# Week2 - Logical reasoning Week 2 Probability theory Bayes...

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Week 2 Probability theory Bayes’ Nets Last week ! Talked about how to formulate an AI problem ! Define your variables ! Determine desired actions ! Build an agent that produces desired action given input • In this course, mostly through learning ! Let’s look at reasoning… Logical reasoning ! In 630, we talked about logic Q: Does everyone love John? John loves John Betty loves John Mary loves John Logical reasoning ! Here, the “variables” are logic sentences S1^S2^S3=> ! x loves(x,J) S3: loves(J,J) S2: loves(B,J) S1: loves(M,J) Q: Does everyone love John? John loves John Betty loves John Mary loves John Logical reasoning ! Values are true, false true (if world only consists of M,B,J) S1^S2^S3=> ! x loves(x,J) Q: Does everyone love John? true S3: loves(J,J) John loves John true S2: loves(B,J) Betty loves John true S1: loves(M,J) Mary loves John Reasoning with uncertainty ! What if we don’t know the answers? P( ! x loves(x,J)) Q: Does everyone love John? P(loves(J,J)) John almost certainly loves John P(loves(B,J)) I’m not sure if Betty loves John P(loves(M,J)) It’s likely Mary loves John

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Reasoning with uncertainty ! Can give the probability of values P( ! x loves(x,J)=true)= 0.8*0.5*0.95=0.38 (assuming above are independent) Q: Does everyone love John? P(loves(J,J)=true)=0.95 John almost certainly loves John P(loves(B,J)=true)=0.5 I’m not sure if Betty loves John P(loves(M,J)=true)=0.8 It’s likely Mary loves John Where do probabilities come from? ! From life experience ! From guessing ! From controlled sample pools ! The quality of the judgments made using this data will depend on the sample that the probabilities came from ! How well does the source match the test conditions? ! Language statistics from newswire applied to childrens books What are probabilities in terms of logic? ! Probabilities describe the degree of belief in a particular proposition ! No longer just true or false ! “The chance of rain today is 10%” P(rain) = .1 ! “80% of the time, squealing indicates bad brakes” … means that we believe 80% of the time Squeal => BadBrakes ! It is not that the proposition is x% true ! P(rain)=.1 does not mean it is raining 10% Random variables ! In order to determine the probability of events, we have to know how many different possibilities there are ! A random variable takes on one or more values ! 6-sided die roll: Roll=1, Roll=2, …, Roll=6 ! Squealing: Squeal=true, Squeal=false ! Random variables have three components: ! The name of the variable ! The range of its elements ! A probability associated with each element • This is called a probability distribution Random variables ! Typically written with a capital letter (particularly ! 3 types, depending on domain ! boolean: <true, false> • Logical propositions • Can abbreviate P(Rain=true)=P(rain), P(Rain=false)=P(~rain) ! discrete: <a,b,c,d> ! continuous: [0,1] ! Examples of each? Unconditional probabilities
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Week2 - Logical reasoning Week 2 Probability theory Bayes...

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