🧠 Predicate Logic -Knowledge Representation

 

🔷 What is Predicate Logic (First-Order Logic)?

Predicate Logic is a powerful form of logic that expresses relationships among objects and includes quantifiers like "for all" (∀) and "there exists" (∃). It allows for structured representation of knowledge.


🧠 Why Use Predicate Logic?

To represent more complex, structured knowledge like relationships, properties of objects, and general rules.

  • Overcomes limitations of propositional logic (no structure, no quantifiers).

  • Useful in natural language processing, knowledge bases, expert systems.


✅ 1. Key Concepts

Concept

Description

Predicate

Function that returns true/false based on the arguments (e.g., Father(John, Mary))

Constant

Represents a specific object (e.g., John, Mary)

Variable

A placeholder (e.g., x, y)

Quantifiers

∀ (universal), ∃ (existential)

Function

Maps inputs to outputs (optional, e.g., MotherOf(x))

Term

A constant, variable, or function


✅ 2. Syntax & Semantics

Symbol

Meaning

Example

Meaning in Words

For all

∀x: Bird(x) → CanFly(x)

All birds can fly

There exists

∃x: Cat(x) ∧ Black(x)

There exists a black cat

AND

Bird(x) ∧ CanFly(x)

x is a bird and x can fly

OR

Bird(x) ∨ Mammal(x)

x is a bird or a mammal

Implication

Bird(x) → CanFly(x)

If x is a bird, x can fly

¬

NOT

¬CanFly(Penguin)

Penguins cannot fly


✅ 3. Real-World Example: Smart Classroom

🧱 Step 1: Define Predicates and Constants

Symbol

Meaning

Student(x)

x is a student

Attends(x, y)

x attends class y

Class(y)

y is a class

Teacher(z)

z is a teacher

Teaches(z, y)

z teaches class y

🧠 Step 2: Build Logical Rules

  1. If someone attends a class, and someone teaches that class, then the student is learning.

    ∀x, y, z: Student(x) ∧ Class(y) ∧ Teacher(z) ∧ Attends(x, y) ∧ Teaches(z, y) → Learning(x)

2. If a person is a teacher of any class, then they are faculty:

∀z, y: Teaches(z, y) → Faculty(z)

🧠 Step 3: Add Facts to Knowledge Base

Fact

Meaning

Student(John)

John is a student

Class(AI101)

AI101 is a class

Teacher(DrSmith)

Dr. Smith is a teacher

Attends(John, AI101)

John attends AI101

Teaches(DrSmith, AI101)

Dr. Smith teaches AI101

🔁 Step 4: Inference Chain

From:

  • Attends(John, AI101)

  • Teaches(DrSmith, AI101)

  • Student(John)

  • Teacher(DrSmith)

Apply rule:

→ Learning(John)

Also:

Teaches(DrSmith, AI101) → Faculty(DrSmith)


✅ Final Inference Summary

Fact(s) Used

Inferred

Attends + Teaches + Student + Class

John is Learning

Teaches

Dr. Smith is Faculty


✅ 4. Use in AI

Application Area

Use Case Example

Expert Systems

Represent medical conditions: HasSymptom(x, Cough)

NLP

Parsing sentence structure: Verb(x) → Action(x)

Robotics

Task planning: HasTool(robot, screwdriver)

Ontology Design

Define entities & relationships in a domain


✅ 5. Advantages over Propositional Logic

Feature

Predicate Logic

Propositional Logic

Can represent structure

✅ Yes (Father(John, Mary))

❌ No

Supports quantifiers

✅ Yes (∀x, ∃x)

❌ No

Scales better with data

✅ General rules for many objects

❌ Each fact must be explicit


✅ 6. Limitations

Limitation

Explanation

More complex syntax

Requires training or tools to use

Harder to compute/infer

May require expensive reasoning engines

No uncertainty by default

Like propositional logic, it's binary unless extended (e.g., fuzzy FOL)



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