Class 34: Game Trees

Held Tuesday, April 4, 2000

Overview

Today we delve into some simple ``intelligent'' programs; interacting with Eliza and discussing how many game-playing programs work.

Question 34 for discussion today: The algorithms Dewdney describes assume that both players make the best possible move. How would the min-max and alpha-beta pruning algorithms change if one player selected a move randomly?

Question 35 for discussion on Wednesday: Model some set of relationships (preferably something other than family trees) with the predicate calculus.

Notes

• For tomorrow, read Dewdney 58 (Predicate Calculus) and 64 (Logic Programming)
• We'll return to the question of how we determine whether a program is intelligent on Friday (or perhaps the following Monday).
• We're meeting in an alternate room today. Sorry for the late notice.

Contents

• A Computer Psychologist
• Game Trees
• Predicate Calculus

Summary

• Eliza
• Game trees
• Predicate logic

A Computer Psychologist

These notes are adapted from notes from Henry Walker.

• In a dtterm window, type emacs
• When emacs opens, type [Esc] X doctor. Note that the [Esc] is the key at the upper-left side of the keyboard.
• Start conversing with Eliza. Type the [Enter] key twice after each of your responses.

• We'll spend a few minutes talking about Eliza, what it's like to interact with Eliza, and what possible algorithms might underlie Eliza.

Game Trees

• In your Answers to today's question, most of you indicated that you didn't really understand the algorithms. Hence, we'll go over them in some more detail.
• The basic mimimax algorithm
  • Draw a game tree
  • Evaluate the leaves
  • Propagate values upward, assuming that one player picks the highest possible value and the other picks the lowest.
• First improvement:
  • Evaluate as you go, rather than building the whole tree.
• Second improvement:
  • Prune unneeded parts of the tree using clever logic.

Predicate Calculus

• One of the first attempts at ``Artificial Intelligence'' predates both computers and the field of AI.
• Starting early this century, a number of mathematicians attempted to formalize ``how mathematicians think''. We typically call their work mathematical logic.
• There were many goals to mathematical logic, but they included:
  • Automated theorem proving
  • Formalizing knowledge of particular domains of mathematics.
• One promising approach to this involves the use of the predicate calculus.
  • No, this is not the same as the calculus you're used to (integral and differential calculus). Basically, ``calculus'' means ``a way to compute using a special notation''.
  • A predicate is a function that returns true or false.
• In the predicate calculus, we work with
  • symbols,
  • variables,
  • functions,
  • predicates,
  • quantifiers, and
  • formulae
• A symbol is a sequence of letters.
• A variable is also a sequence of letters. The context determines whether something is treated as a symbol or a variable.
• A function is a sequence of letters followed by an open paren, followed by a sequence of symbols/variables which are separated by commas, followed by a close paren.
• More to come ...