Defining a Problem as a State Space
1.
2.
3.
4.
Define a state space that contains all the possible
configurations of the relevant objects.
Specify one (or more) state(s) as the initial state(s).
Specify one (or more) state(s) as the goal state(s).
Specify a set of rules that describe available
actions (operators), considering:



What assumptions are present in the informal problem
description?
How general should the rules be?
How much of work required to solve the problem should
be precompiled and represented in the rules?
1
Production Systems

A set of rules (Knowledge Base) :
– LHS  RHS (if-part  then-part)
– Pattern  Action
– Antecedent  Consequent
knowledge/databases containing information
(temporal/permanent) required to solve the
current task. (Working Memory)
 A control strategy to specify the order of
testing patterns and resolving possible
conflicts (Inference Engine)
 A rule applier.

2
Production System Major Components
 knowledge
base
– contains essential information about the problem
domain
– often represented as facts and rules
 inference
engine
– mechanism to derive new knowledge from the
knowledge base and the information provided by
the user
– often based on the use of rules
3
Production (Rule-Based) System
User Interface
Knowledge Base
Inference Engine
Agenda
Working Memory
4
Rule-Based System

knowledge is encoded as IF … THEN rules
– these rules can also be written as production rules

the inference engine determines which rule antecedents
are satisfied
– the left-hand side must “match” a fact in the working memory
satisfied rules are placed on the agenda
 rules on the agenda can be activated (“fired”)

– an activated rule may generate new facts through its righthand side
– the activation of one rule may subsequently cause the
activation of other rules
5
Example Rules
IF … THEN Rules
Rule: Red_Light
IF
the light is red
THEN
stop
Rule: Green_Light
IF
the light is green
THEN
go
antecedent
(left-hand-side)
consequent
(right-hand-side)
Production Rules
antecedent (left-hand-side)
the light is red ==> stop
consequent
the light is green ==> go
(right-hand-side)
6
Inference Engine Cycle

describes the execution of rules by the inference
engine
– match

update the agenda
– add rules whose antecedents are satisfied to the agenda
– remove non-satisfied rules from agendas
– conflict resolution

select the rule with the highest priority from the agenda
– execution



perform the actions on the consequent of the selected rule
remove the rule from the agenda
the cycle ends when
– no more rules are on the agenda, or
– an explicit stop command is encountered
7
Control Stategies

A good control strategy should have the
following properties:
– Cause motion
– Be systematic
8
The Water Jugs Problem – Search Tree
0,0
0,3
0,0
4,0
4,0
4,3
0,3
3,0
4,0
0,3
4,0
0,0
3,3
3,0
3,3
4,2
4,3
0,3
4,2
0,2
2,0
0,0
4,3
4,3
0,3
4,0
1,3
0,3
4,0
1,0
0,1
0,0
0,1
1,3
4,1
4,0
0,0
0,3
4,3
0,0
1,0
3,3
4,3
9
Blind Search – Breadth First
0,0
0,3
4,0
4,3
3,0
3,3
4,3
1,3
1,0
4,2
0,2
0,1
4,1
2,0
10
Blind Search – Depth First
0,0
0,3
4,3
4,0
3,0
3,3
4,2
0,2
2,0
11
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)
12
Travelling salesman problem

A salesman must visit 5 cities. What is the
shortest route?
Aberdeen Brighton
Cardiff
Dover
Edinburgh
Aberdeen
0
594
524
619
127
Brighton
594
0
184
78
467
Cardiff
524
184
0
233
395
Dover
619
78
233
0
493
Edinburgh
127
467
395
493
0
13
Travelling salesman problem
A
594
619
B
C
524
184
78
184
233
C
D
B
D
233
233
D
C
1011
905
78
D
786
No of paths = (n-1)!
D
233
C
78
184
78
B
184
B
B
C
835
1036
881
n=4, p=6
n=5, p=24
n=10, p=362,880
14
Heuristic Search

heuristic = rule of thumb
A
594
B
C
524
127
619
D
E
467
B
395
C
184
B
493
D
233
D
78
784
D
15