Inductive Reasoning

Generalize from instances to rules. The logic of pattern extraction and empirical learning.

Type Signature

Inductive : [Observation] → Pattern → Generalization → ConfidenceBounds

Where:
  Observations     : [Instance] → Dataset
  Pattern          : Dataset → (Regularity × Frequency)
  Generalization   : (Regularity × Frequency) → Rule
  ConfidenceBounds : Rule × SampleSize → (Confidence × Exceptions)

When to Use

Use inductive when:

• Multiple similar observations accumulate
• Looking for recurring patterns across threads
• Building predictive rules from experience
• Identifying systemic behaviors
• Validating or discovering Canvas assumptions
• "This keeps happening" situations

Don't use when:

• Explaining single observation → Use Abductive
• Known causal chain exists → Use Causal
• Transferring one case to another → Use Analogical
• Resolving disagreement → Use Dialectical

Distinction from Other Modes

Mode	Input	Output	Question
Abductive	Single anomaly	Explanation	"Why did this happen?"
Inductive	Multiple instances	Pattern/Rule	"What keeps happening?"
Analogical	One source case	Transferred solution	"How is this like that?"

Key difference from Abductive:

• Abductive: 1 observation → 1 explanation
• Inductive: N observations → 1 generalization

Four-Stage Process

Stage 1: Observation Collection

Purpose: Gather and structure multiple instances for analysis.

Minimum Sample Requirements:

Confidence Target	Minimum N	Notes
Exploratory	3-5	Hypothesis generation only
Tentative	6-10	Directional confidence
Moderate	11-20	Actionable patterns
High	21+	Strong generalizations

Components:

observations:
  dataset:
    - instance_id: "deal-001"
      timestamp: ISO8601
      context: "Enterprise sales"
      attributes:
        deal_size: 400000
        sales_cycle: 120
        stalled_at: "legal_review"
        outcome: "won"

    - instance_id: "deal-002"
      timestamp: ISO8601
      context: "Enterprise sales"
      attributes:
        deal_size: 350000
        sales_cycle: 150
        stalled_at: "legal_review"
        outcome: "lost"

    # ... more instances

  metadata:
    total_instances: 12
    time_range: "Q3-Q4 2024"
    source: "threads/sales/*/6-learning.md"
    collection_method: "automated scan"

  quality:
    completeness: 0.92  # % of fields populated
    consistency: 0.88   # % following same schema
    recency: 0.75       # Weight toward recent

Stage 2: Pattern Detection

Purpose: Identify regularities in the dataset.

Pattern Types:

Type	Description	Example
Frequency	How often X occurs	"7/12 deals stall at legal"
Correlation	X and Y co-occur	"Large deals AND long cycles"
Sequence	X follows Y	"Stall → lose within 30 days"
Cluster	Groups emerge	"Two deal archetypes exist"
Trend	Direction over time	"Cycles getting longer"
Threshold	Breakpoint exists	"Deals >$300K behave differently"

Detection Process:

patterns:
  detected:
    - pattern_id: P1
      type: frequency
      description: "Legal review stalls"
      evidence: "7 of 12 deals (58%) stalled at legal review"
      strength: 0.78

    - pattern_id: P2
      type: correlation
      description: "Deal size correlates with cycle length"
      evidence: "r=0.72 between deal_size and sales_cycle"
      strength: 0.72

    - pattern_id: P3
      type: threshold
      description: "CFO involvement threshold"
      evidence: "Deals >$250K require CFO, adding 30+ days"
      strength: 0.85

    - pattern_id: P4
      type: sequence
      description: "Stall duration predicts outcome"
      evidence: "Stalls >21 days → 80% loss rate"
      strength: 0.80

  rejected:
    - pattern: "Industry affects outcome"
      reason: "No significant difference across industries (p>0.3)"

  insufficient_data:
    - pattern: "Seasonality effects"
      reason: "Only 2 quarters of data, need 4+ for seasonality"

Stage 3: Generalization

Purpose: Form rules from validated patterns.

Rule Formation:

generalizations:
  rules:
    - rule_id: R1
      statement: "Enterprise deals >$250K require CFO approval, adding 30+ days to cycle"
      derived_from: [P2, P3]

      structure:
        condition: "deal_size > 250000"
        prediction: "sales_cycle += 30 days"
        mechanism: "CFO approval requirement"

      applicability:
        domain: "Enterprise sales"
        segments: ["all enterprise"]
        exceptions: ["existing customers with MSA"]

    - rule_id: R2
      statement: "Legal review stalls >21 days predict deal loss with 80% probability"
      derived_from: [P1, P4]

      structure:
        condition: "stall_duration > 21 AND stall_stage = 'legal'"
        prediction: "outcome = 'lost' (p=0.80)"
        mechanism: "Budget cycle expiration, champion fatigue"

      applicability:
        domain: "Enterprise sales"
        segments: ["new customers"]
        exceptions: ["government deals with known long cycles"]

    - rule_id: R3
      statement: "58% of enterprise deals will stall at legal review"
      derived_from: [P1]

      structure:
        condition: "enterprise deal"
        prediction: "P(legal_stall) = 0.58"
        mechanism: "Custom contract requirements"

      applicability:
        domain: "Enterprise sales"
        segments: ["all"]
        exceptions: ["standard contract accepted"]

Stage 4: Confidence Bounds

Purpose: Quantify reliability and identify exceptions.

Confidence Calculation:

Confidence = f(sample_size, pattern_strength, consistency, recency)

Base confidence from sample size:
  N < 5:   max 0.40
  N 5-10:  max 0.60
  N 11-20: max 0.80
  N > 20:  max 0.95

Adjustments:
  × pattern_strength (0-1)
  × consistency (0-1)
  × recency_weight (0.5-1.0)

Components:

confidence_analysis:
  rules:
    - rule_id: R1
      confidence: 0.72
      calculation:
        base: 0.80        # N=12, moderate sample
        strength: 0.85    # Strong pattern
        consistency: 0.88 # Good data quality
        recency: 0.95     # Recent data
        final: 0.72       # base × min(strength, consistency, recency)

      bounds:
        lower: 0.58       # Pessimistic estimate
        upper: 0.82       # Optimistic estimate

      exceptions:
        identified:
          - "Existing customer deal closed in 45 days despite $400K size"
            explanation: "Pre-existing MSA eliminated legal review"
          - "Government deal took 180 days but won"
            explanation: "Known government procurement cycle"
        exception_rate: 0.17  # 2/12 instances

      validity:
        expires: "2025-06-01"  # Re-validate after 6 months
        invalidated_by: 
          - "Process change eliminating legal review"
          - "New contract template adoption"
        strengthened_by:
          - "3+ more instances following pattern"
          - "Causal mechanism confirmed"

    - rule_id: R2
      confidence: 0.68
      # ... similar structure

Output Summary:

inductive_output:
  summary:
    rules_generated: 3
    highest_confidence: R1 (0.72)
    total_observations: 12
    time_range: "Q3-Q4 2024"

  actionable_rules:
    - rule: R1
      action: "Add 30 days to forecast for deals >$250K"
      confidence: 0.72

    - rule: R2
      action: "Escalate intervention when legal stall exceeds 14 days"
      confidence: 0.68

  tentative_rules:
    - rule: R3
      action: "Plan for legal stall in 60% of deals (resource accordingly)"
      confidence: 0.55
      needs: "5+ more observations to reach actionable confidence"

  canvas_implications:
    validate:
      - assumption: "A4: Enterprise sales cycle is 90 days"
        finding: "Actually 120 days for deals >$250K"
        action: "Update assumption"

    new_hypothesis:
      - "H17: Standard contract template would reduce legal stalls by 50%"
        basis: "Legal stall is primary cycle driver"
        test: "Pilot standard contract with 5 deals"

Quality Gates

Gate	Requirement	Failure Action
Sample size	≥5 instances	Collect more data
Data quality	≥80% completeness	Clean dataset
Pattern strength	≥0.6 for at least one	Lower threshold or collect more
Exception rate	<30% for actionable rules	Narrow rule scope
Mechanism identified	Plausible explanation	Add abductive analysis

Common Failure Modes

Failure	Symptom	Fix
Small N	High variance, unstable patterns	Wait for more data
Survivorship bias	Only successful cases analyzed	Include failures
Confounding	Correlation ≠ causation	Test mechanism with intervention
Overfitting	Rule too specific to sample	Simplify rule, test holdout
Recency bias	Old patterns weighted equally	Apply recency weighting
Cherry-picking	Only confirming instances	Systematic collection

Pattern Validation

Before promoting rule to actionable:

Statistical Validation

validation:
  method: "holdout"
  training_set: 8 instances
  test_set: 4 instances
  rule_accuracy_on_test: 0.75
  passed: true

Causal Validation

validation:
  method: "mechanism_test"
  proposed_mechanism: "CFO approval adds 30 days"
  test: "Interview 3 CFOs about approval process"
  result: "Confirmed - CFO review averages 25-35 days"
  passed: true

Temporal Validation

validation:
  method: "stability_check"
  pattern_in_Q3: 0.62
  pattern_in_Q4: 0.54
  drift: -0.08 (acceptable)
  passed: true

Automated Pattern Detection

For continuous learning, run inductive scans:

automated_scan:
  frequency: weekly
  sources:
    - "threads/sales/*/6-learning.md"
    - "threads/marketing/*/6-learning.md"
    - "threads/operations/*/6-learning.md"

  thresholds:
    min_instances: 5
    min_pattern_strength: 0.6

  output:
    location: "ops/patterns.md"
    alert_threshold: 0.75  # Flag high-confidence new patterns

  actions:
    new_pattern_detected: "Flag in ops/today.md for review"
    existing_pattern_strengthened: "Update confidence, log"
    pattern_invalidated: "Alert, review rule"

Output Contract

inductive_output:
  observations:
    count: int
    time_range: string
    sources: [string]
    quality_score: float

  patterns:
    detected: [{
      pattern_id: string
      type: frequency | correlation | sequence | cluster | trend | threshold
      description: string
      strength: float
      evidence: string
    }]
    rejected: [{pattern: string, reason: string}]

  rules:
    - rule_id: string
      statement: string
      confidence: float
      bounds: {lower: float, upper: float}
      exceptions: [{instance: string, explanation: string}]
      applicability: {domain: string, segments: [string], exceptions: [string]}
      validity: {expires: date, invalidated_by: [string]}

  canvas_implications:
    validate: [{assumption: string, finding: string, action: string}]
    invalidate: [{assumption: string, finding: string, action: string}]
    new_hypotheses: [{hypothesis: string, basis: string, test: string}]

  actions:
    immediate: [string]        # High-confidence rules to act on
    monitor: [string]          # Tentative patterns to watch
    collect: [string]          # Data gaps to fill

  next:
    suggested_mode: ReasoningMode
    threads_to_create: [string]

  trace:
    patterns_evaluated: int
    rules_generated: int
    duration_ms: int

Example Execution

Context: "Review last 6 months of marketing content performance"

Stage 1 - Observations:

Collected: 24 content pieces
Sources: threads/marketing/*/6-learning.md
Attributes: topic, format, channel, sessions, conversions, time_to_demo
Quality: 0.88 completeness

Stage 2 - Patterns:

P1 (frequency): Case studies convert 2.3x average (8/24, all above average)
P2 (correlation): Technical depth correlates with enterprise demos (r=0.68)
P3 (threshold): Posts >2000 words perform better on SEO (breakpoint identified)
P4 (trend): LinkedIn declining, organic search rising over 6 months

Stage 3 - Generalizations:

R1: "Case studies should be prioritized for bottom-funnel conversion"
    Confidence: 0.75, based on 8 instances

R2: "Technical content attracts enterprise prospects"
    Confidence: 0.68, based on correlation analysis

R3: "SEO content should target >2000 words"
    Confidence: 0.70, based on threshold analysis

Stage 4 - Confidence Bounds:

R1: 0.75 [0.62, 0.85] - Actionable
R2: 0.68 [0.54, 0.78] - Actionable with caution
R3: 0.70 [0.58, 0.80] - Actionable

Canvas update: 
  - Validate H8 (case studies convert)
  - New H18: "Long-form SEO content drives organic growth"

Action: Shift content mix toward case studies and long-form technical guides