.

• Permission Existence Query: 'Is actor A permitted to perform action X under statute S?' resolves to a boolean answer by checking for a valid, unconflicted permission edge.
• Full Permission Enumeration: 'What are all actions actor A is permitted to take?' returns the complete set of outgoing permission edges, including inherited permissions.
• Authority Gap Detection: 'What actions are neither permitted, prohibited, nor obligated for actor A?' identifies regulatory gaps where the law is silent.
• Delegation Path Tracing: 'Through what chain of authority did actor A receive permission P?' traverses the graph backward to find the originating statutory grant.