Artificial Intelligence - UNIT 3-Topic 3-Predicate logic and logic programming

 

UNIT - III

Topic 3 :  Predicate Logic & Logic Programming

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Part A: Introduction

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✅ What is Logic in AI?

Logic is the foundation of reasoning in Artificial Intelligence. It allows AI systems to make decisions, derive conclusions, and prove facts using rules and facts.

There are two main types of logic used in AI:

• Propositional Logic
• Predicate Logic (First-Order Logic)

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Part B: Predicate Logic (First-Order Logic)

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✅ What is Predicate Logic?

Predicate Logic, also called First-Order Logic (FOL), is a powerful logic system that allows the representation of objects, properties, and relationships among objects.

It is more expressive than Propositional Logic, which only deals with true or false statements.

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✅ Components of Predicate Logic:

Component	Description	Example
Predicate	Represents a property or relationship	Loves(John, Mary) → "John loves Mary"
Variables	Stand for objects	x, y
Constants	Specific objects	John, India
Functions	Map objects to objects	Mother(John) → John's mother
Quantifiers	Express the number of objects for which a statement is true	∀ (for all), ∃ (there exists)

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✅ Common Symbols in Predicate Logic:

Symbol	Meaning
∧	AND
∨	OR
¬	NOT
→	IMPLIES
↔	IF AND ONLY IF
∀	FOR ALL (Universal Quantifier)
∃	THERE EXISTS (Existential Quantifier)

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✅ Examples:

1. Propositional Logic:
• It is raining → A
• A is either true or false
2. Predicate Logic:
• Rains(City) → It is raining in a particular city
• ∀x Loves(x, IceCream) → Everyone loves ice cream
• ∃x Student(x) ∧ Studies(x, Math) → There exists a student who studies Math

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Part C: Advantages of Predicate Logic

Advantage	Explanation
✅ More expressive than propositional logic	Can represent objects and relationships
✅ Supports reasoning and inference	Allows deriving new knowledge
✅ Handles universal and existential conditions	Useful for solving real-world problems

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Part D: Logic Programming

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✅ What is Logic Programming?

Logic Programming is a type of programming where logic is used as the foundation, and programs consist of facts and rules. It is based mainly on predicate logic.

It is used to build AI systems that can perform reasoning, like expert systems and intelligent agents.

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✅ Most Popular Logic Programming Language:

• Prolog (Programming in Logic)

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✅ Structure of a Logic Program

Element	Description	Example
Facts	Basic information known to be true	father(john, david).
Rules	Inference based on facts	grandfather(X, Y) :- father(X, Z), father(Z, Y).
Queries	Questions to be answered	?- grandfather(john, Y).

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✅ Example in Prolog:

% Facts

parent(john, mary).

parent(mary, tom).

 

% Rule

grandparent(X, Y) :- parent(X, Z), parent(Z, Y).

 

% Query

?- grandparent(john, tom).

% Output: true

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Part E: Applications of Predicate Logic and Logic Programming

Area	Use Case
Expert Systems	Rule-based medical diagnosis or tech troubleshooting
Natural Language Processing	Understanding grammar and sentence structure
Robotics	Defining behavior through logical conditions
Databases & Query Engines	Representing relationships between data entities

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✅ Difference Between Propositional Logic and Predicate Logic

Feature	Propositional Logic	Predicate Logic
Expressiveness	Less expressive	Highly expressive
Uses variables?	❌ No	✅ Yes
Can show relationships?	❌ No	✅ Yes
Example	P ∧ Q	Loves(John, Mary)

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📝 Summary

• Predicate Logic allows us to represent objects, their properties, and their relationships using variables and quantifiers.
• Logic Programming uses these logical representations to build intelligent systems that can reason and answer queries.
• Languages like Prolog are built on predicate logic and are widely used in AI, NLP, and knowledge-based systems.

"Predicate logic gives AI the power to not just know facts — but to think through them logically."

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