2: Symbolic AI

1
2 Symbolic AI Search

• Outline
• Tasks for AI
• Physical Symbol System Hypothesis
• AI techniques
• Solving AI problems
• Search
• Blind search
• Heuristic search
• Game playing minimax search
• Learning outcomes
• Reading

2
Artificial Intelligence

• how to make computers do things which, at the
  moment, people do better (Rich Knight, 1991)
• 3 types of task domain
• Mundane tasks
• Formal tasks
• Expert tasks

3
4 questions

• What are our underlying assumptions about
  intelligence?
• What kinds of techniques will be useful for
  solving AI problems?
• At what level of detail are we trying to model
  human intelligence?
• How will we know when we have succeeded in
  building an intelligent program?

4
The Physical Symbol System Hypothesis

• PSS
• Set of symbols which are physical patterns
• Symbol structure a number of instances/tokens
  of symbols related in some physical way
• Processes which operate on expressions to produce
  other expressions
• PSSH A PSS has the necessary and sufficient
  means for general intelligent action

5
The Physical Symbol System Hypothesis

• PSSH cannot be proved or disproved on logical
  grounds
• Must be subjected to empirical validation
• Computers can be programmed with PSSs
• Select a task
• Write a program
• Theory of human intelligence
• Basis of belief that programs can perform
  intelligent tasks

6
AI techniques

• Search
• Forward backward chaining
• Knowledge elicitation
• Neural networks
• Genetic algorithms
• Parsing
• Robotics

7
Solving AI Problems

• Define and analyse the problem
• What knowledge is necessary?
• Choose a problem-solving technique
• e.g. Chess
• What information do we need to represent in a
  chess-playing program?

8
State Space

• Initial state
• operators
• Goal state(s)

9
The Water Jugs Problem

• 2 jugs
• 4 gallon
• 3 gallon
• How can you get exactly 2 gallons into the 4
  gallon jug?
• Possible operators
• Empty jug
• Fill jug from tap
• Pour contents from one jug into another

3
4
10
The Water Jugs Problem Search Tree
0 , 0
4 , 0
0 , 3
4 , 3
1 , 3
0 , 0
0 , 0
3 , 0
4 , 3
4 , 0
0 , 3
4 , 3
0 , 3
1 , 0
4 , 0
0 , 3
0 , 0
4 , 0
0 , 3
3 , 3
0 , 0
4 , 0
1 , 3
0 , 1
3 , 0
0 , 3
4 , 3
4 , 2
4 , 1
0 , 0
1 , 0
4 , 0
3 , 3
4 , 3
0 , 2
0 , 1
4 , 0
3 , 3
4 , 3
0 , 0
4 , 2
2 , 0
0 , 3
11
Blind Search Breadth First
0 , 0
12
Blind Search Depth First
0 , 0
13
Breadth-first vs. depth-first search

• Depth-first
• requires less memory
• may find a solution without searching much of the
  search space
• Breadth-first
• will not get trapped exploring a blind alley
• guaranteed to find solution (if one exists)
• will find minimal solution (if more than one
  exist)

14
Travelling salesman problem

• A salesman must visit 5 cities. What is the
  shortest route?

15
Travelling salesman problem
A
594
619
524
B
C
D
184
184
78
78
233
233
C
C
B
B
D
D
184
233
78
184
78
233
C
D
D
B
C
B
16
Heuristic Search

• heuristic rule of thumb

A
784
17
Heuristic Search hill climbing

• expand node
• sort children according to
• Heuristic Evaluation Function
• choose best value

X
18
Heuristic Search hill climbing

• Problems
• foothill problem - attracted by local maxima
• plateau problem - nowhere to turn on the flat

goal
foothill
plateau
19
Heuristic Search best-first search

• similar to hill-climbing
• choice of next state - all open nodes (not just
  bottom layer)
• finds shortest paths

Heuristic Search beam search

• based on breadth-first
• best n nodes kept each level
• can miss goal altogether

20
Game Playing Noughts and Crosses

• HEF
• Middle5
• Corners3
• Sides1
• Add up squares with noughts
• Subtract squares with crosses

O
O
31-5-3 -4
33-5-3 -2
21
Game Playing Noughts and Crosses
-2
-4
-5
-3
-100
-4
100
-6
100
-4
0
-2
22
Minimax search
a
c
b
max
-4
-2
d
e
f
g
min
-100
-4
-5
-3
h
i
j
k
l
m
max
100
-6
100
-4
0
-2
23
Learning Outcomes

• Understand the physical symbol system hypothesis
• Show awareness of different AI techniques
• Understand blind and heuristic search

24
Reading

• Mindware Chapter 2
• Finlay, J. Dix A. (1996). An introduction to
  artificial intelligence. London UCL Press.
  Chapters 3 5.
• Rich, E. Knight, K. (1991). Artificial
  intelligence. NY McGraw-Hill.
• FOR NEXT WEEK, READ
• Cooper, R. (1996). Explanation and simulation in
  cognitive science. In D. W. Green, Cognitive
  science. Oxford Blackwell.