Module 3: Knowledge Representation

← Previous: Module 2 · Subject index · Next: Module 4 →

Learning outcomes

After completing this module, you should be able to:

• explain the purpose and requirements of knowledge representation;
• represent knowledge using logic, semantic networks, frames, and scripts;
• describe conceptual dependency and partitioned semantic networks;
• distinguish an ontology from a knowledge graph; and
• perform basic inference in propositional logic.

Prerequisites

Complete Module 2 first. Review its quick-revision section if any term below feels unfamiliar.

Study blocks

Study one block at a time. Work through its example and checkpoint before continuing.

Block	Topic	Suggested time
1	Knowledge representation in AI	10-15 minutes
2	Types of knowledge	10-15 minutes
3	Propositional logic	10-15 minutes
4	Semantic networks	10-15 minutes
5	Frames and slot-filler structures	10-15 minutes
6	Scripts	10-15 minutes
7	Conceptual dependency	10-15 minutes
8	Ontologies	10-15 minutes
9	Knowledge graphs	10-15 minutes
10	Representation comparison	10-15 minutes
11	Worked representation	10-15 minutes

Knowledge representation in AI

Knowledge representation (KR) encodes facts, concepts, relationships, rules, and events in a form an AI system can use for reasoning.

A useful representation should provide:

• representational adequacy: it can express the required knowledge;
• inferential adequacy: it supports deriving new knowledge;
• inferential efficiency: it guides reasoning toward relevant conclusions;
• acquisitional efficiency: knowledge can be added and updated easily; and
• clarity and consistency: meanings are unambiguous and contradictions can be managed.

Types of knowledge

Type	Meaning	Example
Declarative	Facts about the world	Pune is in Maharashtra
Procedural	How to perform a task	Steps of an algorithm
Heuristic	Experience-based rule	Prefer the most constrained variable
Meta-knowledge	Knowledge about other knowledge	Source A is more reliable
Structural	Relationships among concepts	A car has an engine

Propositional logic

A proposition is a statement that is either true or false. Complex formulas use:

Notation	Meaning
NOT P	Negation
P AND Q	Conjunction
P OR Q	Disjunction
P -> Q	Implication
P <-> Q	Biconditional

Inference rules

Modus ponens:

P
P -> Q
Therefore Q

Modus tollens:

P -> Q
NOT Q
Therefore NOT P

An inference procedure is sound if every derived statement is entailed by the knowledge base. It is complete if it can derive every entailed statement.

Resolution

Resolution usually works with formulas in conjunctive normal form (CNF). To prove a query, add its negation to the knowledge base and derive a contradiction.

Example clauses:

NOT Rain OR Wet
Rain

Resolving them gives Wet.

Propositional logic is precise and supports formal inference, but it cannot compactly express objects, relations, or universal rules. Predicate logic adds predicates, variables, and quantifiers for these purposes.

Semantic networks

A semantic network represents knowledge as a labelled graph:

• nodes represent objects or concepts;
• edges represent relations such as is-a, instance-of, and has-part.

Canary --is-a--> Bird --is-a--> Animal
Bird --has--> Wings
Canary --colour--> Yellow

Inheritance lets Canary receive properties of Bird and Animal. Exceptions must be handled carefully; for example, a penguin is a bird but normally cannot fly.

Partitioned semantic networks

Partitioning groups nodes and arcs into contexts. It helps represent quantified statements, beliefs, hypothetical situations, and statements whose scope must be kept separate.

Frames and slot-filler structures

A frame is a structured record for a stereotyped object or situation. Slots name attributes and fillers hold values.

Frame: Student
  name: Shreya
  programme: MCA
  semester: 1
  institution: [value]

Slots may contain:

• default values;
• value restrictions;
• inherited values;
• procedures triggered when a value is read or changed; and
• links to other frames.

Frames are intuitive and efficient for structured domain knowledge, but their inference semantics are less uniform than formal logic.

Scripts

A script represents a common event sequence. A restaurant script might include entering, getting a table, ordering, eating, paying, and leaving. Scripts help an AI system infer omitted events, but they are brittle when events depart greatly from the expected pattern.

Conceptual dependency

Conceptual dependency (CD) represents sentence meaning using a small set of primitive actions. Sentences with the same underlying meaning should receive a similar representation.

Common primitives include:

Primitive	Meaning	Example
ATRANS	Transfer of possession	Riya gives Sam a book
PTRANS	Physical movement	Sam goes to college
MTRANS	Transfer of information	Teacher tells the class
INGEST	Taking something into the body	Sam drinks water
PROPEL	Applying physical force	Sam throws a ball

CD makes implicit roles and causal relations explicit, but building detailed CD representations is labour-intensive and its primitive set may be domain-sensitive.

Ontologies

An ontology gives a shared, formal specification of concepts and relationships in a domain. It normally defines:

• classes and subclasses;
• individuals or instances;
• properties and relations;
• constraints or axioms; and
• controlled vocabulary.

For a university ontology, Student and Course may be classes, enrolledIn a relation, and a particular learner an instance of Student.

Knowledge graphs

A knowledge graph stores entities and relationships as triples:

(Ada Lovelace, occupation, Mathematician)
(Ada Lovelace, workedOn, Analytical Engine)

An ontology defines the schema and meaning of a domain; a knowledge graph often contains the actual instance data. The two are commonly used together.

Representation comparison

Technique	Strength	Limitation
Logic	Precise semantics and formal proof	Can be costly and rigid
Semantic network	Visual and supports inheritance	Relations may be ambiguous
Frame	Natural structured description	No single standard inference model
Script	Captures expected event sequences	Handles unusual cases poorly
Conceptual dependency	Represents language-independent meaning	Complex to construct
Ontology/knowledge graph	Shared vocabulary and linked data	Requires careful schema design

Worked representation

Knowledge: "Every student is a person. Mira is a student."

• Logic: Student(Mira) and Student(x) -> Person(x).
• Semantic network: Mira --instance-of--> Student --is-a--> Person.
• Frame: a Mira frame whose parent is Student, which inherits from Person.

All three support the conclusion that Mira is a person, but they organize and derive that knowledge differently.

Common mistakes

• Confusing a class such as Student with an instance such as Mira.
• Assuming inheritance has no exceptions, for example concluding every bird flies.
• Treating a semantic network edge as meaningful without defining its relation.
• Using propositional logic when objects, relations, or quantifiers are required.
• Confusing an ontology's schema with the instance facts in a knowledge graph.

Quick revision

• Logic provides precise inference; semantic networks provide graph-shaped relations.
• Frames organize attributes in slots and support defaults and inheritance.
• Scripts represent expected event sequences.
• Ontologies define shared concepts and constraints; knowledge graphs store linked facts.
• Sound inference derives only entailed conclusions; complete inference can derive every entailed conclusion.

Important exam questions

1. Explain the requirements of a good knowledge-representation system.
2. Compare semantic networks, frames, scripts, and conceptual dependency.
3. Represent a given domain using a semantic network and explain inheritance.
4. Explain propositional resolution with a worked example.
5. Distinguish ontology, knowledge base, and knowledge graph.
6. Explain partitioned semantic networks and their need.

PDF-aligned additions

Explicit, implicit, domain, and common-sense knowledge

• Explicit knowledge is directly stored as a fact, rule, or definition.
• Implicit knowledge is inferred from stored facts and rules.
• Domain knowledge is specialized knowledge about medicine, law, education, or another field.
• Common-sense knowledge is broad everyday knowledge.

Keep concepts and instances separate: Student is a class, while Mira may be an instance of that class. A knowledge base also contains symbols, relations, rules, constraints, and queries.

Ambiguity, change, and exceptions

A practical representation must support updates and exceptions. “Birds fly” may be a default rule, but Penguin can be represented as a bird that does not fly. Facts that are stored directly are explicit; conclusions derived from rules are implicit.

Propositional-resolution checklist

1. Translate facts and the query into propositions.
2. Convert implications to NOT P OR Q.
3. Convert the knowledge base and negated query to CNF.
4. Resolve clauses containing complementary literals.
5. Derive the empty clause to prove contradiction and entailment.

Propositional logic cannot compactly express variables, objects, or quantified rules; predicate logic is the natural extension when those are required.

Practice ladder

1. Easy - Recall: Define the module's central idea in one or two sentences.
2. Easy - Recognize: Identify the correct method for a small example and explain why it fits.
3. Medium - Apply: Work through one representative problem without copying the example.
4. Medium - Compare: Contrast two methods or concepts from the module.
5. Hard - Integrate: Solve a university-style scenario and justify every major step.

Reveal self-evaluation guide

A complete response uses correct terminology, shows intermediate steps, connects the result to the scenario, and states one assumption or limitation.

---

← Previous: Module 2 · Subject index · Next: Module 4 →