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Error Correction: The Specialization Theory 233

if the maximum number of valence electrons for atoms of element M is
N, and
if the current number of valence electrons for X, V, is less than or equal
to N-1.
then double that bond.

After the two new conditions have been added, the rule will execute only when
the relevant atoms have space left, so to speak, to add another valence electron.
For carbon, it will execute only when the current number of electrons is less
than or equal to 8 – 1 = 7. In this situation, the constraint of a maximum of 8
valence electrons will not be violated, because after the addition, the number
of valence electrons could at most be 8. The rule has been cured of the ten-
dency to make this particular error.
The new rule is not completely correct. It can lead to other types of errors.
For example, there are many situations in which the remaining valence elec-
trons have to be disposed of in some other way than by doubling the bonds
between carbon atoms. The rule has not been miraculously transformed from
incomplete to perfect in a single step. Instead, it has been cured of the ten-
dency to causing one particular type of error. There is no guarantee that it
does not cause other types of errors. If it does, additional conditions might
be imposed on the action of doubling bonds between carbon atoms. In addi-
tion, revising this one rule does not preclude other rules from generating
other types of errors. After modest amounts of practice, HS’s set of rules for
constructing Lewis structures made only occasional errors.

Three Central Concepts

The constraint-based theory of learning from error breaks with past think-
ing about learning from error in three ways. First, it reinterprets declarative
knowledge as prescriptive rather than descriptive and as consisting of con-
straints rather than of truth-bearing propositions. Philosophers, logicians
and, more recently, artificial intelligence researchers have assumed that the
function of declarative knowledge is to support description, inference, expla-
nation and prediction, and the formal notion of a proposition was designed
to support those functions. The constraint-based view instead claims that the
function of declarative knowledge is to support judgment, and that the unit of
declarative knowledge is the constraint. The notion that declarative knowledge
is more normative than descriptive explains how we can catch ourselves mak-
ing errors, why there can be art critics who cannot paint and how it is possible