🔷 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
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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