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

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

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First Source of UncertaintyThe 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 cant represent
  distinguishably

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First Source of UncertaintyThe 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 212 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

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Second source of UncertaintyImperfect
Observation of the World

• Observation of the world can be
• Partial, e.g., a vision sensor cant see through
  obstacles (lack of percepts)

The robot may not know whether there is dust in
room R2
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Second source of UncertaintyImperfect
Observation of the World

• Observation of the world can be
• Partial, e.g., a vision sensor cant see through
  obstacles
• Ambiguous, e.g., percepts have multiple possible
  interpretations

On(A,B) ? On(A,C)
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Second source of UncertaintyImperfect
Observation of the World

• Observation of the world can be
• Partial, e.g., a vision sensor cant see through
  obstacles
• Ambiguous, e.g., percepts have multiple possible
  interpretations
• Incorrect

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Third Source of UncertaintyIgnorance, 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 agents 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

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Representation of Uncertainty

• Many models of uncertainty
• We will consider two important models
• Non-deterministic modelUncertainty is
  represented by a set of possible values, e.g., a
  set of possible worlds, a set of possible
  effects, ...
• Probabilistic modelUncertainty is represented
  by a probabilistic distribution over a set of
  possible values

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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

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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

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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, Ds belief state
  is
• This means that if D believes that a fraction p
  of patients have cavities

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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

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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

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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.

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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

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ES Architecture
interface
user
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ES Architecture
Uses Menus, NLP, etc Which is used to interact
With the users
interface
user
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ES Architecture
interface
user
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ES Architecture
interface
user
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Shells

• General purpose toolkit/shell is problem
  independent
• Shells commercially available
• CLIPS is one such shell
• Freely available

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Reasoning with Uncertainty

• Case Studies
• MYCIN
• Implements certainty factors approach
• INTERNIST Modeling Human Problem Solving
• Implements Probability approach

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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(HE) degree of believe in H, when supporting
  evidence is given, E is the evidence supporting
  hypothesis
• P(HE) conditional probability

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Conditional Probability

• P(HE) conditional probability is given through
  a LAW (RULE)
• P(HE)P(HE)/P(E)
• where P(HE) is the probability of H and E
  occurring together (both are TRUE)

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Evaluating Conditional Probability

• P(HE) P(Heart Attackshooting 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

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Evaluating Conditional Probability

• P(HE) P(Heart Attackshooting arm pain)
  Probability of Disease given symptoms
• VS
• P(EH) P(shooting arm painHeart Attack)
  Probability of symptoms given Disease
• Which is easier to find of the two?
• Perhaps P(EH) is easier

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Evaluating Conditional Probability

• P(HE) P(Heart Attackshooting 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.

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Evaluating Conditional Probability

• P(EH) P(shooting arm painHeart 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

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Evaluating Conditional Probability

• Generally speaking P(EH) P(shooting arm
  painHeart Attack) is easier to find.
• Therefore the we need to convert P(HE) in terms
  of P(EH)
• P(HE)P(HE)/P(E)
• P(HE)P(EH)P(H)/P(E)

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Evaluating Conditional Probability

• More than one evidence
• Independence of events
• P(HE1E2)P(HE1E2)/P(E1E2)
• P(HE1E2)P(E1H) P(E2H) P(H)/P(E1)P(E2)

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Inference through Joint Prob.

• Start with the joint probability distribution

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Inference by enumeration

• Start with the joint probability distribution
• P(toothache) 0.108 0.012 0.016 0.064
  0.2
  

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Inference by enumeration

• Start with the joint probability distribution
• P(toothache) 0.108 0.012 0.016 0.064
  0.2

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Inference by enumeration

• Start with the joint probability distribution
• Can also compute conditional probabilities
• P(?cavity toothache) P(?cavity ? toothache)
• P(toothache)
• 0.0160.064
• 0.108 0.012 0.016 0.064
• 0.4

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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)

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Certainty Factors (CF)

• CF for rules CF(R)
• IF A then B CF(R) 0.6
• CF for Pre-conditions CF(PC)
• IF A (0.4) then B CF(A) 0.4
• CF for conclusions CF(cl)
• CF(B)CF(R)CF(A) 0.60.40.24

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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

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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)

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Example

• Please see the class handouts

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