Skill: Reason About Dependencies

Use this skill when traversing the skill dependency graph to infer what a learner knows, find efficient assessment paths, or identify prerequisite gaps.

When to activate

• •During assessment: to infer skills from demonstrated ability
• •During lesson planning: to identify prerequisite gaps
• •When an educator asks "what does my student need to know before X?"
• •When optimizing assessment order to minimize questions

Graph structure

Skills and dependencies are stored in data/domains/{domain}/:

• •skills.json — skill definitions with Bloom's levels
• •dependencies.json — directed edges with confidence and type

An edge {source: A, target: B} means "A is a prerequisite for B" — knowing B implies knowing A (with some confidence).

Inference rules

Forward inference (what does knowing X imply?)

If a learner demonstrates skill B, and A → B is a prerequisite edge with confidence C, then infer the learner knows A with confidence C.

Demonstrated: "pandas-groupby"
Edge: "select-filter-data" → "pandas-groupby" (confidence: 0.90)
Inference: learner knows "select-filter-data" with confidence 0.90

Multi-hop inference (transitive)

If A → B (confidence C1) and B → C (confidence C2), and the learner demonstrates C, then:

• •Infer B with confidence C2
• •Infer A with confidence C1 × C2 (multiplicative decay)

Demonstrated: "pandas-groupby" (confidence 1.0)
Edge chain: "open-terminal" (0.95) → "navigate-directories" (0.95) →
            "run-python-script" (0.95) → "python-variables-types" (0.90) →
            "python-control-flow" (0.90) → "python-functions" (0.85) →
            ... → "pandas-groupby"

Inferred confidences (multiplicative):
- python-functions: 0.70 (from pandas-groupby edge)
- python-control-flow: 0.85 × 0.70 = 0.60
- python-variables-types: 0.90 × 0.60 = 0.54
- run-python-script: 0.95 × 0.54 = 0.51
- navigate-directories: 0.95 × 0.51 = 0.49
- open-terminal: 0.95 × 0.49 = 0.46

Confidence floor

Stop inferring when confidence drops below 0.3. Below this threshold, the inference is too uncertain to be useful — the skill should be directly assessed.

Confidence from multiple paths

If a skill can be inferred through multiple paths, take the maximum confidence across all paths. Multiple inference chains reinforce each other.

"inspect-dataframe" can be inferred from:
  Path 1: via "select-filter-data" → confidence 0.85
  Path 2: via "handle-missing-data" → confidence 0.80

Result: confidence = max(0.85, 0.80) = 0.85

Edge types affect inference

Finding efficient assessment paths

The goal

Minimize the number of questions while maximizing the skills assessed (directly or inferred). This is the "test high, infer low" strategy.

Algorithm

1. •

   Compute inference reach: For each skill, calculate how many downstream skills would be inferred if the learner demonstrates it. Weight by the confidence of each inference.

2. •

   Rank by reach: Skills with the highest inference reach are the best starting points for assessment.

3. •

   Start with the highest-reach skill the learner might plausibly know (don't ask about "design a data pipeline" if they're a beginner).

4. •

   Branch on result:

   • •Pass: Infer all prerequisites. Move to the next unassessed branch.
   • •Fail: Drop down to the immediate prerequisites and test those.
5. •

   Repeat until all target skills are assessed or inferred.

Example: Efficient path through python-data-analysis

Instead of testing all 25 skills:

Start: "pandas-groupby" (Application level, 6+ inferred skills)
  ├─ Pass → Infer: select-filter-data, inspect-dataframe, import-pandas,
  │         install-packages, python-variables-types, python-control-flow,
  │         python-functions, run-python-script, navigate-directories,
  │         install-python, open-terminal
  │    Next: Test "exploratory-data-analysis" (Analysis level, different branch)
  │    Next: Test "design-data-pipeline" (Synthesis level, highest)
  │
  └─ Fail → Drop to: "select-filter-data"
       ├─ Pass → Infer: inspect-dataframe and below
       │    Note: They can filter but not groupby. Test "handle-missing-data"
       └─ Fail → Drop to: "inspect-dataframe"
            └─ Continue drilling down...

This can assess the full domain in 4–6 questions instead of 25.

Prerequisite gap analysis

For lesson planning

Given a target skill the educator wants to teach, walk the dependency graph backward to find all prerequisites. Compare against the group's learner profiles. Report:

• •Satisfied prerequisites: Skills the group already has (high confidence)
• •Partial prerequisites: Skills some students have but others don't
• •Missing prerequisites: Skills nobody in the group has demonstrated
• •Recommended order: Teach missing prerequisites in dependency order (leaves first)

Cross-domain transfer inference

When to use

Cross-domain transfer activates when:

• •A learner with an existing profile in Domain A is being assessed or placed in Domain B
• •An educator asks about a student's readiness for a new subject
• •Planning a lesson in a new domain for a group with profiles in another domain

The principle

Skills don't exist in isolation across domains. A student who can "analyze habitat health" in ecology exercises the same analytical cognition as "identify data quality issues" in data analysis. The operation — decompose, examine evidence, evaluate against criteria — is structurally similar even though the content is entirely different.

Cross-domain transfer identifies these structural similarities and generates hypotheses (not conclusions) about where a learner might have partial readiness in a new domain.

What transfers and what doesn't

Confidence model

Cross-domain confidence is significantly lower than within-domain inference:

• •Base transfer rate: 0.35 (vs. 0.85–0.95 for within-domain prerequisite edges)
• •Bloom's alignment multiplier:
  • •Same level: 1.0×
  • •Adjacent level (e.g., analysis → synthesis): 0.6×
  • •Two levels apart: 0.3×
  • •Three+ levels apart: 0.0× (no transfer)
• •Cognitive operation bonus: +30% when both skill labels share a cognitive verb (e.g., both involve "analyze" or "compare")
• •Generality bonus: +20% when both skills are high in their respective dependency chains (many prerequisites = more abstract = more transferable)
• •Confidence cap: 0.55 maximum — cross-domain transfer never reaches "confident"

How to use transfer in assessment

1. •Run analyze_cross_domain_transfer with the learner, source domain, and target domain
2. •Review the transfer candidates — skills in the target domain where the learner has partial readiness from their source domain experience
3. •Start assessment higher: If strong transfers exist at analysis/synthesis level, don't begin with knowledge-level questions — jump to the transfer zone
4. •Validate or correct: Treat transfers as priors, not facts. The first assessment question should confirm or refute the transfer hypothesis
5. •Communicate to the educator: "Based on Maria's ecology work, I expect she'll pick up data pattern recognition faster. Let me verify."

Example: Ecology → Python Data Analysis

Learner: Maya Whitehawk
Source: outdoor-ecology (16 assessed skills, up to evaluation level)
Target: python-data-analysis (25 skills, no prior assessment)

Transfer analysis:
- "assess-habitat-health" (analysis) → "exploratory-data-analysis" (analysis)
  Transfer: ~0.31 — shared analytical framework, both require multi-factor evaluation

- "explain-food-web" (analysis) → "identify-data-quality-issues" (analysis)
  Transfer: ~0.28 — shared analysis operation, both high-order

- "compare-ecosystems" (evaluation) → "critique-visualization" (evaluation)
  Transfer: ~0.22 — same Bloom's level, both evaluation operations

- "lead-nature-walk" (synthesis) → "design-data-pipeline" (synthesis)
  Transfer: ~0.25 — both synthesis-level composition tasks

- "identify-common-trees" (knowledge) → "open-terminal" (knowledge)
  Transfer: 0.00 — domain-specific knowledge, no transfer

Recommendation: Start assessment at application level. Maya's analytical
frameworks transfer. Test domain-specific skills (pandas, terminal) from scratch
but expect faster progress on data analysis reasoning.

Labeled in learner profiles

Cross-domain inferences are clearly labeled so educators and the assessment agent know these are estimates, not confirmed skills:

## Cross-Domain Transfer (from outdoor-ecology)

- identify-data-quality-issues: 0.28 transfer confidence (cross-domain from explain-food-web)
- exploratory-data-analysis: 0.31 transfer confidence (cross-domain from assess-habitat-health)

Reference files

• •references/inference-patterns.md — Worked examples of inference chains