Topic 7: Wumpus World Case Study

What is Wumpus World?

Wumpus World is a classic AI environment designed to test logical reasoning agents. It features partial observability, uncertainty, and requires intelligent reasoning to navigate safely.

Why Wumpus World is Perfect for KBAs:

Partial Observability: Agent can't see the whole world
Uncertainty: Multiple possible world states
Logical Inference: Can derive safe actions from percepts
Knowledge Accumulation: Each step adds new information

World Description

Wumpus World is a 4×4 grid where the agent must navigate to find gold while avoiding dangers. The world contains:

Wumpus World Grid (4×4)

W

P

G

A

World Elements:

Dangers:

Wumpus: Deadly monster (1 per world)
Pits: Bottomless holes (0-3 per world)

Goals:

Gold: Treasure to collect (1 per world)
Exit: Return to starting position

PEAS Analysis

Component	Description
Performance	Find gold, avoid wumpus and pits, minimize steps
Environment	4×4 grid, partially observable, stochastic, sequential
Actuators	Move forward, turn left/right, grab gold, shoot arrow
Sensors	Stench (near wumpus), breeze (near pit), glitter (gold present)

Percepts and Actions

Percepts:

Stench

(near wumpus)

Breeze

(near pit)

Glitter

(gold present)

Bump

(hit wall)

Scream

(wumpus killed)

Actions:

Move Forward

Turn Left

Turn Right

Grab Gold

Shoot Arrow

Knowledge Representation

The agent represents its knowledge using propositional logic statements:

Knowledge Base Structure:

Percepts: S₁,₁ (stench), B₁,₁ (breeze), G₁,₁ (glitter)
Dangers: W₁,₁ (wumpus), P₁,₁ (pit)
Safety: Safe₁,₁ (safe to enter)
Visited: V₁,₁ (has been visited)

Inference Rules:

S₁,₁ ↔ (W₁,₁ ∨ W₁,₂ ∨ W₂,₁) (stench means wumpus nearby)
B₁,₁ ↔ (P₁,₁ ∨ P₁,₂ ∨ P₂,₁) (breeze means pit nearby)
¬W₁,₁ ∧ ¬P₁,₁ → Safe₁,₁ (safe if no wumpus and no pit)

Step-by-Step Reasoning Process

Let's trace through a typical reasoning sequence:

Reasoning Steps:

Agent starts at (1,1) - safe by definition
Moves to (1,2), perceives stench
Concludes: W₁,₁ ∨ W₁,₃ ∨ W₂,₂
Moves to (2,1), no stench
Concludes: ¬W₁,₁ ∧ ¬W₂,₂
Updates: W₁,₃ (wumpus must be at (1,3))
Moves to (2,2), perceives breeze
Concludes: P₂,₁ ∨ P₂,₃ ∨ P₁,₂ ∨ P₃,₂
Continues reasoning to find safe path

Example Inference:

Given: S₁,₂ (stench at (1,2))

Rule: S₁,₂ ↔ (W₁,₁ ∨ W₁,₃ ∨ W₂,₂)

Conclusion: W₁,₁ ∨ W₁,₃ ∨ W₂,₂

Additional Info: ¬W₁,₁ (no stench at (2,1))

Final Conclusion: W₁,₃ ∨ W₂,₂

Challenges in Wumpus World

Key Challenges:

Partial Observability: Can't see the whole world
Uncertainty: Multiple possible world states
Logical Inference: Must derive safe actions
Knowledge Management: Must track what's known/unknown
Decision Making: Must choose between multiple safe actions

Why These Challenges Matter:

Real-world Relevance: Many real problems have similar challenges
Logical Reasoning: Tests ability to reason with incomplete information
Knowledge Representation: Tests ability to represent and update knowledge
Decision Making: Tests ability to make intelligent choices

Agent Strategies

Different types of agents can approach Wumpus World differently:

Logical Agent:

Uses knowledge base
Applies inference rules
Derives safe actions
Most intelligent approach

Random Agent:

Chooses actions randomly
No reasoning
Very likely to die
Baseline for comparison

Performance Comparison:

Logical Agent: High success rate, efficient
Random Agent: Very low success rate
Reactive Agent: Medium success rate, no learning
Learning Agent: Improves over time

Wumpus World Extensions

Wumpus World can be extended to test more sophisticated reasoning:

Extensions:

Larger Worlds: 5×5, 10×10 grids
Multiple Wumpuses: More complex reasoning
Probabilistic: Uncertainty in percepts
Learning: Adapt to world patterns

Advanced Features:

Time Constraints: Limited time to find gold
Energy: Limited movement energy
Communication: Multiple agents
Dynamic World: World changes over time

Key Takeaways

Wumpus World:

Classic testbed for logical agents
Tests partial observability
Requires logical reasoning
Demonstrates knowledge-based AI

Lessons Learned:

Knowledge representation is crucial
Logical inference enables safe actions
Partial observability is challenging
Reasoning beats random behavior

Next Steps:

Now that we've seen how logical reasoning works in practice, we'll explore the practical considerations and limitations in Topic 8: Practical Considerations.