by Albert Major

Introduction to Artificial Intelligence

Introduction to Quantifying Uncertainty in AI

Background Context

• Previous lectures focused on scenarios with complete knowledge (like chess)
• This lecture shifts to handling situations with incomplete information
• Real-world AI needs to make rational decisions under uncertainty

Why Pure Logic Is Insufficient

• Example: Dentist diagnosing toothache
  • Can't simply list all possible causes
  • Too many possibilities to consider
  • Some causes might be unknown
  • Need a way to represent degrees of belief rather than certainty

Fundamental Probability Concepts

Possible Worlds (Ω)

• Definition: Different states that could be true
• Requirements:
  • Must be exhaustive (cover all possibilities)
  • Must be mutually exclusive (no overlap)
• Example with dice:
  • Sample space includes all possible combinations (1,1), (1,2), etc.
  • Total of 36 possible combinations for two dice

Random Variables

• Functions mapping from possible worlds to specific values
• Usually written in uppercase letters
• Example:
  • Total sum when rolling two dice
  • Maps from individual dice outcomes to their sum

Types of Probability