Artificial Intelligence CIS 342

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Artificial IntelligenceCIS 342

• The College of Saint Rose
• David Goldschmidt, Ph.D.

February 13, 2007
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Homework 1

• Coverage
• Probability Theory
• Inference Chains (including Prolog)
• Due at beginning of class 2/20
• Submit hardcopy of homework problems, including
  source code printouts and output (e.g. screen
  shots)

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Project 2

• Coverage
• Bayesian Reasoning
• Bayesian Rule-Based Expert System
• Due by midnight on 2/20
• Work in teams of two (optional, but encouraged)
• Submit source code, compilation instructions
• Output of cases from lecture slides
• Submit screen shots or text file output

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Project 2 Review (i)

• Expert is given four conditionally independent
  evidences E1, E2, E3, and E4
• E1 Patient is shaky and disoriented
• E2 Patient is sweating, feels nauseous
• E3 Patient is excessively thirsty
• E4 Patient has blacked out

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Project 2 Review (ii)

• Expert creates three mutually exclusive and
  exhaustive hypotheses H1, H2, and H3
• H1 Patient has a non-diabetes-related ailment
• H2 Patient has diabetes and is currently
  experiencing a sugar low
• H3 Patient has diabetes and is currently
  experiencing a sugar high

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Project 2 Review (iii)

• Expert provides prior probabilities as a baseline
  set of probabilities p(H1), p(H2), p(H3)
• p(H1) Probability patient is currently
  experiencing a non-diabetes-related ailment
  0.90
• p(H2) Probability patient has diabetes and is
  experiencing a sugar low 0.06
• p(H3) Probability patient has diabetes and is
  experiencing a sugar high 0.04

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Project 2 Review (iv)

• Expert identifies conditional probabilities for
  observing each evidence Ei for each hypotheses
  Hk
• p(E1H1) Probability that patient is shaky and
  disoriented given that patient has a
  non-diabetes-related ailment 0.50
• p(E1H2) Probability that patient is shaky and
  disoriented given that patient has diabetes and
  is experiencing a sugar low 0.90
• etc.

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Project 2 Review (v)
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Project 2 Review (vi)

• What are the posterior probabilities given the
  following observations?
• Event E1 is observed
• Event E1 is observed first, then event E2
• Event E1 is observed first, then event E3
• Event E2 is observed first, then event E2,
  followed by event E4

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Fuzzy Logic (i)

• Need the ability to represent expert knowledge
  using vague and inexact terms
• Fuzzy Logic describes fuzziness and degrees using
  English vocabulary
• e.g. degrees of height, speed, distance,
  temperature, beauty, intelligence, etc.

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Fuzzy Logic (ii)

• Boolean logic uses sharp distinctions
• e.g. temperatures above 85? are hot
  temperatures less than or equal to 85? are
  mild etc.
• True or false (0 or 1) leaves little room for
  compromise
• Fuzzy logic attempts to smooth such sharp
  distinctions between terms
• Began with multi-valued logic in 1930s
  (Lukasiewicz)
• Use real numbers between 0 and 1 to represent
  possibility that a given statement was true or
  false

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Fuzzy Logic (iii)

• Concept of a continuum
• Imagine a line of chairs ranging from a perfect
  chair to chairs that are less and less
  chair-like
• A block of wood lies at the other end of the
  continuum
• 1937 paper Vagueness an exercise in logical
  analysis (Max Black)
• Identify vagueness as a matter of probability

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Fuzzy Logic (iv)

• 1965 paper Fuzzy Sets (Lotfi Zadeh)
• Apply natural language terms to a formal
  system of mathematical logic
• http//www.cs.berkeley.edu/zadeh
• Fuzzy Logic is a set of mathematical principles
  for knowledge representation based on
  degrees of membership

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Fuzzy Logic (v)

• Unlike two-valued Boolean logic, fuzzy logic is
  multi-valued
• Fuzzy logic deals with degrees of membership and
  degrees of truth

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Fuzzy Logic (vi)

• Uses the continuum of logical values between 0
  (completely false) and 1 (completely true)
• Employs the full spectrum of truth, accepting
  that things can be part true and part false at
  the same time

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Fuzzy Sets (i)

• Fundamental to mathematics, a set is a collection
  of distinct objects
• A fuzzy set is a set whose
  elements have varying
  degrees of
  membership

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Fuzzy Sets (ii)

• Fuzzy set depicting height
• Compare to Crisp (Boolean) set

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Fuzzy Sets (iii)

• A crisp (or Boolean) set is too sharp
• Low applicability to real-world knowledge/concepts

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Fuzzy Sets (iv)

• A fuzzy set provides a natural fit
• High applicability to real-world
  knowledge/concepts

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Fuzzy Sets (v)

• The x-axis is the universe of discourse, the
  range of all possible values
• The y-axis is the degree of membership

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Fuzzy Sets (vi)

• Let X be the universe of discourse and its
  elements be denoted as x
• In classical set theory, crisp set A of X is
  defined by function fA(x), the characteristic
  function of A
• fA(x) X ? 0, 1 where fA(x)

1, if x ? A
0, if x ? A
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Fuzzy Sets (vii)

• Let X be the universe of discourse and its
  elements be denoted as x
• In fuzzy set theory, fuzzy set A of X is defined
  by function mA(x), the membership function of A
• mA(x) X ? 0, 1 where mA(x) 1, if x is
  entirely in A
• mA(x) 0, if x is not in A
• 0 lt mA(x) lt 1, if x is partly in A

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Representing Fuzzy Sets (i)

• Representing height using crisp sets

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Representing Fuzzy Sets (ii)

• Representing height using fuzzy sets

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Representing Fuzzy Sets (iii)
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Linguistic Variables Hedges (i)

• A linguistic variable is a fuzzy variable
• e.g. the statement John is tall implies
  linguistic variable John takes the linguistic
  value tall
• Use linguistic variables to form fuzzy rules

IF project duration is long THEN risk is
high IF speed is slow THEN stopping distance
is short
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Linguistic Variables Hedges (ii)

• Linguistic variable speed has range 0 to 220
  km/h and is organized into fuzzy subsets slow,
  medium, and fast
• How about very slow and extremely fast?
• Hedges are qualifying terms that modify the shape
  of fuzzy sets, including such adverbs as very,
  somewhat, quite, slightly, extremely, etc.

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Linguistic Variables Hedges (iii)
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Representing Hedges (i)
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Representing Hedges (ii)
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Representing Hedges (iii)
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Representing Hedges (iv)