我在以下代码中的某处有错误：
% Induction of decision trees (program sketched on pages 466-468)
% Below, the sketched program was completed by adding some missing parts
% Note: This program does not pay any attention to efficiency!
induce_tree( Tree) :-
findall( example( Class, Obj), example( Class, Obj), Examples),
findall( Att, attribute( Att, _ ), Attributes),
induce_tree( Attributes, Examples, Tree).
% The form of the tree depends on the following three cases:
% (1) Tree = null if the example set is empty.
% (2) Tree = leaf( Class) if all of the examples are of the same class Class.
% (3) Tree = tree( Attribute, [ Val1 : SubTree1, Val2 : Subtree2, ...]) if examples
% belong to more than one class,
% Attribute is the root of the tree,
% Val1, Val2, ... are Attribute's values, and
% SubTree1, SubTree2, ... are the corresponding decision subtrees.
% These three cases are handled by the following three clauses:
% induce_tree( Attributes, Examples, Tree)
induce_tree( _, [], null) :- !.
induce_tree( _, [example( Class,_ ) | Examples], leaf( Class)) :-
not(member(example(ClassX, _), Examples), % No other example
ClassX \== Class), !. % of different class
induce_tree( Attributes, Examples, tree( Attribute, SubTrees)) :-
choose_attribute( Attributes, Examples, Attribute), !,
del( Attribute, Attributes, RestAtts), % Delete Attribute
attribute( Attribute, Values),
induce_trees( Attribute, Values, RestAtts, Examples, SubTrees).
induce_tree( _, Examples, leaf( ExClasses)) :-
% No (useful) attribute, leaf with class distr.
findall( Class, member( example( Class, _), Examples), ExClasses).
% induce_trees( Att, Values, RestAtts, Examples, SubTrees):
% induce decision SubTrees for subsets of Examples according to Values of Attribute
induce_trees( _, [], _, _, [] ). % No attributes, no subtrees
induce_trees( Att, [Val1 | Vals], RestAtts, Exs, [Val1 : Tree1 | Trees]) :-
attval_subset( Att = Val1, Exs, ExampleSubset),
induce_tree( RestAtts, ExampleSubset, Tree1),
induce_trees( Att, Vals, RestAtts, Exs, Trees).
% attval_subset( Attribute = Value, Examples, Subset):
% Subset is the subset of examples in Examples that satisfy the condition
% Attribute = Value:
attval_subset( AttributeValue, Examples, ExampleSubset) :-
findall( example( Class, Obj),
( member( example( Class, Obj), Examples),
satisfy( Obj, [ AttributeValue])),
ExampleSubset).
% satisfy( Object, Description):
% defined as in Figure 18.11.
satisfy( Object, Conj) :-
not(member(Att = Val, Conj),
member( Att = ValX, Object),
ValX \== Val).
% choose_attribute selects the attribute that discriminates well among the classes.
% This involves the impurity criterion. The following clause minimizes the chosen
% impurity measure using setof.
% setof will order the available attributes according to increasing impurity
choose_attribute( Atts, Examples, BestAtt) :-
setof( Impurity/Att,
( member( Att, Atts), impurity1( Examples, Att, Impurity)),
[ MinImpurity/BestAtt | _] ).
% impurity1( Examples, Attribute, Impurity):
% implements a chosen impurity measure.
% Impurity is the combined impurity of the subsets of examples after
% dividing the list Examples according to the values of Attribute.
%
impurity1( Exs, Att, Imp) :-
attribute( Att, AttVals),
term_sum( Exs, Att, AttVals, 0, Imp). % Weighted sum of impurities over att. values
% term_sum( Exs, Att, AttVals, PartialSum, Sum)
term_sum( _, _, [], Sum, Sum).
term_sum(Exs, Att, [Val | Vals], PartSum, Sum) :-
length( Exs, N),
findall( C, (member( example(C,Desc), Exs), satisfy( Desc, [Att=Val])), ExClasses),
% ExClasses = list of the classes (with repetitions) of all the examples with Att=Val
length( ExClasses, NV), NV > 0, !,
findall( P,
( bagof( 1, member( Class, ExClasses), L), length( L, NVC), P is NVC/NV),
ClassDistribution),
gini( ClassDistribution, Gini),
NewPartSum is PartSum + Gini*NV/N,
term_sum( Exs, Att, Vals, NewPartSum, Sum)
;
term_sum( Exs, Att, Vals, PartSum, Sum). % Here no example satisfied Att = Val
% gini( ProbabilityList, GiniIndex)
% GiniIndex = SUM Pi*Pj over all i, j such that i \= j
% This is equivalent to:
% GiniIndex = 1 - SUM Pi*Pi over all i
gini( Probs, Index) :-
square_sum( Probs, 0, SquareSum),
Index is 1 - SquareSum.
square_sum( [], S, S).
square_sum( [P | Ps], PartS, S) :-
NewPartS is PartS + P*P,
square_sum( Ps, NewPartS, S).
我收到如下错误：
?- induce_tree(Tree).
ERROR: induce_tree/3: Undefined procedure: not/2
ERROR: However, there are definitions for:
ERROR: not/1
Exception: (7) induce_tree([size, shape, holes],
[example(nut, [size=small, shape=compact, holes=1]),
example(screw, [size=small, shape=long, holes=none]),
example(key, [size=small, shape=long, holes=1]),
example(nut, [size=small, shape=compact, ... = ...]),
example(key, [size=large, ... = ...|...]),
example(screw, [... = ...|...]),
example(nut, [...|...]),
example(..., ...)|...], _G251) ?
请帮忙。