Reasoning Systems Reasoning Systems Chapter 4 Chapter 4 Dr Ahmed - - PowerPoint PPT Presentation
Reasoning Systems Reasoning Systems Chapter 4 Chapter 4 Dr Ahmed Rafea Rafea Dr Ahmed Introduction Introduction In this chapter we will explore how the various In this chapter we will explore how the various knowledge
If
If-
then rules became the most popular form of declarative knowledge representation used in AI applications knowledge representation used in AI applications
A knowledge
A knowledge-
based system is the common term to describe a rule-
based processing system. It consists of three major elements: a knowledge base, a working memory (database), and an inference knowledge base, a working memory (database), and an inference engine, which contains the reasoning logic used to process the r engine, which contains the reasoning logic used to process the rules ules
Given the following rule:
Given the following rule:
If num_wheels = 4 and motor = yes
If num_wheels = 4 and motor = yes
then vehicleTypt = automobile then vehicleTypt = automobile
This rule has two antecedent clause joined by a conjunction (If
This rule has two antecedent clause joined by a conjunction (If num_wheels = 4 and motor = yes ) and a single consequent clause num_wheels = 4 and motor = yes ) and a single consequent clause (then vehicleType = automobile). The rule states a relationshi (then vehicleType = automobile). The rule states a relationship p between clauses and depending on the situation, we can generate between clauses and depending on the situation, we can generate new information or prove the truth of the assertion. new information or prove the truth of the assertion.
For example, if we know that the a vehicle has 4 wheels and a mo
For example, if we know that the a vehicle has 4 wheels and a motor, tor, we can conclude that the vehicleType is an automobile and add th we can conclude that the vehicleType is an automobile and add that at fact to our knowledge base. fact to our knowledge base.
A rule whose antecedent clauses are all true is said to be trigg
A rule whose antecedent clauses are all true is said to be triggered ered
use and adding it as a fact to our working memory and adding it as a fact to our working memory
Most rule
Most rule-
based systems allow rules to have labels or names such as Rule1: or Automobile: as Rule1: or Automobile:
For example:
For example:
Rule1: If
Rule1: If num_wheels num_wheels = 4 and motor = yes = 4 and motor = yes
then then vehicleTypt vehicleTypt = automobile = automobile
Another enhancement to rule syntax is the addition of a certaint
Another enhancement to rule syntax is the addition of a certainty y
we cant write rules that applied 100% of the time with 100% we cant write rules that applied 100% of the time with 100%
Rule1: if (
Rule1: if (weather_forecast weather_forecast = rain) and ( = rain) and (weather_probability weather_probability > 80%) > 80%)
Then ( Then (chance_of_rain chance_of_rain = high) with CF:90 = high) with CF:90
Many rule
Many rule-
based systems allow functions to be called from the antecedent clauses. These functions are called sensors. When antecedent clauses. These functions are called sensors. When functions are allowed in the consequent, they are called effecto functions are allowed in the consequent, they are called effectors rs
Rule:2 if
Rule:2 if sensor(mailArrived sensor(mailArrived) then ) then affector(processMail affector(processMail) )
The main problem in rule
The main problem in rule-
based systems is as the number of rules grows, the if rules grows, the if-
then rules lose their effectiveness from a readability perspective . Also as more complex information readability perspective . Also as more complex information comes in, or as things change in the real world, rules that may comes in, or as things change in the real world, rules that may have been true before become false. have been true before become false.
The problem of dealing with changes is called non
The problem of dealing with changes is called non-
monotonic reasoning reasoning
Most reasoning systems, such as predicate logic, are monotonic,
Most reasoning systems, such as predicate logic, are monotonic, they add information but do not retract information from the they add information but do not retract information from the knowledge base knowledge base
This is a an example for a rule-base system. It include nine rules base system. It include nine rules Vehicle Rule Base: Vehicle Rule Base: Bicycle: if Bicycle: if vehicleType vehicleType = cycle = cycle And And num_wheels num_wheels = 2 = 2 And motor = no And motor = no Then vehicle = Bicycle Then vehicle = Bicycle Tricycle: if Tricycle: if vehicleType vehicleType = cycle = cycle And And num_wheels num_wheels = 3 = 3 And motor = no And motor = no Then vehicle = Tricycle Then vehicle = Tricycle Motorcycle: if Motorcycle: if vehicleType vehicleType = cycle = cycle And And num_wheels num_wheels = 2 = 2 And motor = yes And motor = yes Then vehicle = Motorcycle Then vehicle = Motorcycle Sportscar Sportscar: if : if vehicleType vehicleType = automobile = automobile And size = small And size = small And And num_doors num_doors = 2 = 2 Then vehicle = Then vehicle = Sportscar Sportscar
Sedan: if Sedan: if vehicleType vehicleType = automobile = automobile And size = small And size = small And And num_doors num_doors = 4 = 4 Then vehicle = Sedan Then vehicle = Sedan MiniVan MiniVan: if : if vehicleType vehicleType = automobile = automobile And size = medium And size = medium And And num_doors num_doors = 3 = 3 Then vehicle = Then vehicle = MiniVan MiniVan SUV: if SUV: if vehicleType vehicleType = automobile = automobile And size = large And size = large And And num_doors num_doors = 4 = 4 Then vehicle = Then vehicle = Sports_utility_vehicle Sports_utility_vehicle Cycle: if Cycle: if num_wheels num_wheels < 4 < 4 Then Then vehicleType vehicleType = Cycle = Cycle Automobile: if Automobile: if num_wheels num_wheels = 4 = 4 And motor = yes And motor = yes Then Then vehicleType vehicleType = automobile = automobile
Forward chaining is a reasoning process in which a set of rules is is used to derive new facts from an initial set of data. used to derive new facts from an initial set of data.
The forward chaining cycle:
1. 1.
load the rule base into the inference engine and load any facts load the rule base into the inference engine and load any facts from the from the knowledge base into the working memory knowledge base into the working memory
2. 2.
add any additional data into the working memory add any additional data into the working memory
3. 3.
match the rules against the data in the working memory and deter match the rules against the data in the working memory and determine mine which rules are triggered, meaning that all of their antecedent which rules are triggered, meaning that all of their antecedent clauses are clauses are
4. 4.
use the conflict resolution procedure to select a single rule fr use the conflict resolution procedure to select a single rule from the conflict
set set
5. 5.
fire the selected rule by evaluating the consequent clause; eith fire the selected rule by evaluating the consequent clause; either update the er update the working memory if it is a fact working memory if it is a fact-
generating rule, or call the effector procedure, if it is an action rule. This is referred to as the act step if it is an action rule. This is referred to as the act step
6. 6.
repeat steps 3,4, and 5 until the conflict set is empty repeat steps 3,4, and 5 until the conflict set is empty
The match phase can take an enormous amount of processing
The match phase can take an enormous amount of processing
antecedent clauses refer to facts that have been updated by the antecedent clauses refer to facts that have been updated by the prior rule’s firing. This job is done by the “ prior rule’s firing. This job is done by the “Rete Rete” algorithm ” algorithm
In the conflict resolution step we have to make wise decisions i
In the conflict resolution step we have to make wise decisions in n selecting which rule to be fires. We can: selecting which rule to be fires. We can:
Select the first rule in the conflict set
Select the first rule in the conflict set
Select the rule with the highest number of antecedent clauses
Select the rule with the highest number of antecedent clauses
Select the rule that refers to the data that has changed most re
Select the rule that refers to the data that has changed most recently cently
When there is a tie, select a rule randomly
When there is a tie, select a rule randomly
Assign priorities to the rules, and select the one with the high
Assign priorities to the rules, and select the one with the highest priority. est priority. This reduces the number of rules that have to be searched and te This reduces the number of rules that have to be searched and tested in sted in the match phase the match phase
we load our vehicles rule base into the inference engine and define a set of initial ine a set of initial values for variables in the working memory as follows: values for variables in the working memory as follows:
Num_wheels = 4 = 4
Motor = yes
Num_doors = 3 = 3
Size = medium
next we do a match phase to examine the antecedent clauses of each rule to determine ch rule to determine which ones can be triggered. We have no value for which ones can be triggered. We have no value for vehicleType vehicleType so the first seven rules so the first seven rules are not triggered. The last two rules require values for are not triggered. The last two rules require values for num_wheels num_wheels and motor, so they and motor, so they are candidates. The are candidates. The num_wheel num_wheel is 4 and motor is yes are both true so the Automobile is 4 and motor is yes are both true so the Automobile rule is triggered rule is triggered
conflict resolution is easy. We select a single rule and fire it in the act cycle. Firing the in the act cycle. Firing the Automobile rule gives us the following working memory: Automobile rule gives us the following working memory:
Num_wheels = 4 = 4
Motor = yes
Num_doors = 3 = 3
Size = medium
vehicleType = automobile = automobile
now we are ready for our next inferencing inferencing cycle. We do match against the
rules to determine which one to be fires. Now that the rules to determine which one to be fires. Now that the vehicleType vehicleType has a has a value the first seven rules are candidates value the first seven rules are candidates
Only single rule will have all of its antecedent clauses satisfied, the ed, the MiniVan MiniVan: :
MiniVan rule and add the new information that vehicle = rule and add the new information that vehicle = MiniVan MiniVan to the working memory to the working memory
Num_wheels = 4 = 4
Motor = yes
Num_doors = 3 = 3
Size = medium
vehicleType = automobile = automobile
Vehicle = MiniVan MiniVan
We match again to find that the only rule that is triggered is the he MiniVan MiniVan: :
e conflict set
In backward chaining a consequence is evaluated and then we go backward through the rule. It uses rules to answer questions abo backward through the rule. It uses rules to answer questions about ut whether a clause is true or not. whether a clause is true or not.
The backward chaining cycle:
1. 1.
load the rule base into the inference engine and load any facts load the rule base into the inference engine and load any facts from the from the knowledge base into the working memory knowledge base into the working memory
2. 2.
Add any additional data into the working memory Add any additional data into the working memory
3. 3.
specify a goal variable for the inference engine to find specify a goal variable for the inference engine to find
4. 4.
find the set of rules that refer to the goal variable in a conse find the set of rules that refer to the goal variable in a consequent clause. Put quent clause. Put each rule on the goal stack each rule on the goal stack
5. 5.
if the goal stack is empty, halt if the goal stack is empty, halt
6. 6.
take the top rule off the goal stack. take the top rule off the goal stack.
7. 7.
try to prove that the rule is true by testing all the antecedent try to prove that the rule is true by testing all the antecedent clauses to see if clauses to see if they are true, as follows: they are true, as follows:
If the clause is true, go on to the next antecedent clause
If the clause is false, pop the rule off the stack and go to step 5 p 5
If the truth value is unknown, go to step 4
If all antecedent clauses are true, fire the rule, pop the rule off the stack, and go to
step5 step5
This is the rule that must be satisfied:
MiniVan: if : if vehicleType vehicleType = automobile = automobile
And size = medium And size = medium And And num_doors num_doors = 3 = 3 Then vehicle = Then vehicle = MiniVan MiniVan
we start with an empty working memory and we check to see if vehicle = hicle = MiniVan MiniVan is already true. If not, then all the antecedent clauses of the is already true. If not, then all the antecedent clauses of the MiniVan MiniVan rule: must be true to conclude that the vehicle is rule: must be true to conclude that the vehicle is MiniVan
. So we test if the vehicleType vehicleType = automobile is true. The = automobile is true. The vehicleType vehicleType has no value, so we look has no value, so we look for a rule that has the for a rule that has the vehicleType vehicleType = automobile, and we find the = automobile, and we find the Automobile: rule below: Automobile: rule below:
Automobile: if num_wheels num_wheels = 4 = 4 And motor = yes And motor = yes then then vehicleType vehicleType = automobile = automobile
This is backward chaining, we started with the MiniVan MiniVan: rule, and, in the : rule, and, in the course of proving that true, we chained to another rule, the Aut course of proving that true, we chained to another rule, the Automobile: rule
Focused now on the Automobile: rule we need to know if
Focused now on the Automobile: rule we need to know if num_wheels num_wheels = 4. we look in the working memory and see that it = 4. we look in the working memory and see that it has no value. We look for a rule that has the has no value. We look for a rule that has the num_wheels num_wheels = 4 as = 4 as a consequent. There are none. So we ask the user to provide an a consequent. There are none. So we ask the user to provide an
The first antecedent rule is true, so we move to the second The first antecedent rule is true, so we move to the second clause, motor = yes. clause, motor = yes.
we check the working memory, and the motor has no value. We
we check the working memory, and the motor has no value. We again ask the user to provide a value. The user answers that the again ask the user to provide a value. The user answers that the vehicle has a motor. Now that both clauses are true, we proved vehicle has a motor. Now that both clauses are true, we proved that the Automobile rule is true, and we set the that the Automobile rule is true, and we set the vehicleType vehicleType=automobile. =automobile.
Our working memory now contains the following fact:
Num_wheels = 4 = 4
motor = yes
VehicleType = automobile = automobile
back to our original rule. We know the first antecedent clause is true. We is true. We need next to find values for the size and need next to find values for the size and num_doors num_doors. Using the same . Using the same procedure, we end up asking the user for these values. And he in procedure, we end up asking the user for these values. And he indicates that dicates that the size=medium and the size=medium and num_doors num_doors=3. all the antecedent clauses have been =3. all the antecedent clauses have been satisfied, so we can conclude that the vehicle is a satisfied, so we can conclude that the vehicle is a MiniVan
. Our final memory contains: contains:
Num_wheels = 4 = 4
motor = yes
VehicleType = automobile = automobile
Size = medium
Num_doors = 3 = 3
Vehicle = MiniVan MiniVan
Tomorrow there is a 50% chance that it will rain,
Tomorrow there is a 50% chance that it will rain,
Tomorrow it will rain hard
Tomorrow it will rain hard
This is a fuzzy rule to control the speed of the motor of a fan:
This is a fuzzy rule to control the speed of the motor of a fan:
Motor Fuzzy Rule Base
Motor Fuzzy Rule Base
SlowRule SlowRule: if temp is cold : if temp is cold And humidity is pleasant And humidity is pleasant Then motor is slow Then motor is slow MediumRule MediumRule: if temp is medium : if temp is medium And humidity is comfortable And humidity is comfortable Then motor is medium Then motor is medium FastRule FastRule: if temp is hot : if temp is hot And humidity is sticky And humidity is sticky Then motor is fast Then motor is fast VeryFastRule VeryFastRule: if temp is very hot : if temp is very hot And humidity is very sticky And humidity is very sticky Then motor is very fast Then motor is very fast
Reasoning in fuzzy rule systems is a forward chaining procedure.
Reasoning in fuzzy rule systems is a forward chaining procedure. The initial data values are The initial data values are fuzzified fuzzified, that is, turned into fuzzy , that is, turned into fuzzy values using the membership functions. Instead of the match values using the membership functions. Instead of the match and conflict resolution phase, all rules are evaluated (rule can and conflict resolution phase, all rules are evaluated (rule can be be true to some degree 0.0 to 1.0). true to some degree 0.0 to 1.0).
There are two methods of
There are two methods of inferencing inferencing in fuzzy rule systems, the in fuzzy rule systems, the min min-
max approach and the fuzzy additive approach.
In the min
In the min-
max approach the following steps are done:
The antecedent truth values are combined using fuzzy logic opera
The antecedent truth values are combined using fuzzy logic operators tors (and), which takes the minimum value of the antecedent clauses. (and), which takes the minimum value of the antecedent clauses.
the consequent fuzzy set is limited to the minimum of the antece
the consequent fuzzy set is limited to the minimum of the antecedent dent truth value or multiplied by the antecedent truth value truth value or multiplied by the antecedent truth value
The output fuzzy set is computed by taking the maximum of the
The output fuzzy set is computed by taking the maximum of the minimized consequent fuzzy set from each rule. minimized consequent fuzzy set from each rule.
In the additive
In the additive approch approch, the following steps are done: , the following steps are done:
The antecedent truth values are combined using fuzzy logic operators (and), tors (and), which takes the minimum value of the antecedent clauses. which takes the minimum value of the antecedent clauses.
It limits the consequent fuzzy set as in the minmax minmax method. method.
The output fuzzy set is computed by adding the consequent fuzzy set from each set from each rule and limiting it to a maximum value of 1.0. This insures th rule and limiting it to a maximum value of 1.0. This insures that all the rules in at all the rules in the fuzzy set can contribute something to the final result set. the fuzzy set can contribute something to the final result set.
The methods for limiting the height of the consequent based on
The methods for limiting the height of the consequent based on the minimum truth value of the antecedents (minimum the minimum truth value of the antecedents (minimum correlation), truncates the consequent fuzzy set to the minimum correlation), truncates the consequent fuzzy set to the minimum
maintains the shape of the consequent fuzzy set by scaling it by maintains the shape of the consequent fuzzy set by scaling it by the truth value of the antecedent the truth value of the antecedent
After the fuzzy set is computed using one of the correlation and
After the fuzzy set is computed using one of the correlation and inferencing inferencing techniques, the fuzzy set is techniques, the fuzzy set is defuzzified defuzzified. .