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Project 9: Analytical Learning
Exercise 11.1
Consider the problem of learning the target concept "pairs of people
who live in the same house," denoted by the predicate
HouseMates ( x, y ). Below is a positive example of the concept.
HouseMates ( Joe, Sue )
Person ( Joe ) Person ( Sue )
Sex ( Joes, Male ) Sex ( Sue, Female )
HairColor ( Joe, Black ) HairColor ( Sue, Brown )
Height ( Joe, Short ) Height ( Sue, Short )
Nationality ( Joe, US ) Nationality ( Sue, US )
Mother ( Joe, Mary ) Mother ( Sue, Mary )
Age ( Joe, 8 ) Age ( Sue, 6 )
The following domain theory is helpful for acquiring the HouseMates
concept:
HouseMates ( x, y ) <- InSameFamily ( x, y )
HouseMates ( x, y ) <- FraternityBrothers ( x, y )
InSameFamily ( x, y ) <- Married ( x, y )
InSameFamily ( x, y ) <- Youngster ( x ) ^
Youngster ( y ) ^ SameMother ( x, y )
SameMother ( x, y ) <- Mother ( x, z ) ^ Mother ( y, z )
Youngster ( x ) <- Age ( x, a ) ^ LessThan ( a, 10 )
Apply the Prolog-EBG algorithm to the task of generalizing
from the above instance, using the above domain theory. In particular,
-
Show a hand trace-trace of the
Prolog-EBG algorithm
applied to this problem; that is, show the explanation generated
for the training instance, show the result of regressing the target
concept through this explanation, and show the resulting
Horn clause rule.
Joe = J
Sue = S
Mary = M
HouseMates ( J, S )
^
|
InSameFamily ( J, S )
^
________________|________________________
^ ^ ^
| | |
SameMother ( J, S ) Youngster ( J ) |
^ ^ |
________|________________ | Youngster ( S )
^ ^ | ^
| | | ________|
Mother ( J, M ) Mother ( S, M ) | ^ ^
________________________| | |
^ ^ | |
| | Age ( S, 6 ) |
| | |
Age ( J, 8 ) LessThan ( 8, 10 ) LessThan ( 6, 10 )
HouseMates ( x, y )
^
|
InSameFamily ( x, y )
^
________________|________________________
^ ^ ^
| | |
SameMother ( x, y ) Youngster ( x ) |
^ ^ |
________|________________ | Youngster ( y )
^ ^ | ^
| | | ________|
Mother ( x, z ) Mother ( y, z ) | ^ ^
________________________| | |
^ ^ | |
| | Age ( ya, 6 ) |
| | |
Age ( x, xa ) LessThan ( xa, 10 ) LessThan ( ya, 10 )
HouseMates ( x, y ) <- SameMother ( x, y ) ^
( Age ( x, xa ) ^ LessThan ( xa, 10 ) ) ^
( Age ( y, ya ) ^ LessThan ( ya, 10 ) )
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Suppose that the target concept is "people who live with Joe"
instead of "pairs of people who live together." Write down this target
concept in terms of the above formalism. Assuming the same
training instance and domain theory as before, what Horn clause rule
will
Prolog-EBG produce for this new target concept?
LivesWithJoe ( y ) <- SameMother ( Joe, y ) ^
( Age ( y, ya ) ^ LessThan ( ya, 10 ) )
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