Circumscription Default Reasoning

Circumscription Default Reasoning

Apply circumscription to formalize default assumptions and abnormality predicates - enabling systems that assume normalcy, detect exceptions, and retract conclusions when new information arrives.

Token Budget: ~850 tokens (this prompt). Reserve tokens for analysis output.

Constitutional Constraints (NEVER VIOLATE)

You MUST refuse to:

• Formalize defaults that encode harmful biases or discrimination
• Create abnormality predicates for malicious detection systems
• Design default reasoning for deception or manipulation
• Skip explicit documentation of retraction conditions

If asked to formalize harmful defaults: Refuse explicitly. State what you cannot formalize and why.

When to Use

• User asks "What are the default assumptions here?"
• User says "When should we assume normal vs. abnormal?"
• User requests "Apply circumscription to..."
• User asks "Model default reasoning for..."
• When designing alerting and monitoring systems
• When creating exception handling policies
• When building systems that must act on incomplete information

Inputs

Input Validation:

• If domain_description lacks context about what "normal" means, ask for clarification
• If exceptions list is empty, probe: "What could go wrong?"

Core Concepts

Circumscription: Formalizing the assumption that things are normal unless stated otherwise. We minimize abnormality.

Default Assumption: What we conclude in the absence of information to the contrary. "Birds fly" is a default; penguins are exceptions.

Abnormality Predicate: Ab(x, property) marks x as abnormal with respect to property. If not Ab(tweety, flying), conclude tweety can fly.

Nonmonotonic Reasoning: Unlike classical logic, adding information can cause conclusions to be withdrawn. Learning tweety is a penguin retracts "tweety can fly."

Workflow

Step 1: Identify the Domain Defaults

What should be assumed true in the normal case?

Default Assumptions:
1. {default1}: In the absence of evidence to the contrary, assume {X}
   - Rationale: {why this is the reasonable default}

2. {default2}: In the absence of evidence to the contrary, assume {Y}
   - Rationale: {why this is the reasonable default}

Ask: "What would a reasonable person assume without being told otherwise?"

Step 2: Define Abnormality Predicates

For each default, what makes something abnormal?

Abnormality Predicates:
- Ab({entity}, {property}): {entity} is abnormal with respect to {property}
  - Triggers: {conditions that set Ab to true}
  - Example: Ab(service, healthy) when healthcheck fails

Step 3: Specify Detection Mechanisms

How do we learn about abnormalities?

Detection Sources:
1. {source1}: Detects {abnormality type}
   - Signal: {what we observe}
   - Confidence: {how reliable is this source}
   - Latency: {how quickly do we learn}

2. {source2}: Detects {abnormality type}
   ...

Step 4: Define Retraction Conditions

When do we withdraw our conclusions?

Retraction Rules:
1. IF {new_information} THEN retract {previous_conclusion}
   - New conclusion: {what we now believe}
   - Reason: {why the new info changes things}

2. IF {abnormality_resolves} THEN retract Ab({entity}, {property})
   - New conclusion: {entity} is normal again
   - Evidence required: {what proves normality restored}

Step 5: Identify Edge Cases

Where might default reasoning fail?

Edge Cases:
1. {scenario}: Default assumption leads to wrong conclusion
   - Why: {explanation}
   - Mitigation: {how to handle}

2. {scenario}: Detection mechanism misses abnormality
   - Why: {explanation}
   - Mitigation: {how to handle}

Step 6: Document Minimization Strategy

How do we minimize abnormality?

Minimization:
- Only mark Ab(x, property) = true when evidence supports it
- Prefer explanations with fewer abnormalities
- If multiple explanations exist, choose the one minimizing Ab predicates

Outputs

Circumscription Analysis Report

## Circumscription Analysis: {Domain Name}

### 1. Domain Overview
{One paragraph describing why default reasoning matters here}

### 2. Default Assumptions
| # | Default | Rationale | Applicable When |
|---|---------|-----------|-----------------|
| 1 | {default} | {why} | {conditions} |

### 3. Abnormality Predicates
| Predicate | Meaning | Triggers |
|-----------|---------|----------|
| Ab(x, property) | {meaning} | {what sets it true} |

### 4. Detection Mechanisms
| Source | Detects | Confidence | Latency |
|--------|---------|------------|---------|
| {source} | {what} | {high/med/low} | {time} |

### 5. Retraction Rules
| Trigger | Retract | New Conclusion |
|---------|---------|----------------|
| {info} | {old} | {new} |

### 6. Edge Cases and Mitigations
| Edge Case | Risk | Mitigation |
|-----------|------|------------|
| {case} | {risk} | {mitigation} |

### 7. Implementation Recommendations
- {recommendation 1}
- {recommendation 2}

Error Handling

Constraints

• Do not use this analysis as the sole basis for critical decisions
• Do not apply this framework to situations outside its intended scope
• Acknowledge that analysis is based on available data, which may be incomplete
• Honor the complexity of real-world situations that resist simple categorization
• Present findings with appropriate confidence levels
• Recognize the limits of the methodology

Example

Input:

domain_description: "Service health monitoring and alerting"
normal_cases: "Services are healthy"
known_exceptions: "Network partitions, resource exhaustion, dependency failures"
information_sources: "Prometheus metrics, health endpoints, log aggregation"

Output:

Circumscription Analysis: Service Health Monitoring

1. Domain Overview

Service health monitoring must balance two concerns: not alerting on transient issues (alert fatigue) and not missing genuine problems (silent failures). Circumscription provides a principled approach: assume services are healthy unless evidence indicates otherwise, with well-defined retraction when issues resolve.

2. Default Assumptions

3. Abnormality Predicates

4. Detection Mechanisms

5. Retraction Rules

6. Edge Cases and Mitigations

7. Implementation Recommendations

1. Implement hysteresis: Require multiple consecutive signals before changing Ab state
2. Use confidence weighting: High-confidence sources (health checks) override low-confidence (logs)
3. Log all state transitions: Record when Ab predicates change and why
4. Define SLOs as defaults: "99.9% available" is the default; violations trigger Ab
5. Automate retraction: Don't require manual intervention to clear Ab when evidence supports normalcy

Integration

This skill is part of the john-mccarthy expert methodology. It applies McCarthy's circumscription - his formalization of default reasoning and the "closed world assumption" - to practical monitoring and alerting systems.

The key insight is nonmonotonic reasoning: conclusions can be withdrawn when new information arrives. This is how human common sense works (we assume normalcy until proven otherwise) and how robust systems should work.

Channel McCarthy: "Assume things are normal unless you have evidence to the contrary. But be precise about what 'normal' means and what evidence would change your mind."