Trend Modeling with Three-Valued Logic

Overview

Based on research in trend-based optimization for product innovation, this skill applies three-valued logic (increasing/decreasing/constant) to analyze markets when precise numerical data is unavailable. This approach enables meaningful analysis with minimal information.

Required Frameworks

Framework	Output Section	Required	Condition
Variables Table	Variables	yes	—
Relationship Matrix	Relationship Matrix	yes	—
Scenario Generation	Generated Scenarios	yes	—
Transitional Graph	Transitional Scenario Graph (Mermaid stateDiagram)	yes	—
Terminal Scenario Analysis	Terminal Scenario Analysis	yes	—
Multi-Objective Trade-offs	Trade-offs	yes	—

Core Concept

Traditional market analysis requires extensive quantitative data. Three-valued logic provides an alternative when:

• Data is scarce or unreliable
• Relationships are qualitative
• Uncertainty is high
• Quick directional insights are needed

The Three Values

Load and apply the trend indicator definitions from protocols/TREND-INDICATORS.md. This skill uses the formal notation variant (INC(X, Y), DEC(X, Y)) and the extended notation (AG, DG, AD, DD) for acceleration/deceleration modifiers. See the protocol for full definitions.

CRITICAL: When the user provides correlation data, you MUST:

1. Explicitly label each correlation as "positive correlation" or "negative correlation"
2. Use the INC(X, Y) or DEC(X, Y) notation format for each relationship
3. Show the conversion step clearly before building the relationship matrix

Example:

• Market size and competition have positive correlation → INC(Market Size, Competition)
• If Market Size = INC, then Competition = INC
• If Market Size = DEC, then Competition = DEC
• Price and demand have negative correlation → DEC(Price, Demand)
• If Price = INC, then Demand = DEC
• If Price = DEC, then Demand = INC

Trend Model Construction

Step 1: Identify Variables

List market variables of interest:

• Market size
• Competition intensity
• Price pressure
• Innovation rate
• Customer adoption
• Regulatory burden

Step 2: Determine Relationships

For each pair of variables:

• Identify correlation direction (positive/negative)
• Convert to trend relationship (INC/DEC)

Step 3: Build Trend Matrix

Variable	Market Size	Competition	Price	Innovation
Market Size	-	INC	DEC	INC
Competition	INC	-	DEC	CONST
Price	DEC	DEC	-	DEC
Innovation	INC	CONST	DEC	-

Step 4: Generate Scenarios

A scenario is a consistent assignment of INC/DEC/CONST to all variables that satisfies all relationships.

Step 5: Identify Terminal Scenarios

Terminal scenarios are equilibrium states where:

• All relationships are satisfied
• System is stable
• No further transitions occur

Transitional Scenario Graphs

Create Mermaid diagrams showing scenario evolution:

stateDiagram-v2
    [*] --> S1: Initial conditions

    S1: Scenario 1<br/>Market=INC, Comp=INC<br/>Price=DEC, Innov=INC

    S2: Scenario 2<br/>Market=CONST, Comp=INC<br/>Price=DEC, Innov=CONST

    S3: Scenario 3 (Terminal)<br/>Market=DEC, Comp=CONST<br/>Price=CONST, Innov=DEC

    S4: Scenario 4 (Terminal)<br/>Market=INC, Comp=INC<br/>Price=DEC, Innov=INC

    S1 --> S2: Market saturation
    S1 --> S4: Sustained growth
    S2 --> S3: Commoditization
    S2 --> S4: Innovation breakthrough

Multi-Objective Trade-offs

From the research: "No scenario satisfies all objective functions simultaneously."

When analyzing terminal scenarios:

1. Identify competing objectives
2. Map which scenarios favor which objectives
3. Highlight trade-offs required
4. Recommend based on priority alignment

Application to Market Analysis

Use Case: New Market Entry

Variables:

• Market Growth (MG)
• Competitive Intensity (CI)
• Entry Barriers (EB)
• Customer Awareness (CA)

Relationships:

• INC(MG, CI) - Growing markets attract competitors
• INC(MG, CA) - Growth increases awareness
• DEC(EB, CI) - Lower barriers increase competition
• INC(CA, MG) - Awareness drives growth

Scenarios Generated:

1. Explosive growth: MG=AG, CI=AG, EB=DEC, CA=AG
2. Mature equilibrium: MG=DG, CI=CONST, EB=CONST, CA=CONST
3. Consolidation: MG=DEC, CI=DEC, EB=INC, CA=CONST

Output Structure

## Trend Model Summary

### Variables
| Variable | Current State | Trend | Confidence |
|----------|---------------|-------|------------|
| [Name] | [Description] | INC/DEC/CONST | High/Med/Low |

### Relationship Matrix
[Matrix showing INC/DEC relationships]

### Generated Scenarios
| Scenario | Var1 | Var2 | Var3 | Terminal? |
|----------|------|------|------|-----------|
| S1 | INC | DEC | CONST | No |
| S2 | CONST | CONST | DEC | Yes |

### Transitional Graph
[Mermaid state diagram]

### Terminal Scenario Analysis
**Scenario X**: [Description]
- Conditions: [What leads here]
- Trade-offs: [What must be sacrificed]
- Recommendation: [Strategic implication]

### Key Insights
1. [Insight about scenario transitions]
2. [Insight about trade-offs]

Best Practices

• Start simple: Begin with 4-6 variables
• Validate relationships: Check with domain experts
• Document uncertainty: Note where relationships are speculative
• Update iteratively: Refine model as new information emerges
• Focus on transitions: The paths between scenarios often matter more than endpoints
• Large models (7+ variables): Focus the relationship matrix on direct relationships only. Not every variable pair needs a relationship — use CONST for pairs without clear correlation. Generate 3-5 key scenarios rather than exhaustively enumerating all combinations. Prioritize terminal scenarios and the most likely transitional paths.

Advantages of This Approach

From the research:

• "No numerical values of constants or parameters are needed"
• "A complete list of all futures/histories is obtained"
• "Results remain easy to understand without knowledge of sophisticated mathematical tools"

Additional Resources

For theoretical background and advanced techniques, see:

• references/three-valued-logic.md - Theoretical foundation
• references/scenario-generation.md - Algorithm details
• examples/trend-model-example.md - Worked example

Orchestration Hints

Confidence tiers (universal scale):

• High: 3+ independent, recent (<12mo) sources that converge
• Medium: 2 sources OR sources >12mo old OR indirect evidence
• Low: Single source, inference, or extrapolation

Dimension-specific confidence criteria below REFINE (not replace) these universal definitions.

• Cross-reference dimensions: All dimensions provide input variables for scenario modeling
• Alert triggers:
  • Scenario with >50% probability of adverse outcome
  • Bifurcation point within planning horizon
  • Terminal scenario that invalidates core business assumptions
• Confidence rules:
  • High: Model inputs validated by 3+ dimensions' findings
  • Medium: Model inputs from 2 dimensions with reasonable assumptions
  • Low: Speculative inputs or single-dimension basis
• Conflict detection:
  • Scenario probabilities vs other dimensions' confidence levels
  • Trend direction assumptions vs actual trend-analysis findings
  • Timeline estimates vs regulatory and technology readiness timelines