Planning Chapter 7 article 7.4 Production Systems Chapter 5 article 5.3 RBSChapter 7 article 7.2

2 RBS CS 331/531 Dr M M Awais RBS: Handling Uncertainties How to handle vague concepts? Why vagueness occurs? All rules are not 100% deterministic Certain rules are often true but not always Headache may be caused in flu, but may not always occur An expert may not always be sure about certain relations and associations

3 RBS CS 331/531 Dr M M Awais First Source of Uncertainty: The Representation Language  There are many more states of the real world than can be expressed in the representation language  So, any state represented in the language may correspond to many different states of the real world, which the agent can’t represent distinguishably A BC A BC A BC On(A,B)  On(B,Table)  On(C,Table)  Clear(A)  Clear(C)

4 RBS CS 331/531 Dr M M Awais First Source of Uncertainty: The Representation Language  6 propositions On(x,y), where x, y = A, B, C and x  y  3 propositions On(x,Table), where x = A, B, C  3 propositions Clear(x), where x = A, B, C  At most 2 12 states can be distinguished in the language [in fact much fewer, because of state constraints such as On(x,y)   On(y,x)]  But there are infinitely many states of the real world A BC A BC A BC On(A,B)  On(B,Table)  On(C,Table)  Clear(A)  Clear(C)

5 RBS CS 331/531 Dr M M Awais Second source of Uncertainty: Imperfect Observation of the World Observation of the world can be:  Partial, e.g., a vision sensor can’t see through obstacles (lack of percepts) R1R1 R2R2 The robot may not know whether there is dust in room R2

6 RBS CS 331/531 Dr M M Awais Second source of Uncertainty: Imperfect Observation of the World Observation of the world can be:  Partial, e.g., a vision sensor can’t see through obstacles  Ambiguous, e.g., percepts have multiple possible interpretations A B C On(A,B)  On(A,C)

7 RBS CS 331/531 Dr M M Awais Second source of Uncertainty: Imperfect Observation of the World Observation of the world can be:  Partial, e.g., a vision sensor can’t see through obstacles  Ambiguous, e.g., percepts have multiple possible interpretations  Incorrect

8 RBS CS 331/531 Dr M M Awais Third Source of Uncertainty: Ignorance, Laziness, Efficiency  An action may have a long list of preconditions, e.g.: Drive-Car: P = Have(Keys)   Empty(Gas-Tank)  Battery-Ok  Ignition-Ok   Flat-Tires   Stolen(Car)...  The agent’s designer may ignore some preconditions... or by laziness or for efficiency, may not want to include all of them in the action representation  The result is a representation that is either incorrect – executing the action may not have the described effects – or that describes several alternative effects

9 RBS CS 331/531 Dr M M Awais Representation of Uncertainty  Many models of uncertainty  We will consider two important models: Non-deterministic model: Uncertainty is represented by a set of possible values, e.g., a set of possible worlds, a set of possible effects,... Probabilistic model: Uncertainty is represented by a probabilistic distribution over a set of possible values

10 RBS CS 331/531 Dr M M Awais Example: Belief State  In the presence of non-deterministic sensory uncertainty, an agent belief state represents all the states of the world that it thinks are possible at a given time or at a given stage of reasoning  In the probabilistic model of uncertainty, a probability is associated with each state to measure its likelihood to be the actual state

11 RBS CS 331/531 Dr M M Awais What do probabilities mean?  Probabilities have a natural frequency interpretation  The agent believes that if it was able to return many times to a situation where it has the same belief state, then the actual states in this situation would occur at a relative frequency defined by the probabilistic distribution This state would occur 20% of the times

12 RBS CS 331/531 Dr M M Awais Example  Consider a world where a dentist agent D meets a new patient P  D is interested in only one thing: whether P has a cavity, which D models using the proposition Cavity  Before making any observation, D’s belief state is:  This means that if D believes that a fraction p of patients have cavities Cavity  Cavity p 1-p

13 RBS CS 331/531 Dr M M Awais Where do probabilities come from?  Frequencies observed in the past, e.g., by the agent, its designer, or others  Symmetries, e.g.: If I roll a dice, each of the 6 outcomes has probability 1/6  Subjectivism, e.g.: If I drive on Highway 280 at 120mph, I will get a speeding ticket with probability 0.6 Principle of indifference: If there is no knowledge to consider one possibility more probable than another, give them the same probability

14 RBS CS 331/531 Dr M M Awais Expert System: A SYSTEM that mimics a human expert Human experts always have in most case some vague (not very precise) ideas about the associations Handling uncertainties is a essential part of an expert system Expert systems are RBS with some level of uncertainty incorporated in the system

15 RBS CS 331/531 Dr M M Awais Choosing a Problem Costs: Choose problems that justify the development cost of the expert systems Technical Problems: Choose a problem that is highly technical in nature problems with Well-formed knowledge are the best choice. Highly specialized expert requirements, solution time for the problem is not short time. Cooperation from an expert: Experts are willingly to participate in the activity.

16 RBS CS 331/531 Dr M M Awais Choosing a Problem Problems that are not suitable Problems for which experts are not available at all, or they are not willingly to participate Problems in which high common sense knowledge is involved Problems which involve high physical skills

17 RBS CS 331/531 Dr M M Awais ES Architecture interface user Explanation system Inference engine Knowledge Base editor Case specific Data Knowledge Base Expert System Shell

18 RBS CS 331/531 Dr M M Awais ES Architecture interface user Explanation system Inference engine Knowledge Base editor Case specific Data Knowledge Base Expert System Shell Uses Menus, NLP, etc… Which is used to interact With the users

19 RBS CS 331/531 Dr M M Awais ES Architecture interface user Explanation system Inference engine Knowledge Base editor Case specific Data Knowledge Base Expert System Shell Explains why a decision is taken, uses keywords Such as HOW, WHY etc… Implements the reasoning methods Generally backward chaining Updates the KB

20 RBS CS 331/531 Dr M M Awais ES Architecture interface user Explanation system Inference engine Knowledge Base editor Case specific Data Knowledge Base Expert System Shell Pre-solved problems, Frequently referred cases Collection of facts And rules

21 RBS CS 331/531 Dr M M Awais Shells General purpose toolkit/shell is problem independent Shells commercially available CLIPS is one such shell Freely available

22 RBS CS 331/531 Dr M M Awais Reasoning with Uncertainty Case Studies: MYCIN Implements certainty factors approach INTERNIST: Modeling Human Problem Solving Implements Probability approach

23 RBS CS 331/531 Dr M M Awais Probability based ES Probability: Degree of believe in a fact ‘x’, P(x) P(H): degree of believe in H, when supporting evidence is NOT given, H is the hypothesis P(H|E): degree of believe in H, when supporting evidence is given, E is the evidence supporting hypothesis P(H|E): conditional probability

24 RBS CS 331/531 Dr M M Awais Conditional Probability P(H|E): conditional probability is given through a LAW (RULE)P(H|E)=P(H^E)/P(E) where P(H^E) is the probability of H and E occurring together (both are TRUE)

25 RBS CS 331/531 Dr M M Awais Evaluating: Conditional Probability P(H|E): P(Heart Attack|shooting arm pain) Two approaches can be adopted: Asking an expert about the frequency of it happening Finding the probability from the given data Second Approach Collect the data for all the patients complaining about the shooting arm pain. Find the proportion of the patients that had an heart attack from the data collected in step 1

26 RBS CS 331/531 Dr M M Awais Evaluating: Conditional Probability P(H|E): P(Heart Attack|shooting arm pain) Probability of Disease given symptoms VS P(E|H): P(shooting arm pain|Heart Attack) Probability of symptoms given Disease Which is easier to find of the two? Perhaps P(E|H) is easier

27 RBS CS 331/531 Dr M M Awais Evaluating: Conditional Probability P(H|E): P(Heart Attack|shooting arm pain) Probability of Disease given symptoms Headache is mostly experienced when a patient suffers from flu, fever, tumor, etc… Find out whether a patient suffers from tumor, given headache Collect the data for all the headache patients, and then find the proportion of patients that have tumor.

28 RBS CS 331/531 Dr M M Awais Evaluating: Conditional Probability P(E|H): P(shooting arm pain|Heart Attack) Probability of symptoms given Disease Headache is mostly experienced when a patient suffers from flu, fever, tumor, etc… Find out whether a tumor patient suffers from headache Collect the data for all the tumor patients, and then find the proportion of patients that have headache

29 RBS CS 331/531 Dr M M Awais Evaluating: Conditional Probability Generally speaking P(E|H): P(shooting arm pain|Heart Attack) is easier to find. Therefore the we need to convert P(H|E) in terms of P(E|H) P(H|E)=P(H^E)/P(E)P(H|E)=[P(E|H)*P(H)]/P(E)

30 RBS CS 331/531 Dr M M Awais Evaluating: Conditional Probability More than one evidence Independence of events P(H|E1^E2)=P(H^E1^E2)/P(E1^E2) P(H|E1^E2)=[P(E1|H)* P(E2|H)* P(H)]/P(E1)*P(E2)

31 RBS CS 331/531 Dr M M Awais Inference through Joint Prob. Start with the joint probability distribution:

32 RBS CS 331/531 Dr M M Awais Inference by enumeration Start with the joint probability distribution: P(toothache) = = 0.2

33 RBS CS 331/531 Dr M M Awais Inference by enumeration Start with the joint probability distribution: P(toothache) = = 0.2

34 RBS CS 331/531 Dr M M Awais Inference by enumeration Start with the joint probability distribution: Can also compute conditional probabilities: P(  cavity | toothache) = P(  cavity  toothache) P(toothache) = = 0.4

35 RBS CS 331/531 Dr M M Awais Certainty Factors (CF) CF for rules CF(R) From the experts CF for Pre-conditions CF(PC) From the end user CF for conclusions CF(cl) CF(cl)=CF(R)*CF(PC)

36 RBS CS 331/531 Dr M M Awais Certainty Factors (CF) CF for rules CF(R) IF A then BCF(R) = 0.6 CF for Pre-conditions CF(PC) IF A (0.4) then BCF(A)= 0.4 CF for conclusions CF(cl) CF(B)=CF(R)*CF(A)= 0.6*0.4=0.24

37 RBS CS 331/531 Dr M M Awais Finding Overall CF for PC If A(0.1) and B(0.4) and C(0.5) Then D Overall CF(PC)=min(CF(A),CF(B),CF(C)) CF(PC)=0.1 If A(0.1) or B(0.4) or C(0.5) Then D Overall CF(PC)=max(CF(A),CF(B),CF(C)) CF(PC)=0.5

38 RBS CS 331/531 Dr M M Awais Combining Certainty factors When the conclusions are same and certainty factors are positive: CF(R1)+CF(R2) – CF(R1)*CF(R2) When the conclusions are same and the certainty factors are both negative CF(R1)+CF(R2) + CF(R1)*CF(R2) Otherwise: both conclusions are same but have different signs [CF(R1)+CF(R2)] / [1 – min ( | CF(R1) |, | CF(R1) |]

39 RBS CS 331/531 Dr M M Awais Example Please see the class handouts

40 RBS CS 331/531 Dr M M Awais