微信扫一扫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