Law Conflict Resolution Algorithm

This is the core intellectual engine of CLE-Net.

1. What is a Conflict?

A conflict exists when two laws cannot both hold in the same context.

Formally, laws $l_1$ and $l_2$ conflict if:

$$\exists c \in \text{Contexts}: l_1(c) = \text{true} \land l_2(c) = \text{false}$$

2. Law Representation

Each law is represented as:

$$l = (P, C, A, \theta)$$

Symbol	Meaning
$P$	Predicates
$C$	Conditions
$A$	Action or implication
$\theta$	Confidence distribution

3. Conflict Resolution Pipeline

Step 1: Detection

Conflicts are detected via:

Graph inconsistencies
Contradictory outcomes
Validator challenges

Step 2: Context Expansion

CLE-Net attempts to separate contexts:

$$C_1 \neq C_2 \Rightarrow \text{No conflict}$$

Many conflicts dissolve here.

Step 3: Dominance Evaluation

If conflict remains, compute dominance score:

$$D(l) = \omega_1 \cdot \theta + \omega_2 \cdot S(l) + \omega_3 \cdot CCS_{author} + \omega_4 \cdot \text{Recency}$$

Weight	Purpose
$\omega_1$	Confidence matters
$\omega_2$	Stability rewarded
$\omega_3$	Author reliability
$\omega_4$	Recent laws prioritized

Step 4: Resolution Decision

Case	Outcome
$D(l_1) \gg D(l_2)$	Deprecate $l_2$
Similar dominance	Split contexts
Unclear	Mark both as provisional

No forced deletion unless confidence is high.

Step 5: Learning from Conflict

The conflict itself generates a meta-law:

“In context X, rule Y overrides rule Z”

This improves future reasoning.

4. Formal Algorithm

def resolve_conflict(l1: Law, l2: Law) -> ResolutionResult:
    """
    Resolve a conflict between two laws.
    
    Returns:
        ResolutionResult with decision and reasoning
    """
    
    # Step 1: Check if contexts can be separated
    if can_separate_contexts(l1.context, l2.context):
        return ResolutionResult(
            decision="separate",
            reason="Contexts can be distinguished",
            meta_law=generate_meta_law(l1, l2)
        )
    
    # Step 2: Calculate dominance scores
    d1 = calculate_dominance(l1)
    d2 = calculate_dominance(l2)
    
    # Step 3: Make resolution decision
    threshold = 0.3  # Significant dominance threshold
    
    if d1 - d2 > threshold:
        return ResolutionResult(
            decision="deprecate_l2",
            reason=f"l1 dominance ({d1:.2f}) >> l2 ({d2:.2f})",
            surviving_law=l1,
            deprecated_law=l2
        )
    elif d2 - d1 > threshold:
        return ResolutionResult(
            decision="deprecate_l1",
            reason=f"l2 dominance ({d2:.2f}) >> l1 ({d1:.2f})",
            surviving_law=l2,
            deprecated_law=l1
        )
    else:
        return ResolutionResult(
            decision="provisional",
            reason="Dominance unclear, marking both provisional",
            requires_evidence=True
        )


def can_separate_contexts(c1: Context, c2: Context) -> bool:
    """
    Check if two contexts can be distinguished.
    
    Returns True if contexts are separable,
    meaning the conflict is only apparent.
    """
    # Check for explicit context differences
    if c1.domain != c2.domain:
        return True
    
    # Check temporal separation
    if c1.time_range and c2.time_range:
        if not ranges_overlap(c1.time_range, c2.time_range):
            return True
    
    # Check actor differences
    if c1.actors != c2.actors:
        return True
    
    return False


def calculate_dominance(law: Law) -> float:
    """
    Calculate dominance score for a law.
    """
    weights = {
        'confidence': 0.3,
        'survival': 0.25,
        'author_ccs': 0.25,
        'recency': 0.2
    }
    
    score = (
        weights['confidence'] * law.confidence +
        weights['survival'] * law.survival_score +
        weights['author_ccs'] * law.author_ccs +
        weights['recency'] * law.recency_score
    )
    
    return score

5. Meta-Law Generation

When conflicts are resolved, meta-laws are generated:

def generate_meta_law(l1: Law, l2: Law) -> MetaLaw:
    """
    Generate a meta-law from conflict resolution.
    """
    return MetaLaw(
        rule=f"In {l1.context}, prefer {l1.predicate} over {l2.predicate}",
        precedence=l1.dominance_score - l2.dominance_score,
        conditions=l1.context,
        confidence=abs(l1.dominance_score - l2.dominance_score)
    )

6. Example Resolution

Conflict Example

Law 1: “VIP clients ignore delays” Law 2: “VIP clients must acknowledge all delays”

Resolution Process

Detection: Contradictory outcomes detected
Context Expansion:
- Law 1: “standard VIP policy”
- Law 2: “security context”
Separation: Contexts can be distinguished
Result: Meta-law generated

Generated Meta-Law

“In security contexts, acknowledgment is required. In standard VIP policy, delays may be ignored.”

7. Properties

7.1 Convergence

The conflict resolution algorithm is designed to converge:

Each resolution reduces ambiguity
Meta-laws encode decisions
Future conflicts reference meta-laws

7.2 No Deletion

Important property: Laws are never deleted.

They may be:

Deprecated (confidence → 0)
Marked provisional (requires evidence)
Contextually limited (applies only in specific contexts)

But the historical record is preserved.

7.3 Transparency

Every resolution is:

Recorded in the ledger
Accompanied by reasoning
Subject to challenge

8. Implementation Notes

Confidence Thresholds

Threshold	Action
> 0.8	Strong confidence
0.5 - 0.8	Moderate confidence
< 0.5	Weak (requires evidence)

Dominance Thresholds

Difference	Decision
> 0.3	Clear dominance
0.1 - 0.3	Similar (provisional)
< 0.1	Unclear (needs review)