Reasoning Systems Chapter 4. Dr Ahmed Rafea

Transcription

1 Reasoning Systems Chapter 4 Dr Ahmed Rafea

2 Introduction In this chapter we will explore how the various knowledge representations can be used for reasoning We will explore : Reasoning with rules Forward chaining Backward chaining Fuzzy rule systems

3 Reasoning with Rules-1 If-then rules became the most popular form of declarative knowledge representation used in AI applications 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 engine, which contains the reasoning logic used to process the rules r or data Given the following rule: If num_wheels = 4 and motor = yes then vehicletypt = automobile This rule has two antecedent clause joined by a conjunction (If num_wheels = 4 and motor = yes ) and a single consequent clause (then vehicletype = automobile). The rule states a relationship between clauses and depending on the situation, we can generate new information or prove the truth of the assertion. For example, if we know that the a vehicle has 4 wheels and a motor, we can conclude that the vehicletype is an automobile and add that fact to our knowledge base.

4 Reasoning with Rules-2 A rule whose antecedent clauses are all true is said to be triggered or ready to fire. We fire a rule by asserting the consequent clause and adding it as a fact to our working memory Most rule-based systems allow rules to have labels or names such as Rule1: or Automobile: For example: Rule1: If num_wheels = 4 and motor = yes then vehicletypt = automobile Another enhancement to rule syntax is the addition of a certainty factor. This enables us to have a large knowledge base because we cant write rules that applied 100% of the time with 100% confidence. For example: Rule1: if (weather_forecast( = rain) and (weather_probability( > 80%) Then (chance_of_rain( = high) with CF:90

5 Reasoning with Rules-3 Many rule-based systems allow functions to be called from the antecedent clauses. These functions are called sensors. When functions are allowed in the consequent, they are called effectors Rule:2 if sensor(mailarrived) ) then affector(processmail) The main problem in rule-based systems is as the number of rules grows, the if-then rules lose their effectiveness from a readability perspective. Also as more complex information comes in, or as things change in the real world, rules that may have been true before become false. The problem of dealing with changes is called non-monotonic reasoning Most reasoning systems, such as predicate logic, are monotonic, they add information but do not retract information from the knowledge base

6 Reasoning with Rules-4 This is a an example for a rule-base system. It include nine rules Vehicle Rule Base: Bicycle: if vehicletype = cycle And num_wheels = 2 And motor = no Then vehicle = Bicycle Tricycle: if vehicletype = cycle And num_wheels = 3 And motor = no Then vehicle = Tricycle Motorcycle: if vehicletype = cycle And num_wheels = 2 And motor = yes Then vehicle = Motorcycle Sportscar: if vehicletype = automobile And size = small And num_doors = 2 Then vehicle = Sportscar

7 Reasoning with Rules-5 Sedan: if vehicletype = automobile And size = small And num_doors = 4 Then vehicle = Sedan MiniVan: if vehicletype = automobile And size = medium And num_doors = 3 Then vehicle = MiniVan SUV: if vehicletype = automobile And size = large And num_doors = 4 Then vehicle = Sports_utility_vehicle Cycle: if num_wheels < 4 Then vehicletype = Cycle Automobile: if num_wheels = 4 And motor = yes Then vehicletype = automobile

8 Forward chaining-1 Forward chaining is a reasoning process in which a set of rules is used to derive new facts from an initial set of data. The forward chaining cycle: 1. load the rule base into the inference engine and load any facts from the knowledge base into the working memory 2. add any additional data into the working memory 3. match the rules against the data in the working memory and determine which rules are triggered, meaning that all of their antecedent clauses are true. This set is called conflict set 4. use the conflict resolution procedure to select a single rule from the conflict set 5. fire the selected rule by evaluating the consequent clause; either er update the 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 6. repeat steps 3,4, and 5 until the conflict set is empty

9 Forward chaining-2 The match phase can take an enormous amount of processing time. Thus, we would like to only test those rules whose antecedent clauses refer to facts that have been updated by the prior rule s firing. This job is done by the Rete Rete algorithm In the conflict resolution step we have to make wise decisions in i selecting which rule to be fires. We can: Select the first rule in the conflict set Select the rule with the highest number of antecedent clauses Select the rule that refers to the data that has changed most recently When there is a tie, select a rule randomly Assign priorities to the rules, and select the one with the highest priority. This reduces the number of rules that have to be searched and tested in the match phase

10 A Forward Chaining Example-1 we load our vehicles rule base into the inference engine and define a set of initial values for variables in the working memory as follows: Num_wheels = 4 Motor = yes Num_doors = 3 Size = medium next we do a match phase to examine the antecedent clauses of each rule to determine which ones can be triggered. We have no value for vehicletype so the first seven rules are not triggered. The last two rules require values for num_wheels and motor, so they are candidates. The num_wheel is 4 and motor is yes are both true so the Automobile rule is triggered conflict resolution is easy. We select a single rule and fire it in the act cycle. Firing the Automobile rule gives us the following working memory: Num_wheels = 4 Motor = yes Num_doors = 3 Size = medium vehicletype = automobile

11 A Forward Chaining Example-2 now we are ready for our next inferencing cycle. We do match against the rules to determine which one to be fires. Now that the vehicletype has a value the first seven rules are candidates Only single rule will have all of its antecedent clauses satisfied, the MiniVan: rule. So we fire the MiniVan rule and add the new information that vehicle = MiniVan to the working memory Num_wheels = 4 Motor = yes Num_doors = 3 Size = medium vehicletype = automobile Vehicle = MiniVan We match again to find that the only rule that is triggered is the t MiniVan: rule. However because it has already fired we don t add it to the e conflict set

12 Backward Chaining In backward chaining a consequence is evaluated and then we go backward through the rule. It uses rules to answer questions about whether a clause is true or not. The backward chaining cycle: 1. load the rule base into the inference engine and load any facts from the knowledge base into the working memory 2. Add any additional data into the working memory 3. specify a goal variable for the inference engine to find 4. find the set of rules that refer to the goal variable in a consequent clause. Put each rule on the goal stack 5. if the goal stack is empty, halt 6. take the top rule off the goal stack. 7. try to prove that the rule is true by testing all the antecedent clauses to see if 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 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

13 A Backward Chaining Example-1 This is the rule that must be satisfied: MiniVan: : if vehicletype = automobile And size = medium And num_doors = 3 Then vehicle = MiniVan we start with an empty working memory and we check to see if vehicle = MiniVan is already true. If not, then all the antecedent clauses of the MiniVan rule: must be true to conclude that the vehicle is MiniVan.. So we test if the vehicletype = automobile is true. The vehicletype has no value, so we look for a rule that has the vehicletype = automobile, and we find the Automobile: rule below: Automobile: if num_wheels = 4 And motor = yes then vehicletype = automobile This is backward chaining, we started with the MiniVan: : rule, and, in the course of proving that true, we chained to another rule, the Automobile: rule

14 A Backward Chaining Example-2 Focused now on the Automobile: rule we need to know if num_wheels = 4. we look in the working memory and see that it has no value. We look for a rule that has the num_wheels = 4 as a consequent. There are none. So we ask the user to provide an answer. And he says that there are four wheels on the vehicle. The first antecedent rule is true, so we move to the second clause, motor = yes. 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 vehicle has a motor. Now that both clauses are true, we proved that the Automobile rule is true, and we set the vehicletype=automobile.

15 A Backward Chaining Example-3 Our working memory now contains the following fact: Num_wheels = 4 motor = yes VehicleType = automobile back to our original rule. We know the first antecedent clause is true. We need next to find values for the size and num_doors.. Using the same procedure, we end up asking the user for these values. And he indicates that the size=medium and num_doors=3. all the antecedent clauses have been satisfied, so we can conclude that the vehicle is a MiniVan.. Our final memory contains: Num_wheels = 4 motor = yes VehicleType = automobile Size = medium Num_doors = 3 Vehicle = MiniVan

16 Fuzzy Rule System-1 Fuzzy logic has provided an alternative to Boolean logic-based system. It is not just probability in a different guise. Probability theory deals with the likelihood that an event will occur Tomorrow there is a 50% chance that it will rain, While fuzzy logic deals with the degree to which an event will occur, Tomorrow it will rain hard Unlike Boolean logic, fuzzy logic deals with truth values which range continuously from 0.0 to 1.0. Therefore, something could be half true (0.5) or very likely true (0.9)

17 Fuzzy Rule System-2 This is a fuzzy rule to control the speed of the motor of a fan: Motor Fuzzy Rule Base SlowRule: : if temp is cold And humidity is pleasant Then motor is slow MediumRule: : if temp is medium And humidity is comfortable Then motor is medium FastRule: : if temp is hot And humidity is sticky Then motor is fast VeryFastRule: : if temp is very hot And humidity is very sticky Then motor is very fast

18 Fuzzy Rule System-3 Reasoning in fuzzy rule systems is a forward chaining procedure. The initial data values are fuzzified,, that is, turned into fuzzy values using the membership functions. Instead of the match and conflict resolution phase, all rules are evaluated (rule can be true to some degree 0.0 to 1.0). There are two methods of inferencing in fuzzy rule systems, the min-max max approach and the fuzzy additive approach. In the min-max max approach the following steps are done: The antecedent truth values are combined using fuzzy logic operators (and), which takes the minimum value of the antecedent clauses. the consequent fuzzy set is limited to the minimum of the antecedent truth value or multiplied by the antecedent truth value The output fuzzy set is computed by taking the maximum of the minimized consequent fuzzy set from each rule.

19 Fuzzy Rule System-4 In the additive approch,, the following steps are done: The antecedent truth values are combined using fuzzy logic operators (and), which takes the minimum value of the antecedent clauses. It limits the consequent fuzzy set as in the minmax method. The output fuzzy set is computed by adding the consequent fuzzy set from each rule and limiting it to a maximum value of 1.0. This insures that all the rules in the fuzzy set can contribute something to the final result set. The methods for limiting the height of the consequent based on the minimum truth value of the antecedents (minimum correlation), truncates the consequent fuzzy set to the minimum of the antecedent s truth value, while the product correlation, maintains the shape of the consequent fuzzy set by scaling it by the truth value of the antecedent After the fuzzy set is computed using one of the correlation and inferencing techniques, the fuzzy set is defuzzified.

20 Fuzzy Rule System-5 There are two techniques for defuzzification, centroid and maximum height. In centroid defuzzification,, the center of gravity of the fuzzy set is found by computing a weighted mean of the fuzzy set. This means that half of the area under the membership function is above the centroid point, and the other half is below it. The maximum height finds the center point in the region with the maximum truth value. Consequently if the fuzzy set came to a plateau, the defuzzified value would be the center of the plateau