Rule Base Stratification

Stratification imposes a total or partial order on rule sets, assigning each norm to a discrete stratum based on its precedence. Higher layers represent superior authority—such as constitutional provisions or lex superior principles—while lower layers contain default or general rules.

• Layer 0 (Highest): Constitutional or peremptory norms
• Layer 1: Specific statutory mandates
• Layer 2: General regulatory provisions
• Layer N (Lowest): Default or fallback rules

When a conflict is detected, the system consults layers sequentially, applying the first applicable rule and ignoring lower-strata contradictions. This mirrors the lex specialis and lex superior maxims in a computationally tractable form.

While defeasible reasoning allows conclusions to be retracted with new evidence, stratification provides a static, pre-compiled conflict resolution structure. The key distinction is when precedence is resolved:

• Stratification: Pre-resolves conflicts at design time by assigning rules to fixed layers. The reasoning engine never backtracks across strata.
• Defeasible Logic: Resolves conflicts dynamically at inference time, allowing lower-priority rules to surface when higher-priority rules are inapplicable.

Stratification is ideal for highly regulated domains where the normative hierarchy is well-defined and stable, such as tax codes or building regulations.

Within a single stratum, sub-stratification handles exceptions to general rules without requiring a full layer promotion. A general rule at Layer 2 might have an exception clause that activates only under specific rule applicability conditions.

• The exception is placed in a higher sub-stratum within the same layer
• The system checks sub-strata before applying the general rule
• This implements lex specialis derogat legi generali without fragmenting the overall layer architecture

This technique prevents the combinatorial explosion of layers while maintaining precise control over exception handling.

A properly stratified rule base guarantees that the maximal consistent subset (MCS) of rules is always retrievable through deterministic traversal. The algorithm:

1. Begins at the highest stratum
2. Collects all applicable rules whose rule applicability conditions are satisfied
3. Checks for internal conflicts within the stratum using a normative collision matrix
4. If consistent, proceeds to the next stratum only for rules not already covered
5. Lower-strata rules conflicting with already-adopted higher norms are preempted

The output is a provably conflict-free rule set, eliminating the need for runtime deontic conflict detection.

Stratification can encode the lex posterior derogat priori principle by assigning temporal precedence as a secondary ordering dimension. When two rules occupy the same authority stratum, the system consults a temporal sub-layer:

• Enactment timestamps or effective dates determine priority
• Later-enacted rules override earlier ones within the same authority level
• This creates a three-dimensional stratification: Authority × Specificity × Temporality

This approach is essential for modeling regulatory change detection scenarios where new statutes must seamlessly override prior versions without manual rule base reconstruction.

When a normative coherence metric detects unacceptable inconsistency, stratification enables normative repair operators to restore consistency through layer reassignment rather than rule deletion. The repair protocol:

• Identifies the conflicting rule pair using a normative collision matrix
• Promotes the preferred rule to a higher stratum
• Demotes or suspends the disfavored rule to a lower stratum
• Re-verifies consistency across all strata

This preserves the full rule base while resolving the conflict, avoiding the information loss inherent in norm abrogation.

The foundational legal maxim that a specific rule overrides a general rule, directly implemented by stratification layers. When a rule base is organized by specificity, the lex specialis principle is applied algorithmically by consulting higher-strata exception rules before lower-strata default rules. This ensures that carve-outs for particular fact patterns are never erroneously preempted by broader provisions.

A hierarchical conflict rule where higher-authority norms defeat lower-authority norms. In stratified rule bases, this maps to a distinct precedence axis separate from specificity. A constitution occupies the top stratum, statutes the middle, and administrative regulations the bottom. Multi-dimensional stratification systems must resolve collisions between the specificity axis and the authority axis using predefined meta-priority rules.

A directed acyclic graph (DAG) representing precedence relationships between rules. Each node is a rule, and each edge denotes 'overrides.' Stratification flattens this graph into ordered layers for efficient traversal. The graph must remain acyclic to prevent paradoxical loops where Rule A overrides Rule B, which overrides Rule C, which overrides Rule A. Cycle detection is a critical validation step before stratification.

A mode of inference where conclusions can be retracted when new information or superior rules are introduced. Rule base stratification directly enables defeasibility: a conclusion drawn from a lower stratum is automatically defeated when a conflicting rule from a higher stratum becomes applicable. This implements non-monotonic logic without requiring full theorem-prover recomputation on every update.

A resolution strategy where a higher-priority rule completely nullifies a conflicting lower-priority rule within its scope. Unlike exception carving—which creates a narrow gap in the general rule—preemption suppresses the lower rule entirely for overlapping fact patterns. Stratification layers encode preemption semantics: rules in Stratum 1 preempt conflicting rules in Stratum 2, not merely except them.

A computational method that identifies the largest non-contradictory subset of rules from an inconsistent rule base. Stratification provides a deterministic alternative to MCS computation: instead of searching for maximal subsets, the system simply applies rules in priority order and discards lower-strata rules that conflict with already-applied higher-strata rules. This is computationally cheaper but requires careful stratum assignment.