Appendix A: StructLang Unified Symbolic System v5.0 | StructLang

Complete Technical Manual (Revised Edition)

Instructions for Use

This appendix is the complete technical manual for the StructLang symbol system and can be used as a standalone document.

How to Use This Manual:

• Beginners: Read Parts 1-5 in sequence
• Users: Refer to Part 2 (Symbol Table) and Part 5 (Operation Manual)
• Advanced Users: Consult Part 4 (Inference Rules) and Part 7 (Extension Mechanisms)
• Troubleshooting: Jump directly to Part 9 (Common Questions)

v5.0 Update Notes:

• Added intention space symbols (T-B-R)
• Added origin weight symbols
• Added perspective and grouping symbols
• Clarified exclusive use of <> symbol
• Added vectorization representation methods
• Added network structure symbols

Part 1: Design Principles

Core Principles

1. Direct Keyboard Input: All symbols available on standard keyboards, no special input methods required
2. Hierarchical Progression: Point→Line→Surface→Volume→Subject-Object, symbols reflect this progression
3. Composability: Lower-level symbols can be combined into higher-level symbols
4. Operability: Each symbol corresponds to clear analytical steps
5. Clear Boundaries: Explicit about what can and cannot be expressed
6. Simplicity: Avoid symbol overload, maintain intuitiveness
7. Handwriting Friendly: Simple lines, quick to write

Part 2: Basic Symbol Table

1. Point Structure Symbols

Symbol Rules:

• Point symbols must be bound to intention: *[intention] or *@intention
• Example: *@refund = manifestation point under “refund” intention
• Example: *dog@refund = in refund intention, the dog object manifested

2. Line Structure Symbols

Symbol Rules:

• Line symbol format: Object=(value)[dimension]
• Value range: between -1.0 and +1.0
• Example: merchant=(-0.8)[integrity] = merchant scores -0.8 on integrity dimension
• Shorthand: merchant=(-)[integrity] or merchant=-0.8[integrity]

3. Surface Structure Symbols

Symbol Rules:

• Surface symbol format: Object[x, y](dimension1 x dimension2)
• Example: project[+0.7, -0.5](profit x risk) = high profit, high risk project
• Shorthand: project[+ -](profit x risk) or project[+-]

4. Volume Structure Symbols (Eight States)

Symbol Rules:

• Standard volume symbol format: Object(A, Q, T)[dimension description]
• General format: Object(x, y, z)[dimension1, dimension2, dimension3]
• Example: employee(+, -, +)[Action, Quality, aTtitude] = enthusiastic but incapable state
• Shorthand: employee(+-+) or employee(+ - +) (spacing recommended)

Important Note:

A/Q/T (Action-Quality-aTtitude) is commonly used but not the only three-dimensional choice:

• Evaluating subjects: typically use A/Q/T
• Evaluating projects: can use (profit, risk, duration)
• Evaluating cities: can use (economy, environment, culture)
• Dimensions must: be mutually independent, under same intention, impact decision-making

5. Subject-Object Structure Symbols

Symbol Rules:

• Complete subject-object symbol format: Subject(A+, Q+, T+) <> Object(A-, Q+, T-)
• Shorthand format: Subject(+ + +) <> Object(- + -) or Subject(+++) vs Object(-+-)
• Example: me(+ + +) <> merchant(- + -) or me(+++) vs merchant(-+-)

Important Clarification:

• <> exclusively for subject-object structure, not for other purposes
• Intention marking uses @intention or explicit context

6. Intention Space Symbols (New)

Three-Dimensional Definitions:

• T (Time): Temporal orientation
  • +1: Short-term orientation (pursuing quick results)
  • -1: Long-term orientation (pursuing lasting impact)
  • 0: Medium-term balance
• B (Benefit): Benefit orientation
  • +1: Self-interested orientation (prioritizing own interests)
  • -1: Altruistic orientation (prioritizing others’ welfare)
  • 0: Mutual benefit balance
• R (Risk): Risk orientation
  • +1: Aggressive orientation (willing to take risks)
  • -1: Conservative orientation (risk-averse)
  • 0: Moderate risk

Symbol Rules:

• Complete format: I(+1, +1, -1) = short-term, self-interested, conservative
• Shorthand: I(+ + -)
• Usage: @refund intention I(+1,+1,-1) or employee(++-) @project delivery I(+++)

Examples:

Fake dog refund: I(+1, +1, -1)  # Quick money, conservative
Art project: I(-1, 0, +1)       # Long-term quality, risk-taking
Intention distance: d = 3.0 (not transferable)

7. Trend Symbols

Symbol Rules:

• Trends must be anchored to intention
• Overall notation: employee(+ + -)v = overall decline
• Dimension-specific notation: employee(A+^, Q+v, T+->) = action rising, quality declining, attitude stable
• Time frame determined by intention

8. Structural Leap Symbols

Symbol Rules:

• Leap format: Structure1 |trigger| => Structure2
• Example: merchant(- + -) |manager's phone call| => merchant(+ + +)
• Trigger can be shortened to: |event| or directly write event name

9. Time Window Symbols

Symbol Rules:

• Time window: [T0-T1]: structure description

• Moment marker: @T3: event

• Example:

  [T0-T3]: me(+++)-> <> merchant(-+-)-> @T3: |manager's slip| => [T4-T5]: merchant(+++)-> 

10. Origin Weight Symbols (New)

Symbol Rules:

• Weight range: 0 to 1.0
• Structure weight: Structure(+ + -)[w=0.8] = 80% confident in this state
• Origin weight: Origin merchant[w=0.3] = 30% trust in merchant as reference system
• Probability representation: employee(+ - +)~0.7 = 70% confidence this is the state

Examples:

My narrative: Method A works[w=0.9]
Friend's verification: Method A works[w=0.6]
Their friend's verification: Method A doesn't work[w=-0.5]

Weight affects credibility and propagation

11. Perspective and Grouping Symbols (New)

Symbol Rules:

Perspective Annotation:

[Observer's perspective]:
  Company A(+ + +) vs Company B(- + -)

Upper-Lower Grouping:

[Upper: Company A(+ + +)]
[Lower: Company B(- + -)]
Judgment: Imbalanced structure, upper advantage

Three-Layer Compression:

Event{
  Base layer: [++ ]  # Sufficient resources
  Interaction layer: [+- ]  # Insufficient coordination
  Goal layer: [- -]  # Unclear goals
}
Judgment: Good foundation but poor execution, not optimistic

Parallel Representation:

employee(+ + +) @work // employee(- - -) @family
Same moment, different states under different intentions

12. Network Structure Symbols (New)

Symbol Rules:

Network Representation:

Network{
  Core(+ + +),
  Member1(- + +),
  Member2(+ - -)
}

Transmission Chain:

A(+ + +) -> B(- + -) -> C(- - +)
Influence path: A's strength drives B, B affects C

Leverage Point Identification:

Change B → Maximum transmission effect
Because B connects multiple nodes

13. Vectorization Representation (New)

Symbol Rules:

Dot Product Calculation:

I = (+1, +1, -1)  # Intention vector
S = (-1, +1, -1)  # State vector
I·S = -1+1+1 = 1  # Alignment degree

Distance Calculation:

Current state: S_now
Historical cases: S1, S2, S3
d1 = |S_now - S1| = 0.3  ← Nearest case
d2 = |S_now - S2| = 0.8
d3 = |S_now - S3| = 1.2
→ Apply S1's strategy

Intention Fusion:

Personal intention: I_p = (+1, +1, -1)
Organizational intention: I_o = (-1, +1, +1)
Actual decision: I = 0.3·I_p + 0.7·I_o
              = (-0.4, 1.0, 0.4)

14. Auxiliary Symbols

Symbol Rules:

• Comment: # This is a comment

• Probability: employee(+ + -)~0.7 = 70% confidence this is the state

• Grouping:

  [T0-T3]: {me(+++)-> <> merchant(-+-)->  Stable situation}

• Options: Strategy A | Strategy B = A or B

• Compound: Condition1 & Condition2 = Both satisfied

Part 3: Well-Formed Formulas

What Are Legal Symbol Combinations

Rule 1: Point structures must have intention

• ✅ Legal: *@refund or *dog@refund
• ❌ Illegal: * or *dog (missing intention)

Rule 2: Line structures must have dimension and value

• ✅ Legal: merchant=(-0.8)[integrity] or merchant=(-)[integrity]
• ❌ Illegal: merchant= or merchant=(-0.8) (missing dimension)

Rule 3: Surface structures must have two dimensions

• ✅ Legal: project[+0.7, -0.5](profit x risk)
• ✅ Legal shorthand: project[+ -](profit x risk) or project[+-]
• ❌ Illegal: project[+0.7](profit) (only one dimension)

Rule 4: Volume structures must have three dimensions

• ✅ Legal: employee(+, -, +)[A,Q,T] or employee(+ - +) or employee(+-+)
• ✅ Custom: project(+, -, +)[profit, risk, duration]
• ❌ Illegal: employee(+ -)[A,Q] (only two dimensions)

Rule 5: Subject-object structures must have shared intention

• ✅ Legal: Subject(+ + +) <> Object(- + -) @refund
• ✅ Shorthand: Subject(+++) vs Object(-+-) (intention in context)
• ❌ Illegal: Subject(+ + +) <> Object(- + -) (intention unclear and no context)

Rule 6: Leaps must annotate trigger

• ✅ Legal: Structure1 |trigger| => Structure2
• ❌ Illegal: Structure1 => Structure2 (missing trigger, unless context is clear)
• ⚠️ Acceptable: If context is clear, can be omitted

Rule 7: Time windows must have boundaries

• ✅ Legal: [T0-T3]: structure description
• ❌ Illegal: [T0-?]: structure description (ending boundary unclear)
• ⚠️ Special: Currently ongoing can write [T5-now]:

Rule 8: Trends must be anchored to intention

• ✅ Legal: employee(+ + -)v @project delivery
• ✅ Shorthand: employee(+ + -)v (intention clear in context)
• ❌ Illegal: employeev (missing structure)

Rule 9: Intention vectors must have three dimensions

• ✅ Legal: I(+1, +1, -1) or I(+ + -)
• ❌ Illegal: I(+ +) (missing R dimension)

Rule 10: Weights must be in reasonable range

• ✅ Legal: Structure[w=0.8] or Structure~0.7
• ❌ Illegal: Structure[w=1.5] (weight exceeds 1.0)

Part 4: Inference Rules

Rule 1: Compression Rule (From Point to Line)

Premise: *1@intention, *2@intention, ..., *n@intention
         (Multiple manifestation points under same intention)
         
Operation: Extract common dimension D
          
Conclusion: Object=(value)[D]
           (Form line structure)

Example:

Premise: *1@judge merchant = fake goods
        *2@judge merchant = no qualification
        *3@judge merchant = poor attitude
        
Operation: Extract dimension "integrity"
          
Conclusion: merchant=(-0.9)[integrity]

Rule 2: Combination Rule (From Line to Surface)

Premise: Object=(x)[dimension1]
        Object=(y)[dimension2]
        (Two line structures of same object)
        
Condition: dimension1 ≠ dimension2
          Unified intention
          
Conclusion: Object[x, y](dimension1 x dimension2)

Example:

Premise: project=(+0.8)[profit]
        project=(-0.6)[risk]
        
Conclusion: project[+0.8, -0.6](profit x risk)
          -> In quadrant [+ -] (high profit, high risk)

Rule 3: Extension Rule (From Surface to Volume)

Premise: Object[x, y](dimension1 x dimension2)
        Object=(z)[dimension3]
        
Condition: dimension3 ∉ {dimension1, dimension2}
          Unified intention
          
Conclusion: Object(x, y, z)(dimension1, dimension2, dimension3)

Example:

Premise: employee[+0.7, +0.8](action x quality)
        employee=(-0.5)[attitude]
        
Conclusion: employee(+0.7, +0.8, -0.5)[A, Q, T]
          -> (+ + -) Capable but Resistant state

Rule 4: Structural Leap Rule

Premise: Structure1 @T1
        Trigger event E @T2 (T2 > T1)
        
Condition: Tension accumulation >= threshold
          OR External forced intervention
          
Conclusion: Structure1 |E| => Structure2 @T2

Forbidden Leaps:

• ❌ Leap without trigger: Structure1 => Structure2 (when no context)
• ❌ Reverse-time leap: @T2 => @T1 (T2 > T1)
• ❌ Cross-intention leap: Structures under different intentions cannot leap directly

Allowed Leap Types:

Type 1: Dimensional Leap (under same intention)

merchant(- + -) |manager's phone call| => merchant(+ + +)
# Both action and attitude flip, but still under "refund" intention

Type 2: Origin Leap (intention switch)

employee(+ + +) @work |family crisis| => employee(- - -) @survival
# Intention switch causes entire evaluation system to change

Type 3: Subject-Object Leap (relationship reorganization)

me(+ + +) <> merchant(- + -)
|mayor hotline threat|
=>
me(+ + +) <> merchant(+ + +)
# Object party completely flips

Rule 5: Window Rule

Premise: Structure S stable @[T0, Tn]
        
Condition: No leap occurs
          
Conclusion: Window W = [T0-Tn]
          delta = Tn - T0 (window length)

Window Boundary Determination:

• Window start = after last leap
• Window end = before next leap
• Window interior: Structure stable, may fluctuate slightly but no leap

Rule 6: Trend Accumulation Rule

Premise: Structure(A, Q, T)^  # Upward trend
        Duration delta
        
Condition: delta >= critical time
          OR Trigger event appears
          
Conclusion: Structure1 |accumulation complete| => Structure2
          # Trend transforms into leap

Example:

[T0-T5]: employee(+ - +)^  # Quality improvement trend
@T6: |training cycle complete| => employee(+ + +)
# Trend accumulates to threshold, leap occurs

Rule 7: Trend Reversal Rule

Premise: Structurev  # Downward trend
        
Condition: Effective intervention I
          
Conclusion: Structurev |intervention I| -> Structure^
          # Trend reverses but no leap yet

Example:

[T0-T3]: team(+ + +)v @project deadline
@T3: |additional resources| -> team(+ + +)^
# Resources stabilize trend, leap avoided

Rule 8: Intent Matching Rule

Premise: Intent I1 = (t1, b1, r1)
         Intent I2 = (t2, b2, r2)
     
Operation: Calculate distance
           d = √[(t1-t2)² + (b1-b2)² + (r1-r2)²]
     
Conclusion:
           d < 0.5  → Highly similar, transferable
           0.5 ≤ d < 1.0 → Partially similar, requires caution
           d ≥ 1.0  → Large difference, not transferable

Example:

Return intent: I1 = (+1, +1, -1)
Art project: I2 = (-1, 0, +1)
d = √[4+1+4] = 3.0
Conclusion: Not transferable

Rule 9: Weight Evolution Rule

Premise: Initial weight w0 of experience E
     
Operation: Each validation
           - Successful validation: w = w + α(1-w)
           - Failed validation: w = w - β(w+1)
     
Where: α is reinforcement coefficient (typically 0.1-0.3)
       β is decay coefficient (typically 0.2-0.5)

Example:

Initial: Method A effective [w=0.5]
After 1st success: w = 0.5 + 0.2(0.5) = 0.6
After 2nd success: w = 0.6 + 0.2(0.4) = 0.68
After 1st failure: w = 0.68 - 0.3(1.68) = 0.176
Weight affects invocation probability

Rule 10: Network Propagation Rule

Premise: Node A influences Node B
         Node B influences Node C
     
Condition: Structural leap in A
     
Conclusion: Propagation path A -> B -> C
            Propagation strength = wAB × wBC
     
Where: wAB is influence weight from A to B
       wBC is influence weight from B to C

Example:

Core(+ + +) -> Member1(- + +) -> Member2(- - +)
         w=0.8            w=0.6
Core leaps to (- - -):
→ Member1 influence probability = 0.8
→ Member2 influence probability = 0.8 × 0.6 = 0.48

Part 5: Operation Manual

Basic Operations

Operation 1: Manifestation Anchoring

When to Use: When attention focuses on an object

Steps:

1. Identify current intention
2. Mark manifested object: *object@intention
3. Assess initial polarity if needed: *+, *-, or *0

Example:

Intention: Evaluate merchant credibility
Operation: *merchant@judge merchant
         *product quality@judge merchant
         *service attitude@judge merchant

Operation 2: Dimensional Extraction

When to Use: When multiple manifestation points share common features

Steps:

1. Collect manifestation points
2. Identify common dimension
3. Form line structure: Object=(value)[dimension]

Example:

Input: *fake goods, *no qualification, *poor attitude
Extract dimension: integrity
Output: merchant=(-0.9)[integrity]

Operation 3: Multi-Dimensional Combination

When to Use: When object needs evaluation across multiple independent dimensions

Steps:

1. Ensure dimensions are independent
2. Ensure under unified intention
3. Form surface structure (2D) or volume structure (3D)

Example (2D):

profit=(+0.8)
risk=(-0.6)
→ project[+0.8, -0.6](profit x risk)

Example (3D):

action=(+0.7)
quality=(+0.8)
attitude=(-0.5)
→ employee(+0.7, +0.8, -0.5)[A,Q,T]

Operation 4: Trend Prediction

When to Use: When predicting future development

Steps:

1. Observe current structure
2. Identify changing dimensions
3. Mark trend direction: ^ v ->
4. Anchor time frame

Example:

Current: employee(+ + -)
Observation: Attitude declining, other stable
Prediction: employee(A+, Q+, T-)v @next quarter

Operation 5: Structural Leap Identification

When to Use: When discontinuous change occurs or is about to occur

Steps:

1. Identify pre-leap structure
2. Identify trigger factor
3. Identify post-leap structure
4. Mark: Structure1 |trigger| => Structure2

Example:

Before: merchant(- + -) @refund
Trigger: |manager's phone call|
After: merchant(+ + +) @refund
Notation: merchant(- + -) |manager's phone call| => merchant(+ + +)

Operation 6: Time Window Division

When to Use: When analyzing events over time

Steps:

1. Identify stable periods
2. Mark time boundaries
3. Annotate structural state for each window

Example:

[T0-T3]: employee(+ + +)-> Stable state
@T3: |public criticism| Trigger event
[T4-T6]: employee(- - -)-> New stable state

Operation 7: Subject-Object Analysis

When to Use: When analyzing bilateral interaction or game

Steps:

1. Identify subject (me) and object (other party)
2. Analyze both parties’ three-dimensional states
3. Form subject-object structure
4. Identify relationship type (cooperation/opposition)

Example:

Subject (me): (+ + +) Strong capability, positive
Object (merchant): (- + -) Capable but passive
Structure: me(+ + +) <> merchant(- + -)
Relationship: Advantageous but unstable

Advanced Operations

Advanced Operation 1: Intention Vector Analysis

When to Use: When comparing different intentions or judging experience transferability

Steps:

1. Decompose intention into T-B-R three dimensions
2. Calculate intention vector: I(t, b, r)
3. Calculate intention distance (if comparing)
4. Judge transferability

Example:

Intention 1: Quick refund I(+1, +1, -1)
Intention 2: Long-term relationship I(-1, 0, +1)
Distance: d = √[(2)²+(1)²+(2)²] = 3.0
Judgment: Cannot transfer (d >= 1.0)

Advanced Operation 2: Origin Weight Annotation

When to Use: When recording experience or evaluating reference system

Steps:

1. Assess experience verification frequency
2. Annotate weight: [w=value]
3. Update weight with new evidence
4. Use weight to guide decision

Example:

Personal experience: Strategy A works [w=0.9]
Friend says: Strategy A works [w=0.6]
Stranger says: Strategy A doesn't work [w=0.2]
→ Comprehensive judgment leans toward "works"

Advanced Operation 3: Network Structure Analysis

When to Use: When analyzing multi-agent complex systems

Steps:

1. Identify all nodes (agents)
2. Mark each node’s state
3. Identify transmission relationships
4. Find leverage points

Example:

Network{
  A(+ + +) -> B(- + -) -> C(- - +)
  A(+ + +) -> D(+ - +)
}

Analysis: A is core node, changing A has maximum impact
       B is bottleneck, changing B has better efficiency

Advanced Operation 4: Vectorization Calculation

When to Use: When precisely measuring tension, matching, or completion degree

Steps:

1. Express intention and state as vectors
2. Select appropriate operation (dot product/distance/projection)
3. Calculate numerical result
4. Interpret result meaning

Dot Product (Measure tension):

I = (+1, +1, -1)
S = (-1, +1, -1)
I·S = -1+1+1 = 1
Interpretation: Moderate tension, controllable pressure to change

Distance (Experience matching):

Current: S_now
Historical case: S1, distance d1 = 0.3
             S2, distance d2 = 1.2
Choose: Apply S1's strategy (closer)

Operation Flowchart

Start
  ↓
Identify Intention → Clear intention
  ↓
Observe Manifestation → Mark *objects
  ↓
Extract Dimensions → Form = line
  ↓
Combine Dimensions → Form [] surface or () volume
  ↓
Predict Trend? → Yes → Mark ^ v ->
  ↓ No
Leap Occurred? → Yes → Mark |trigger| =>
  ↓ No
Multiple Parties? → Yes → Form <> subject-object
  ↓ No
Need Time Division? → Yes → Mark [T0-T1]
  ↓ No
Annotate Weight? → Yes → Mark [w=value]
  ↓ No
End → Record experience, update case library

Part 6: Symbol Hierarchy

Hierarchy Structure

The symbol system has clear hierarchy and dependency:

Level 0: Meta-symbols
  @intention    - Intention anchor
  I(t,b,r)     - Intention vector
  
Level 1: Point structure
  *  o  *+  *-  *0
  ↓ (Compression)
  
Level 2: Line structure
  =  =(+)  =(-)  =(+-)
  ↓ (Combination)
  
Level 3: Surface structure
  []  [++]  [+-]  [-+]  [--]
  ↓ (Extension)
  
Level 4: Volume structure
  ()  (+ + +)  (+ + -)  ... (- - -)
  ↓ (Relationship expansion)
  
Level 5: Subject-Object structure
  <>  Subject() <> Object()
  
Orthogonal dimensions:
  Time: [T0-T1]  @T3
  Trend: ^  v  ->
  Leap: =>  |trigger|
  Weight: [w=value]  ~value
  Network: {}  ->  <->
  Vectorization: ·  |·|  Proj

Symbol Composition Rules

Bottom-Up Construction:

1. Start with intention @ or I()
2. Anchoring manifestation *
3. Extract dimensions =
4. Combine to surface []
5. Extend to volume ()
6. Expand to subject-object <>

Top-Down Analysis:

1. Observe subject-object interaction <>
2. Decompose to volume state ()
3. Analyze dimensional composition []
4. Examine line judgments =
5. Trace back to manifestation points *
6. Verify intention @

Part 7: Extension Mechanisms

How to Define New Symbols

Principles:

1. Must serve clear cognitive needs
2. Must be keyboard-input friendly
3. Must maintain consistency with existing system
4. Must have clear operational definition

Process:

Step 1: Identify Need

Question: What scenario requires new symbol?
Answer: [Specific scenario description]

Step 2: Design Symbol

Symbol shape: [Keyboard input method]
Symbol meaning: [Precise definition]
Usage scenario: [When to use]

Step 3: Define Rules

Format specification: [Symbol combination rules]
Usage constraints: [What conditions must be met]
Relation to existing symbols: [How it connects]

Step 4: Test Verification

Annotate several real cases
Check: Clarity? Consistency? Necessity?

Domain-Specific Extensions

The basic symbol system is domain-general, but different domains can define specialized symbols:

Finance Domain Example:

Extended symbols:
  $+ : Bullish market
  $- : Bearish market
  $~ : Volatile market
  
Usage:
  Stock(+, +, -) @investment [$+]
  = Invest in good fundamentals stock in bull market

Education Domain Example:

Extended symbols:
  L1, L2, L3... : Learning stages
  G(level) : Goal level
  
Usage:
  Student(+, -, +) [L1] G(L3)
  = Enthusiastic beginner aiming for advanced level

Management Domain Example:

Extended symbols:
  P1, P2, P3 : Priority levels
  D(days) : Deadline
  
Usage:
  Task(+, +, -) [P1] D(3)
  = High priority task with poor attitude, 3 days deadline

Extending Inference Rules

Besides base rules, domain-specific inference rules can be added:

Example: Team Formation Rule

IF Team has members in (+ + +), (+ - +), (- + +) three states
THEN Team has complete capability configuration
   (+ + +): Executor
   (+ - +): Motivator
   (- + +): Reserve

IF All members in (+ + -) or (+ - -)
THEN Team has attitude risk, needs intervention

Part 8: Quick Reference

Comprehensive Symbol Table

Eight States Quick Reference

T-B-R Intention Space Quick Reference

Common Combinations:

• I(+1,+1,-1): Short-term, self-interested, conservative (fake dog refund)
• I(-1,0,+1): Long-term, mutual benefit, risk-taking (art project)
• I(0,0,0): Neutral balance (daily decisions)

Keyboard Input Quick Reference

Standard keyboard symbols:
* = shift + 8
= = direct input
() = shift + 9/0
[] = direct input
^ = shift + 6
v = direct input
< > = shift + ,/.
| = shift + \
@ = shift + 2
~ = shift + `
# = shift + 3
{} = shift + [/]
/ = direct input

Combined symbols:
=> = equals + greater
-> = minus + greater
<-> = less + minus + greater
<> = less + greater
// = slash + slash

Part 9: Common Questions

Q1: How to distinguish trend from structural leap?

Trend: Predictive, gradual, may happen

• Symbols: ^ v ->
• Example: employee(+ + -)v = attitude deteriorating (prediction)

Structural Leap: Discontinuous, abrupt, happening/happened

• Symbol: =>
• Example: employee(+ + -) |public criticism| => employee(- - -) = already leaped

Key: Trends continue within time window; leaps mark window boundaries.

Q2: What time range corresponds to trends?

Depends on intention’s time frame:

• Project delivery (looking at “weeks”): employee(+ + -)v @this quarter
• Strategic development (looking at “years”): company(+ + +)^ @next 3 years
• Daily management (looking at “days”): morale(+ + -)v @this week

No fixed standard; analyst determines based on intention.

Q3: Can the symbol system handle multiple intentions?

Yes, but requires clear annotation.

Method 1: Temporal Separation

[T0-T2] @work: employee(+ + +)->
[T2-T4] @family: employee(- - -)v

Method 2: Parallel Annotation

employee(+ + +) @work // employee(- - -) @family
# Same moment, different states under different intentions

Core principle: Intentions must be explicit to avoid confusion.

Q4: Must volume structure be A/Q/T?

No. A/Q/T is just the standard template.

Can customize three dimensions:

project(profit+, risk-, duration+)
candidate(expertise+, communication-, stability+)
city(economy+, environment-, culture+)

Principles:

• Three dimensions must be mutually independent
• Must be meaningful under same intention
• Must impact decision-making

Recommendation: Most interpersonal/organizational scenarios use A/Q/T; other scenarios customize.

Q5: Does the symbol system have a learning curve?

Yes, but not steep.

Beginner Path:

• Hour 1: Learn volume structure (+ + +) and basic trends ^ v ->
• Hour 2: Learn structural leaps => and triggers |event|
• Hour 3: Learn subject-object structure Subject() <> Object()
• Hour 4: Learn time windows [T0-T3]
• Hour 5: Comprehensive application, analyze real cases

3 hours to get started, 10 hours to become proficient, 30 hours to master.

Q6: Can the symbol system be used for team communication?

Yes, and it’s very suitable.

Advantages:

• Unified language, reduces ambiguity
• Structured discussion, improves efficiency
• Visual presentation, easy to understand
• Can be documented, facilitates review

Recommendations:

• Train team on basic symbols first (2-3 hours)
• Use on whiteboard/Miro tools
• Organize into formal documents after meetings
• Build team case library

Q7: Won’t the symbol system oversimplify?

Yes, but it’s necessary.

Why simplify:

1. Human brain has limited processing capacity
2. Decisions need to be completed in limited time
3. Complexity leads to analysis paralysis

How to balance:

1. Core with symbols: Key structures, major leaps
2. Details with text: Supplementary explanations, background information
3. Combined use: Symbols sketch skeleton, text fills in flesh

Q8: How to calculate intention vector?

Step 1: Decompose intention

Intention: Quickly complete project, gain profit, control risk
→ T = +1 (quick = short-term)
→ B = +1 (gain profit = self-interested)
→ R = -1 (control risk = conservative)
Result: I(+1, +1, -1)

Step 2: Calculate distance

Intention1: I1 = (+1, +1, -1)
Intention2: I2 = (-1, 0, +1)
d = √[(1-(-1))² + (1-0)² + (-1-1)²]
  = √[4 + 1 + 4] = 3.0

Step 3: Judge transferability

d < 0.5: Highly similar, transferable
0.5 ≤ d < 1.0: Partially similar, use with caution
d ≥ 1.0: Large difference, not transferable

Q9: What exactly is the <> symbol for?

Clear Definition: <> exclusively for subject-object structure

Correct Usage:

Subject(+ + +) <> Object(- + -)
me(+++) <> merchant(-+-)

Incorrect Usage:

<refund>  # This is intention, should use @refund
<intention>  # Same as above

Correct Ways to Mark Intention:

@refund
@intention name
I(+1,+1,-1)

Q10: What’s the difference between weight and probability?

Weight [w=value]:

• Represents experience credibility
• Comes from verification frequency
• Evolves over time
• Example: Strategy A works[w=0.8] = this experience verified many times

Probability ~value:

• Represents judgment uncertainty
• Comes from current information insufficiency
• One-time assessment
• Example: employee(++-)~0.7 = 70% confidence this is the state

Usage Scenarios:

• Weight: For experience library, case library, structural lexicon
• Probability: For current judgment, real-time analysis, temporary assessment

Part 10: Usage Guide

Entry Path (5-Week Plan)

Week 1: Basic Symbols

Goal: Familiarize with point, line, volume structures
Practice:
- Annotate 3 daily judgments each day
- Analyze 3 people using volume structure
- Record: Person(+ - +) type

Week 2: Trend Judgment

Goal: Master trend symbols
Practice:
- Observe trends in people/events around you
- Record: Object(++)v or ^
- Predict: Will it leap?

Week 3: Structural Leap Analysis

Goal: Understand leap mechanism
Practice:
- Recall a real leap event
- Annotate: Structure1 |trigger| => Structure2
- Analyze: Why did it leap?

Week 4: Subject-Object Game

Goal: Analyze interactive relationships
Practice:
- Analyze a real game situation
- Annotate: Subject() <> Object()
- Review: Where were key leap points?

Week 5: Complete Cases

Goal: Comprehensive application
Practice:
- Fully analyze a complex event
- Include: Time windows, trends, leaps
- Extract: Experience and strategies

Common Errors and Corrections

Error 1: Overly complex symbols

❌ Wrong: *[intention1]∩*[intention2]∪o[background]&employee(+,-,+)~0.7^...
✅ Right: First determine single intention, simplify analysis
        employee(+ - +)^ @core intention

Error 2: Missing time annotation

❌ Wrong: employee(+ - +) => employee(+ + +)
        (When did it leap?)
✅ Right: @T3: employee(+ - +) |training complete| => employee(+ + +)

Error 3: Confusing trend and leap

❌ Wrong: employee(+ + -)=> or employeev =>
✅ Right: [T0-T3]: employee(+ + -)v  # Trend
        @T3: |trigger| => employee(- - -)  # Leap

Error 4: Mixing different intentions

❌ Wrong: Using @family dimensions under @work intention
✅ Right: Keep intentions unified or explicitly switch
        [T0-T2] @work: ...
        [T2-T4] @family: ...

Error 5: Symbol stacking without logic

❌ Wrong: employee(+ - +) merchant(- + -) project[+ -] ...
        (What's the relationship between these?)
✅ Right: Explain relationships between structures
        employee(+ - +) responsible for project[+ -]
        OR
        me(+ + +) <> merchant(- + -) @transaction

Error 6: Unclear intention

❌ Wrong: Object(+ + +)
        (+++under what intention?)
✅ Right: Object(+ + +) @project delivery
        OR explain intention in context

Error 7: Misuse of <> symbol

❌ Wrong: <refund> or <intention>
✅ Right: @refund or I(+1,+1,-1)
        <> exclusively for subject-object structure

Best Practices

Practice 1: Build personal case library

Structure:
- Time: YYYY-MM-DD
- Event: [Event name]
- Intention: @core intention or I(t,b,r)
- Symbol notation: [Complete annotation]
- Weight: [w=0.8]
- Experience summary: [What learned]
- Next application: [How to improve]

Practice 2: Regular review

Frequency: Weekly or monthly
Content:
- Review symbol notations
- Identify patterns (events with same structure)
- Extract experience (structural lexicon)
- Update weights
- Update strategies

Practice 3: Team sharing

Build: Team case library
Format: Unified symbol notation
Purpose:
- Experience sharing
- Avoid repeating mistakes
- Improve team decision-making capability
- Build organizational memory

Practice 4: Tool assistance

Recommended tools:
- Note-taking software (Notion/Obsidian)
- Mind mapping (Xmind/MindNode)
- Whiteboard tools (Miro/FigJam)
- Text editors (VS Code + Markdown)

Practice 5: Intention distance calculation

Before cross-scenario application:
1. Clarify original scenario intention: I1
2. Clarify new scenario intention: I2
3. Calculate distance: d = |I1 - I2|
4. Judge transferability: d < 0.5 usable, d > 1.0 not usable
5. Record results, update experience weight

Part 11: Advanced Applications

Vectorization Analysis

Dot Product Calculation: Measure Tension

Intention: I = (+1, +1, -1)
State: S = (-1, +1, -1)
Dot product: I·S = -1+1+1 = 1

Interpretation: Moderate tension, system has pressure to change but controllable

Distance Calculation: Experience Matching

Current: S_now = (+0.5, -0.3, +0.7)
Case 1: S1 = (+0.6, -0.2, +0.8), d1 = 0.17
Case 2: S2 = (-0.3, +0.4, -0.5), d2 = 1.32

Choice: Apply case 1's strategy (closest distance)

Vector Addition: Intention Fusion

Personal: I_p = (+1, +1, -1)
Organizational: I_o = (-1, +1, +1)
Actual: I = 0.3·I_p + 0.7·I_o = (-0.4, 1.0, 0.4)

Interpretation: Actual decision leans toward organizational intention

Projection Calculation: Completion Degree

Goal: I = (+1, +1, -1)
Current: S = (+0.5, +0.8, -0.5)
Projection: Proj_I(S) = 0.6

Interpretation: 60% completion, continue current strategy

Network Analysis

Transmission Chain Identification

Network{
  A(+ + +) -> B(- + -) -> C(- - +)
       w=0.8         w=0.6
}

A leaps to (- - -):
→ B affected probability = 0.8
→ C affected probability = 0.48

Leverage Point Identification

Key node judgment:
- Most connections
- Highest transmission weight
- Most central position

Change key node → Maximum system impact

Transferability Analysis

Nine-Layer Judgment Framework

Layer -3: Completely non-transferable (framework conflict)
Layer -2: High-risk transfer (normative issues)
Layer -1: Major adjustment needed (large structural differences)
Layer 0:  Can attempt (needs verification)
Layer +1: Basically transferable (minor adjustment)
Layer +2: Relatively easy transfer (direct application)
Layer +3: Highly transferable (pattern level)
Layer +4: Very easy transfer (principle level)
Layer +5: Extremely easy transfer (meta-principle)

Judgment basis:
1. Intention distance: d_I < 0.5
2. Framework consistency
3. Normative boundaries
4. Structural isomorphism

Summary

Essence of the Symbol System

This symbol system is a notation language for cognitive maps:

1. * Point symbols: Mark attention focus
2. = Line symbols: Mark value judgments
3. [] Surface symbols: Mark two-dimensional combinations
4. () Volume symbols: Mark three-dimensional states
5. <> Subject-object symbols: Mark relational structures
6. ^ v -> Trend symbols: Mark dynamic predictions
7. => Leap symbols: Mark discontinuous changes
8. [T-T] Time symbols: Mark stable periods
9. I(t,b,r) Intention vectors: Mark decision frameworks
10. [w=] Weight symbols: Mark credibility levels

Core Value

For Individuals:

• Clear thinking tool
• Decision analysis framework
• Cognitive training method
• Experience documentation carrier
• Transferability judgment tool

For Teams:

• Unified communication language
• Structured discussion tool
• Case encoding standard
• Collective wisdom accumulation
• Organizational memory system

For Research:

• Pattern recognition foundation
• Theory verification tool
• Cross-case comparison method
• Experience pattern extraction
• Cognitive science application

Usage Principles

1. Simplicity First: Express clearest thoughts with simplest symbols
2. Clear Intention: All analysis must anchor intention (@intention or I(t,b,r))
3. Time Annotation: Important events must have time windows
4. Weight Recording: Experience must annotate credibility
5. Distance Calculation: Calculate intention distance before cross-scenario application
6. Continuous Refinement: Symbol system constantly improves in use
7. Tool Not Goal: Symbols are for seeing structure clearly, not showing off
8. Boundary Awareness: Know what can and cannot be used

Final Words

The value of the symbol system is to:

1. Help you see structures clearly
2. Help you record processes
3. Help you communicate thinking
4. Help you accumulate experience
5. Help you judge transferability
6. Help you understand cognitive essence

Remember:

• Symbols are tools, not goals
• Simplicity is more powerful than complexity
• Practicality is more important than perfection
• Action is more critical than symbols
• Use theory in instrumental situations
• Let go of theory in value situations

Version Information: v5.0 | Last Updated: 2025

Major Updates:

• Added intention space symbols (T-B-R)
• Added origin weight symbols
• Added perspective and grouping symbols
• Added network structure symbols
• Added vectorization representation methods
• Clarified <> symbol exclusivity
• Added transferability judgment tools
• Enhanced matching with project chapters

Feedback and Improvement: This symbol system continuously improves in use, welcome improvement suggestions.