Knowledge Representation Methods (W3L1)

🎯 考试重要度

🟡 中频 | Week 3 Lecture 1 (44 slides) | 为后续 KG Embeddings (Sample Test Q3)、MYCIN (W4L1) 的理论基础

Why study this? This lecture defines ALL five KR methods tested in this course: Symbolic Logic, Semantic Networks, Frames, Rule-Based Systems, and Knowledge Graphs. Comparison questions across these methods are a natural exam question type. Understanding each method’s strengths and weaknesses is essential for design-type questions. The exercises from this lecture test inference reasoning – a skill required across Q1 (logic), Q3 (KG embeddings), and Q5 (MYCIN).

📖 核心概念（Core Concepts）

🧠 费曼草稿（Feynman Draft）

The Filing Cabinet Analogy

Imagine you just got hired to organize ALL the knowledge in a hospital – every disease, every symptom, every treatment, every patient record. You need the knowledge organized so that a robot doctor can not only look things up but also reason about new patients it has never seen before. The question is: what filing system do you use?

It turns out there is no single best system. Different filing systems are good at different things. This lecture covers five of them.

System 1: Symbolic Logic – The Mathematician’s Notebook

You write everything as precise mathematical statements:

• “For all x, if x has flu, then x has a fever”: $\forall x\ (\text{Flu}(x) \rightarrow \text{HasSymptom}(x, \text{Fever}))$
• “If a patient has fever AND cough, then likely diagnosis is flu”: $\forall x\ (\text{HasSymptom}(x, \text{Fever}) \wedge \text{HasSymptom}(x, \text{Cough}) \rightarrow \text{LikelyDiagnosis}(x, \text{Flu}))$

Strengths: absolutely precise, supports formal proof. Weakness: extremely rigid – try expressing “70% chance of flu” in pure logic!

System 2: Semantic Networks – The Mind Map

Think of a giant mind map on a whiteboard. Each sticky note is a concept (Cat, Mammal, Animal, Fur), and you draw labeled arrows between them:

Cat ──is-a──► Mammal ──is-a──► Animal
Cat ──has──► Fur
Mammal ──has-property──► Warm-blooded

Now here’s the magic: because Cat is-a Mammal, and Mammal has-property Warm-blooded, the system can infer that Cat is Warm-blooded – even though you never wrote that explicitly. This is called transitive inheritance.

Toy example: Given these three facts:

1. “Dog is-a Mammal”
2. “Mammal is-a Animal”
3. “Mammal has-property Warm-blooded”

The system infers: “Dog is-a Animal” (transitive IS-A) and “Dog has-property Warm-blooded” (property inheritance).

System 3: Frames – The Object-Oriented Database

Imagine describing a car using a form you fill out:

Each frame is like an object in programming – it has attributes (slots) and values (fillers). Frames can do four clever things:

1. Default values: If you create a new “Dog” frame and don’t specify legs, it defaults to 4 (inherited from “Mammal” frame)
2. Inheritance: A “Dog” frame inherits “Has Hair = True” from the “Mammal” frame
3. Slot constraints: A “Student” frame requires Age > 5
4. Procedural attachment: Accessing the “Check-in Time” slot of a “Hotel Reservation” frame automatically triggers sending a confirmation email

System 4: Rule-Based Systems – The Decision Flowchart

You encode every decision as an IF-THEN rule:

R1: IF Fever AND Cough                    THEN Possible Diagnosis = Flu
R2: IF Fever AND Joint Pain AND Travel     THEN Possible Diagnosis = Dengue Fever
R3: IF Cough AND Difficulty Breathing      THEN Possible Diagnosis = Pneumonia

Patient comes in with Fever + Cough + Joint Pain + Recent Travel? R1 fires (Flu) and R2 fires (Dengue Fever). The system considers both.

This is the simplest form – it’s transparent (you can trace exactly which rules fired) but brittle (you need a rule for every possible situation, and they don’t generalize).

System 5: Knowledge Graphs – The Fact Encyclopedia

You store millions of specific facts as triples:

(Albert Einstein, Born In, Germany)
(Albert Einstein, Discovered, Theory of Relativity)
(Theory of Relativity, Related To, Physics)

The power is in graph traversal for inference: if you ask “Did Einstein contribute to Physics?”, the system walks the graph: Einstein → Discovered → Theory of Relativity → Related To → Physics. Yes!

⚠️ Common Misconception: Students often think these five methods are “versions” of the same thing (1.0, 2.0, etc.). They are NOT. They are five different paradigms – each stores knowledge in a fundamentally different way and supports different kinds of reasoning. The slide explicitly states: “They are different KR paradigms, not different types of Knowledge Graphs.”

⚠️ Common Misconception: Semantic Networks and Knowledge Graphs look similar (both are graphs), but they differ in standardization and scale. Semantic Networks have no unified standard and are typically small/domain-specific (1960s–1980s research). Knowledge Graphs use standardized RDF triples and are designed for web-scale (billions of facts, 2000s–present).

💡 Core Intuition: KR is about choosing which “filing system” to organize knowledge – as logic, mind maps, forms, rules, or fact graphs – so machines can reason, not just store.

📐 正式定义（Formal Definition）

What is Knowledge Representation?

Definition (from slides): Knowledge Representation (KR) refers to the methods used in AI to store, retrieve, and handle knowledge to enable intelligent reasoning.

Why do we need KR?

• Bridges raw data and intelligent decision-making
• Allows AI to reason logically and infer new facts
• Enables knowledge-driven applications (expert systems, search engines, autonomous robots, chatbots)

Five Key Requirements of KR

Case Study from slides: Self-Driving Car

• Expressiveness → represents road conditions, traffic signals, vehicle movement
• Computational Efficiency → processes sensor data in real-time for immediate decisions
• Scalability → expands knowledge of new routes and driving patterns
• Interpretability → AI must explain why it brakes or changes lanes
• Modifiability → updates driving models based on new road conditions

Structured vs Unstructured Knowledge

Examples of Structured: Relational databases (SQL), Knowledge Graphs (Google KG), Ontologies (medical taxonomy)

Examples of Unstructured: News articles, research papers, videos, images, audio recordings, conversations, emails

Symbolic Logic in KR

Definition: Represents knowledge using formal symbols and logical expressions. Used for reasoning, inference, and formal verification.

Two types used in KR:

• Propositional Logic (PL) – simple true/false statements
• First-Order Logic (FOL) – allows relationships between entities with quantifiers

FOL Rules Example (Medical Diagnosis):

• $\forall x\ (\text{Flu}(x) \rightarrow \text{HasSymptom}(x, \text{Fever}))$ – “If a patient has the flu, they will have a fever”
• $\forall x\ (\text{HasSymptom}(x, \text{Fever}) \wedge \text{HasSymptom}(x, \text{Cough}) \rightarrow \text{LikelyDiagnosis}(x, \text{Flu}))$ – AI can infer from known symptoms to diagnose patients

Semantic Networks – Formal Structure

A graph-based KR where:

• Nodes (Entities/Concepts): represent objects, ideas, or concepts (e.g., “Cat”, “Mammal”, “Animal”)
• Edges (Relationships/Connections): define how entities are related (e.g., “is-a”, “has-part”, “related-to”)

Two key inference mechanisms:

1. Hierarchical Reasoning (IS-A Inference): Given “Cat → is-a → Mammal” and “Mammal → is-a → Animal”, AI infers “Cat is an Animal” via transitive inheritance

2. Property Inheritance: Given “Mammal → has-property → Warm-blooded” and “Dog → is-a → Mammal”, AI infers “Dog is warm-blooded” (inherits properties from parent)

Strengths of Semantic Networks:

1. Natural Representation – mimics human thought; relationships are intuitive and visually clear
2. Supports Logical Inference – AI can deduce new facts through IS-A and HAS-PROPERTY relationships
3. Efficient Knowledge Retrieval – graph structures allow fast lookups using connected nodes

Weaknesses of Semantic Networks:

1. Can Become Too Complex – large networks with millions of nodes can be hard to manage
2. No Standardized Representation – different AI models use different graph structures; integration is difficult
3. Poor Handling of Uncertainty – assumes relationships are deterministic (e.g., “Birds can fly” – but what about penguins?)

Frames – Formal Structure

A frame is a structured representation that groups related information about an entity into a slot-filler structure.

• A frame = concept/object
• A slot = attribute/property
• A filler = value for that slot

Frame-Based Reasoning (four mechanisms):

1. Default Values: If a slot is empty, AI uses default knowledge. Example: Frame Dog, Slot Has legs → Default value = 4. AI infers a newly introduced dog has 4 legs unless specified otherwise.

2. Inheritance (Frame Hierarchies): Frames inherit attributes from higher-level frames (similar to OOP). Example: Frame Mammal → Has Hair = True; Frame Dog (inherits from Mammal) → Has Hair = True.

3. Slot Constraints & Conditions: Some slots have restrictions on valid values. Example: Frame Student, Slot Age → Constraint: Must be > 5 years old.

4. Procedural Attachment: Some slots trigger actions when accessed. Example: Frame Hotel Reservation, Slot Check-in Time → Action: Send confirmation email.

Strengths of Frames:

1. Structured & Organized – groups related knowledge into slot-filler structures for efficient retrieval
2. Inheritance and Default Reasoning – infers missing values using defaults and hierarchical inheritance
3. Procedural Knowledge – slots can trigger actions (procedural attachments)
4. Easy to Update & Modify – slots and fillers can be modified dynamically

Weaknesses of Frames:

1. Rigid Structure & Limited Flexibility – struggle with ambiguous or novel cases (e.g., a “Vehicle” frame might not account for futuristic self-driving cars)
2. Poor Handling of Uncertainty – assume knowledge is complete; difficult to reason with probabilities
3. Hard to Scale for Large Knowledge Bases – grow complex as entities and slots increase
4. Limited Logical Reasoning – do not perform deep logical deductions (can store “All birds can fly” but don’t automatically reason exceptions like penguins)

Rule-Based Systems – Formal Structure

A Rule-Based System (RBS) represents knowledge as a set of IF-THEN rules that trigger actions when conditions are met.

Structure: IF (Condition) → THEN (Action/Conclusion). AI checks facts and applies the appropriate rule.

Strengths:

1. Transparent and Explainable – every decision is based on clear, human-readable IF-THEN rules
2. Easy to Implement for Well-Defined Problems – works effectively in structured domains with known rules
3. Works Without Large Training Data – does not require massive datasets (unlike ML)

Weaknesses:

1. Hard to Scale with Complex Knowledge – managing thousands of IF-THEN rules becomes difficult
2. Poor Adaptability to New Situations – cannot generalize beyond predefined rules
3. Requires Expert Knowledge to Define Rules – rules must be handcrafted by domain experts

Knowledge Graphs – Formal Structure

A KG is a graph-based representation that connects entities (nodes) with relationships (edges) and properties.

Components:

• Nodes = Entities/Subjects (people, places, objects)
• Edges = Relationships/Predicates
• Properties = Attributes of entities or relations

RDF Triple format: (Subject, Predicate, Object) = (Head, Relation, Tail)

Four types of KG inference (from slides):

1. Transitive Inference: $(A \rightarrow B, B \rightarrow C) \Rightarrow (A \rightarrow C)$. Example: “Einstein discovered Theory of Relativity” + “Theory of Relativity is part of Physics” ⇒ “Einstein contributed to Physics”
2. Relationship Expansion: Identify hidden connections. Example: if two lectures are taught by the same professor, infer a collaboration link
3. Entity Disambiguation: Distinguish entities with similar names. Example: “Apple (Company)” vs. “Apple (Fruit)”
4. Question Answering: Retrieve structured answers. Example: “Who invented the telephone?” → Alexander Graham Bell (from graph relations)

Strengths of Knowledge Graphs:

1. Highly Structured & Interpretable – provides clearly defined relationships between entities
2. Enables Inference & Knowledge Discovery – infer missing knowledge based on known relationships
3. Scalable for Large-Scale KR – works well with millions of facts and relationships
4. Supports Multi-Domain Knowledge Integration – combine medical, scientific, business knowledge into one system

Weaknesses of Knowledge Graphs:

1. Incomplete Knowledge & Data Sparsity – if information is missing, AI cannot infer accurate answers
2. High Maintenance & Complexity – requires constant updates to add new entities and relationships

🔄 机制与推导（How It Works）

How Semantic Network Inference Works – Step by Step

Given knowledge:
  Cat ──is-a──► Mammal ──is-a──► Animal
  Mammal ──has-property──► Warm-blooded
  Cat ──has──► Fur

Step 1: Query "Is Cat an Animal?"
  Traverse: Cat → is-a → Mammal → is-a → Animal
  Answer: YES (transitive IS-A inference)

Step 2: Query "Is Cat warm-blooded?"
  Cat → is-a → Mammal → has-property → Warm-blooded
  Answer: YES (property inheritance)

Step 3: Query "Does Dog have Fur?"
  Dog → is-a → Mammal (known)
  Mammal ──has──► ? (no "has Fur" on Mammal)
  Answer: CANNOT INFER (Fur is a property of Cat specifically, 
          not inherited through Mammal)

How Frame Reasoning Works – Step by Step

Scenario (Exercise 3 from slides): An AI healthcare assistant uses Frames.

Patient Alice reports: fever and headache.

Reasoning process:

1. Slot matching: Alice’s symptoms (Fever, Headache) match Malaria’s Common Symptoms (Fever, Headache, Chills) – 2 out of 3 match
2. Cross-frame inference: Alice’s Recent Travel = “Tropical regions” matches Malaria’s Transmission Risk = “High in tropical regions”
3. Default/constraint check: Alice has no travel vaccines (Vaccination History slot) and Malaria’s Prevention = Vaccination → increased susceptibility
4. Conclusion: Malaria flagged as potential diagnosis

How Rule-Based Systems Work – Step by Step

Scenario (Exercise 4 from slides): Fire detection system.

Current sensor readings: Temperature = 85C, Smoke = YES, Carbon Monoxide = Safe, Sprinklers = NO

Forward chaining:

1. Check R1: Temperature (85) > 60C ✅ AND Smoke Detected ✅ → Fire Alarm triggered
2. Check R2: Temperature (85) > 80C ✅ → Emergency Evacuation triggered
3. Check R3: Carbon Monoxide = Safe ❌ → R3 does NOT fire
4. Check R4: Sprinklers = NO ❌ → R4 does NOT fire

Final actions: Trigger Fire Alarm (R1) + Trigger Emergency Evacuation (R2)

How Knowledge Graph Inference Works – Step by Step

Scenario (Exercise 5 from slides): Historical figures KG.

Query: “Did Isaac Newton’s discoveries influence Albert Einstein?”

Graph traversal:

Newton ──Discovered──► Law of Gravity
                            │
                      Influenced ▼
                  Theory of Relativity ◄──Developed── Einstein

Path: Newton → Discovered → Law of Gravity → Influenced → Theory of Relativity ← Developed ← Einstein

Answer: YES – Newton’s Law of Gravity influenced Einstein’s Theory of Relativity. The graph does not connect them directly, but AI can infer the relationship by traversing the graph.

⚖️ 权衡分析（Trade-offs & Comparisons）

Complete KR Methods Comparison Table

Differences Between KR Methods (from slides)

Key distinction (from slides):

• Semantic Network: Early graph-based KR using nodes and links. No unified standard. Small/domain-specific.
• Knowledge Graph: A large-scale, standardized graph using RDF triples. Designed for web-scale.
• KGs can be viewed as a modern, large-scale implementation and extension of the original Semantic Network concept.

When to Choose Which?

KR Landscape (from slides)

                Knowledge Representation
                         │
          ┌──────────────┼──────────────┐
     Logic-based     Graph-based    Structured/Rule-based
          │           │       │           │          │
    Symbolic     Semantic   Knowledge   Frames   Rule-based
     Logic      Networks    Graphs               Systems

Key takeaway from slides: “There is no single best KR method. Different methods have different strengths in representation, inference, scalability, and interpretability. In practice, AI systems may combine multiple KR methods to solve real-world problems.”

🏗️ 设计题答题框架

Prompt type: “Compare different KR methods and explain which you would choose for [scenario]. Justify your choice.”

WHAT

Identify which KR methods are relevant:

• “For this scenario, I would compare Semantic Networks, Frames, Rule-Based Systems, and Knowledge Graphs as candidate approaches…”
• “The primary representation would be a Knowledge Graph with an ontology providing the schema…”

WHY

Justify based on the 5 KR requirements:

• Expressiveness: “A KG can represent diverse entity types and relationship types via flexible triples”
• Computational Efficiency: “Rule-based systems offer fast decision-making via direct rule matching”
• Scalability: “KGs scale to billions of triples; frames and rule-based systems do not”
• Interpretability: “Rule-based systems are the most transparent – every conclusion traces to a human-readable rule”
• Modifiability: “KGs can be updated by adding new triples without restructuring the entire system”

HOW

Describe the architecture:

1. Choose the primary KR method and explain its structure
2. Show how knowledge is stored (e.g., as triples, as frames, as rules)
3. Explain how inference works (e.g., graph traversal, property inheritance, forward chaining)

TRADE-OFF

Discuss what you sacrifice:

• “Semantic Networks are intuitive but lack standardization and cannot handle uncertainty”
• “Rule-Based Systems are transparent but brittle and hard to scale beyond ~10K rules”
• “Frames are structured but rigid and cannot reason with probabilities”
• “KGs are scalable but may be incomplete and require maintenance”

EXAMPLE

Walk through a concrete scenario:

• “A medical AI receives symptom data. Using a KG: (Patient, hasSymptom, Fever), (Patient, hasSymptom, Cough). Graph traversal finds: (Flu, hasSymptom, Fever), (Flu, hasSymptom, Cough). Match! Suggest Flu as possible diagnosis.”

📝 历年真题 + 课堂练习（Exercises 1–5 from Slides）

Exercise 1 – Structured vs Unstructured Knowledge

Question: Which of the following is an example of structured knowledge?

A) A collection of handwritten medical prescriptions. B) A database storing customer purchase histories. C) A video recording of a classroom lecture. D) A set of research papers in PDF format.

Exercise 2 – Semantic Network Inference

Question: Which of the following best demonstrates inference in a Semantic Network?

A) A chatbot randomly generating responses. B) AI deducing that “whales are mammals” based on an “is-a” relationship. C) A search engine ranking web pages based on popularity. D) A neural network recognizing images of cats.

Exercise 3 – Frame-Based Reasoning (Healthcare)

Scenario: An AI-powered healthcare assistant uses Frames to manage patient medical records and suggest possible diagnoses.

Patient Alice reports: fever and headache.

Frame: Patient	Slot	Filler
Alice	Age	25
	Symptoms	Fever, Headache
	Family History	None
	Recent Travel	Tropical regions (2 weeks ago)
	Vaccination History	No recent travel vaccines

Frame: Malaria	Slot	Filler
Malaria	Common Symptoms	Fever, Headache, Chills
	Transmission Risk	High in tropical regions
	Prevention	Vaccination

Question: What is the most likely reason the AI flags Malaria as a potential diagnosis?

A) Alice has a family history of malaria. B) Malaria is common in all patients with pain in the lungs. C) Malaria is common in Age from 20 to 30. D) Alice recently traveled to a high-risk area and shows matching symptoms.

Exercise 4 – Rule-Based System (Fire Detection)

Scenario: Rule-Based AI system for fire detection in a smart building.

Rule ID	IF Condition	THEN Conclusion
R1	Temperature > 60C AND Smoke Detected	Trigger Fire Alarm
R2	Temperature > 80C	Trigger Emergency Evacuation
R3	Carbon Monoxide > Safe Limit	Alert Building Manager
R4	Sprinklers Activated AND Smoke Detected	Confirm Fire

Current Sensor Readings: Temperature = 85C, Smoke Detected = YES, Carbon Monoxide = Safe, Sprinklers Activated = NO

Question: What actions will the AI take?

A) Trigger Fire Alarm and Emergency Evacuation. B) Only Alert the Building Manager. C) Only Trigger the Fire Alarm. D) Confirm Active Fire and Trigger Evacuation.

Exercise 5 – Knowledge Graph Inference (Historical Figures)

Scenario: An AI system uses a Knowledge Graph for historical figures and scientific discoveries.

Entity (Node)	Relation (Edge)	Entity (Node)
Isaac Newton	Discovered	Law of Gravity
Law of Gravity	Related To	Physics
Albert Einstein	Contributed To	Physics
Albert Einstein	Developed	Theory of Relativity
Theory of Relativity	Related To	Gravity
Theory of Relativity	Influenced By	Law of Gravity

Question: Did Isaac Newton’s discoveries influence Albert Einstein?

A) No, no direct link between Newton and Einstein. B) Yes, Einstein contributed to Physics, and Physics includes Gravity. C) Yes, Newton discovered Law of Gravity, and Theory of Relativity was influenced by it. D) No, Einstein worked on different theories.

🌐 英语表达要点（English Expression）

Defining KR Methods

"Knowledge Representation refers to the methods used in AI to store,
 retrieve, and handle knowledge to enable intelligent reasoning."

"A Semantic Network is a graph-based KR method where nodes represent
 concepts and edges represent relationships such as IS-A and HAS-PROPERTY."

"A Frame is a structured representation that groups related information
 about an entity into a slot-filler structure, enabling inheritance
 and default reasoning."

"A Rule-Based System encodes domain knowledge as a set of IF-THEN
 production rules, providing transparent and explainable decision-making."

"A Knowledge Graph is a graph-based representation that connects
 entities (nodes) with relationships (edges), storing facts as
 RDF triples in the form (Subject, Predicate, Object)."

Comparing Methods

"While Semantic Networks represent knowledge as interconnected concept
 nodes, Knowledge Graphs use standardized RDF triples and are designed
 for web-scale applications with billions of facts."

"Unlike Rule-Based Systems, which require manually crafted IF-THEN rules,
 Knowledge Graphs can be populated semi-automatically using NLP techniques
 such as Named Entity Recognition and Relation Extraction."

"Frames organize knowledge similarly to objects in programming, with
 slots (attributes) and fillers (values), whereas Semantic Networks
 focus on the relationships between concepts rather than their attributes."

"The fundamental trade-off between Rule-Based Systems and Knowledge Graphs
 is interpretability versus scalability: rules are transparent but brittle
 at scale, while KGs scale to billions of facts but paths can be opaque."

Discussing Requirements

"A good KR system must balance five requirements: expressiveness,
 computational efficiency, scalability, interpretability, and modifiability."

"The choice of KR method depends on the application's priorities --
 for example, medical diagnosis systems prioritize interpretability,
 while web search engines prioritize scalability."

易错词汇

✅ 自测检查清单

• Can I define Knowledge Representation and its purpose in one sentence?
• Can I list and explain the 5 key requirements of KR (Expressiveness, Computational Efficiency, Scalability, Interpretability, Modifiability)?
• Can I explain the difference between Structured and Unstructured Knowledge with examples?
• Can I describe how Symbolic Logic (PL + FOL) is used in KR?
• Can I draw a Semantic Network and explain IS-A inference and property inheritance?
• Can I name 3 strengths and 3 weaknesses of Semantic Networks?
• Can I describe a Frame with its slots and fillers, and explain the 4 reasoning mechanisms (defaults, inheritance, constraints, procedural attachment)?
• Can I name 4 strengths and 4 weaknesses of Frames?
• Can I write an IF-THEN rule and trace forward chaining through a set of rules?
• Can I name 3 strengths and 3 weaknesses of Rule-Based Systems?
• Can I explain Knowledge Graph structure (nodes, edges, properties) and write RDF triples?
• Can I name the 4 types of KG inference (transitive, relationship expansion, entity disambiguation, QA)?
• Can I name 4 strengths and 2 weaknesses of Knowledge Graphs?
• Can I compare all five KR methods in a table (core idea, representation, reasoning, strengths, weaknesses)?
• Can I explain the KR Landscape diagram showing logic-based, graph-based, and structured/rule-based categories?
• Can I solve all 5 exercises from the lecture slides?

Cross-references:

• For Symbolic Logic in depth, see Propositional Logic & FOL chapter
• For Knowledge Graphs, TransE, and RAG in depth, see KG for AI chapter
• For Expert Systems and MYCIN, see MYCIN chapter