Rule Based Systems
Rule based systems / Knowledge based systems/ Expert Systems
have played and plays an important role in the AI industry.
A report from from 1993 by John Durkin:
Reports on Over 2500 Developed Expert Systems
Application areas:
Agriculture, Business, Chemistry, Communications, Computer Systems,
Education, Electronics, Engineering, Environment, Geology, Image processing,
Information Management, Law, Manufacturing, Mathematics, Medicine,
Meteorology, Military, Mining, Power Systems, Science, Space Technology,
Transportation
Types of systems:
Rule Based, Frame Based, Fuzzy Logic, Case Based, Neural Network
Architecture of a typical expert system
User
interface:
Question-andanswer
Knowledge base
Knowledgebase editor
Menu driven
User
Natural
language
Graphic
inteface
Expert system shell
Inference
engine
General
knowledgebase
Case-specific
data
Explanation
subsystem
AI in Medicine (USA 1970)
•
Stanford
MYCIN - blood infections
•
Rutgers
CASNET - casual reasoning
•
MIT
PIP - renal disease
•
Stanford
•
Pittsburgh
Internist – internal medicine
- ”the primary goal of this field is to develop
computer programs that perform efficiently and are
able to explain their reasoning and conclusions to
their users”
MYCIN’S knowledge base
•About 400 diagnostic rules
•About 5 therapy rules
Why Mycin?
•Diagnose likely infecting organisms in blood and
meningitis infections
•Use test results and information about patient supplied by
doctor
•Prescribe an effective antibiotic treatment
•Do this early in the course of the disease, before all
possible information is available
•To counteract:
- overuse of antibiotics
- irrational use of antibiotics
-maldistribution of expertise
Mycin system for diagnosis og meningitis and
bacteremia (bacterial infections)
IF
the site of the culture is blood, and
the identity of the organism is
not known with certainty, and
the stain of the organism is gramneg, and
the morphology of the organism is rod, and
the patient has been seriously burned
THEN
there is weakly suggestive evidence (0.4) that
the identity of the
organism is pseudomonas
MYCIN diagnosis rule (2)
IF
the site of the culture is blood, and
the identity of the organism is gramneg, and
the morphology of the organism is rod, and
the patient
is a compromised host
THEN
there is
suggestive evidence (0.6) that
the identity of the organism is pseudomonas-Aeruginosa
MYCIN diagnosis rule (3)
Rule 3
IF (1) stain of organism is gram-positive and
(2) morphology of organism is coccus and
(3) growth-conformation of the organism is clumps
THEN there is suggestive evidence (0.7) that
identity of organism is staphylococcus.
MYCIN diagnosis rule (3)
(CEFAX notation )
rule 3
if
stain of organism is gram_positive and
morphology of organism is coccus and
growth_conformation of organism is clumps
then 0.7 certainty
identity of organism is staphylococcus.
MYCIN: Therapy Selection Rule
IF You are considering giving chloramphenicol,
and
the patient is less than 1 week old
THEN it is definite (1.0) that chlorampericol is
contraindicated for this patient
[Justification: Newborn infants may develop
vasomusculular collapse due to an immaturity of
the liver and kidney functions resulting in
decreased metabolism of chloramphenicol]
How does MYCIN create confidence
in the user
Answering ”Why?” (Why did you ask that?)
Answering ”How” (How did you arraive at that conclusion?)
Answering ”Why not X?” (Why did you not consider X?)
Mycin’s simple rule format and friendly explanations in
”English” are the key.
MYCIN Explanation
User:
Why didn’t you consider Streptococcus as a possiblity
for Organism- 1
MYCIN: The following rule could have been used to
determine that the identoty of Organism-1 was streptococcus:
Rule 33
But Clause 2 (”the morphology of the organism is
Coccus”) was already known to be false for Organism-1, so the
rule was never tried.
How MYCIN looks to the user:
Therapy recommendation
[REC-1] My preferred therapy recommendation is as
follows:
In order to cover for items <1 2 3 4 5Z:
Give the following in combination
1: Kanamycin
Dose 750 mg (7.5 mg(kg)q12h IM (or IV)
for 28 days
Comments: Modify dose in renal failure
2: Penicillin
Dose: 2,500,000 units (2500 units/kg) q4h IV
for 28 days
Emycin and expert system shell
MYCIN has later been developed, and separated into
to parts:
An expert system shell EMYCIN (empty MYCIN)
A knowledg base
The expert system shell EMYCIN is ”the mother of
all expert system shells”.
One simplified version is called CEFAX is
implemented at NTNU in Prolog
Rule based system as a reasoning system
If we look aside from the uncertainties in MYCIN, the system
can be regarded as logical inference system, where the
explanation is the proof tree of the reasoning.
A bank clerk shall approve loans for customers. He collects the
basic information about the customer, which is represented as a
set of variables:
Basic variables
APP (the appraisal on the collateral is greater than the loan amount)
RATING (The applicant has a good credit rating)
INC (The applicant’s income exceeds his expenses)
BAL (The applicant has an excellent balance sheet)
Derived variables
OK (The loan should be approved)
COLLAT(The collateral for the loan is satisfactory)
PYMT (The applicant is able to make the loan payments)
REP (The applicant has a good financial reputation)
The loan approval rule base
He follows the banks guidelines, which can be stated as follows
(1)
(2)
(3)
(4)
(5)
COLLAT  PYMT  REP  OK
APP  COLLAT
RATING  REP
INC  PYMT
BAL  REP  OK
A loan application case
Mr John Smith has applied for a loan. His case is:
APP is true, INC is true, RATING is true, BAL is true
That his loan can be approved follows from the following proof tree
(Rule numbers in parentheses)
approval
OK
OK
(1)
(5)
COLLAT PYMT REP
(2)
APP
BAL
REP
(4)
(3)
(3)
INC
RATING
RATING
The loan approval as a rule based system
rule 1
if
collat is true and
pymt is true and
rep is true
rule 4
if
inc is true
then 1.0 certainty
pymt is true.
then 1.0 certainty
ok is true.
rule 2
if app is true
then 1.0 certainty
collat is true.
rule 3
if
rating is true
then 1.0 certainty
rep is true.
rule 5
if
and
bal is true
rep is true
then 1.0 certainty
ok is true.
A loan approval “real” dialog
User: Why do you believe that the loan should be approved
System: Because the collateral for the loan is satisfactory, and the applicant is able to
make the loan payments, and the applicant has a good financial reputation.
User: Why do you believe that the applicant has a good financial reputation ?
System: Because the credit-rating service said that the applicant has a good credit rating.
User: Why did you ask me about whether or not the applicant’s income exceeds his
expenses ?
System: Because I was trying to establish whether or not the applicant is able to make
the loan payments.
User: Why are you trying to establish whether or not the applicant is able to make loan
payments.
System: Because that is one of the criteria whether or not the loan should be approved.
User: Why are you trying to establish whether or not the loan should be approved ?
System: Because you asked me to.
An expert system loan approval dialog
?- eval ok.
What is the certainty of app is true --> 1.0.
What is the certainty of inc is true --> why.
I ask because
rule 4 if inc is true
then 1.00 certainty pymt is true .
I ask because
rule 1 if collat is true and pymt is true and
then 1.00 certainty ok is true .
The last conclusion was your original problem .
What is the certainty of inc is true --> 1.0.
What is the certainty of rating is true --> 1.0.
What is the certainty of bal is true --> 1.0.
ok is true IS PROVED ( 1.00)
(help./ how./ ok./ quit./ ) ?
rep is true
Loan approval proof
Dialog and proof of Loan approval are
shown here
PRO/loanapproval.txt
PRO/loanproof.txt
ok is true IS PROVED ( 1.00)
rep is true IS PROVED ( 1.00)
(help./ how./ ok./ quit./ ) ?
BECAUSE
|: how.
by rule 3 :
BECAUSE
rep is true IS PROVED ( 1.00)
contributions
BECAUSE
by rule 1 :
rating is true IS PROVED ( 1.00)
ok is true IS PROVED ( 1.00)
BECAUSE
BECAUSE
rating is true is given
collat is true IS PROVED ( 1.00)
BECAUSE
by rule 5 :
ok is true IS PROVED ( 1.00)
by rule 2 :
BECAUSE
collat is true IS PROVED ( 1.00)
bal is true IS PROVED ( 1.00)
BECAUSE
BECAUSE
app is true IS PROVED ( 1.00)
bal is true is given
BECAUSE
app is true is given
AND
AND
pymt is true IS PROVED ( 1.00)
BECAUSE
by rule 4 :
rep is true IS PROVED ( 1.00)
BECAUSE
by rule 3 :
rep is true IS PROVED ( 1.00)
pymt is true IS PROVED ( 1.00)
BECAUSE
inc is true IS PROVED ( 1.00)
BECAUSE
inc is true is given AND
BECAUSE
rating is true IS PROVED ( 1.00)
BECAUSE
rating is true is given
The Certainty Factor model for
uncertainty handling
Rule 3
IF (1) stain of organism is gram-positive and
(2) morphology of organism is coccus and
(3) growth_conformation of the organism is
clumps
THEN there is suggestive evidence (0.7) that
identity of organism is staphylococcus.
The uncertainty model is based on certainties which are numbers
between –1 and +1. The example 0.7 is a rule parameter that
modifies the certainty of the conclusion.
Uncertainty vs Ignorance
0
0
0 0
0
1
MB
MI
MD
The origin is based on belief intervals.
Measure of Belief [0.0 -- 1.0]
Measure of Disbelief [0.0 -- 1.0]
Certainty Factor = MB – MD = [ - 1.0 -- + 1.0]
Measurements of Ignorance 1.0 – (MB+MD)
Measurement of inconsistency MB+MD –1.0 (= -MI)
Uncertainty: Is it raining in Trondheim tomorrow ?
Ignorance : Is it raining in Kuala Lumpur tomorrow ?
Statistical interpretations
Characteristics
Ranges
Values
0 <= MB <= 1
0 <= MD <= 1
-1 <= CF <= 1
Certain True Hypothesis
MB=1
P(H|E) =1
MD=0
CF =1
Certain False Hypothesis
MB=0
P(-H|E) =1
MD=1
CF = -1
Lack of evidence
MB=0
P(H|E) =P(H)
MD=0
CF = 0
Contradictory evidence
MB=1
MD=1
CF = 0
Manipulation of CF-values
Usually, we use only one CF value, so we don’t distinguish
between ignorance and inconsistency.
CF rule principle
if
P
then
CF certainty Q
CF(P)
computed
CF(Q) =
parameter
CF(Q)
defined
computed
CF(P) *CF
CF(P) >0
0
otherwise
Antecedent Combination Rule
The CF values of the premise is computed together
If A and B then CF
C
(CF = 0.6)
A
CF(A)
B
CF(B)
(0.5)
(0,7)
CF(A and B) = min(CF(A),CF(B)) = (0.5)
CF (C ) = CF * CF(A and B) = (0.3)
Similarily
CF(A or B) = max (CF(A),CF(B))
CF(not B) = - CF(B)
Serial Combination Rule
The CF-values are chained together with the
rule applications
IF AA
THEN
CF1
CF(AA)=0.5
IF B THEN
(0.35)
(0.7)
CF2
(0.3)
B
=> CF(B)=0.35
C
=> CF(C) = 0.105
Paralell combination rule
Accumulation of CF-values, contribution from several rules
(1) IF AA1 then xx
R ( CF(R1)= P)
(2) IF AA2 then yy
R
CF(R) = P + Q – P*Q
R
P
Q
( CF(R1)= Q)
(in the simple case)
Motivation for Parallel rule
Supppose B1 and B2 are two independent stochastic
variables, and that B = B1 or B2
Then
P(B) = P(B1 or B2)
= P(B1) + P(B2) – P(B1 and B2)
= P(B1) + P(B2) – P(B1)*P(B2)
which corresponds to the rule
CF(R) = CF(R1) + CF(R2) – CF(R1)*CF(R2)
The complete parallel rule
CF1 + CF2 – CF1*CF2 (CF1,CF2 >0)
CFparallel(CF1,CF2) =
_
CF1 + CF2 – CF1*CF2 (CF1,CF2 < 0)
(CF1 + CF2)
_________________
(1 – min(|CF1|,|CF2|))
(CF1*CF2 <0)
Motivation for complete parallel rule
Historically, the parallel rule for CF values of opposite sign was just
CF = CF1 + CF2
e.g.
CF1=0.999
(damn sure)
CF2= - 0.799
=>
CF = 0.2 which is unreasonably low
The revised rule gives
CF = 0.995
(almost damn sure)
BUT the old rule also had the defect that
it was not associative and not commutative
Mathematical properties of the revised parallel rule
The parallel rule has some good and obviously required properties
The CF parallel combination rule has some very nice (and obviously
required) mathematical properties:
- it is associative, i.e. evidence may be grouped arbitrarily
- it is commutative, i.e. the sequence of evidence is irrelevant
- it has a zero element, (CF = 0) that has no effect
- it is symmetric, i.e. equal but opposite evidence cancel out
However, the CF parallel combination rule is not idempotent:
C + C - C*C > C (if C >0)
(If you repeat the same weakly supported postulate sufficiently often,
it will be regarded as certain after a while . :-)