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

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RBS

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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RBS

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

B C

A

BC

A

B C

On(A,B) On(B,Table) On(C,Table) Clear(A) Clear(C)

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RBS 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 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

A

B C

A

BC

A

B C

On(A,B) On(B,Table) On(C,Table) Clear(A) Clear(C)

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RBSSecond 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)R1 R2

The robot may not know whether there is dust in room R2

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RBSSecond 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

BCOn(A,B) On(A,C)

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RBSSecond 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

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RBS

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

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RBS

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

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RBS

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

0.2 0.3 0.4 0.1

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RBS

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

0.2 0.3 0.4 0.1

This state would occur 20% of the times

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RBS

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 Cavityp 1-p

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RBS

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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RBS

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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RBS

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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RBS

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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RBS

ES Architecture

interface

user

Explanationsystem

Inferenceengine

KnowledgeBaseeditor

Case specific

Data

KnowledgeBase

Expert System Shell

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RBS

ES Architecture

interface

user

Explanationsystem

Inferenceengine

KnowledgeBaseeditor

Case specific

Data

KnowledgeBase

Expert System Shell

Uses Menus, NLP, etc… Which is used to interact With the users

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RBS

ES Architecture

interface

user

Explanationsystem

Inferenceengine

KnowledgeBaseeditor

Case specific

Data

KnowledgeBase

Expert System Shell

Explains why a decision is taken, uses keywordsSuch as HOW, WHY etc… Implements the

reasoning methodsGenerally backward chaining

Updates the KB

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RBS

ES Architecture

interface

user

Explanationsystem

Inferenceengine

KnowledgeBaseeditor

Case specific

Data

KnowledgeBase

Expert System Shell

Pre-solved problems, Frequently referred cases

Collection of factsAnd rules

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RBS

Shells General purpose toolkit/shell is

problem independent Shells commercially available CLIPS is one such shell Freely available

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RBS Reasoning with Uncertainty

Case Studies: MYCIN

Implements certainty factors approach INTERNIST: Modeling Human Problem

Solving Implements Probability approach

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RBS

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

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RBS

Conditional Probability P(H|E): conditional probability is

given through a LAW (RULE)

P(H|E)=P(H^E)/P(E)P(H|E)=P(H^E)/P(E)

where P(H^E) is the probability of H where P(H^E) is the probability of H and E occurring together (and E occurring together (both are both are TRUETRUE))

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RBSEvaluating: 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

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RBSEvaluating: 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

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RBSEvaluating: 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.

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RBSEvaluating: 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

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RBSEvaluating: 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)P(H|E)=[P(E|H)*P(H)]/P(E)

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RBSEvaluating: Conditional Probability

More than one evidence Independence of eventsP(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)P(H|E1^E2)=[P(E1|H)* P(E2|H)* P(H)]/P(E1)*P(E2)

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RBS

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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RBS

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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RBS

Inference by enumeration Start with the joint probability distribution:

Can also compute conditional probabilities:P(cavity | toothache) = P(cavity toothache)P(toothache)= 0.016+0.064 0.108 + 0.012 + 0.016 + 0.064= 0.4

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RBS

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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RBS

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)= 0.6*0.4=0.24

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RBS

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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RBS 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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RBS

Example Please see the class handouts

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RBS