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238 Adaptation

Table 7.2. Summary of the initial HS model of children’s counting skill.

Ontology
Entities: X, Y, Z, …, of types object, number, set
Objects: O 1 , O 2 , O 3 , …
Numbers: N = 1, 2, 3, …
Sets: {O i }, i = 1, 2, 3, …
Properties: first(X), current(X), origin(X)
Relations: associate(N, O), member(O i , {O}), successor(N, M), after(O j , O i )
Counting tasks: count({O})
Answers to counting tasks: answer(N, count({O}))
Actions and operators
FirstObject (O) ==> first(O)
NextObject(O i , O j ) ==> after(O j , O i )
FirstNumber (N) ==> first(N)
NextNumber(N, M) ==> after(M, N)
AssNumObj(N, O) ==> ass(N, O)
Answer(N, count({O})) ==> answer(N, count({O}))
Initial, overly general skill:
R1: count({O}) object(O i ) ===> FirstObject(O i )
R2: count({O}) current(O i ), object(O j ) ===> NextObject(O j , O i )
R3: count({O}) number(N) ===> FirstNumber(N)
R4: count({O}) current(N) number(M) ===> NextNumber(M, N)
R5: count({O}) current(N) current(O) ===> AssNumObj(N, O)
R6: count({O}) current(N) ===> Answer(N, count({O}))
Based on Ohlsson and Rees, 1991a, Tables 2 and 3.

case of skill acquisition for which there are strong empirical reasons to believe
that there is a prior declarative knowledge base. Children can learn to count
with minimal and haphazard instruction because they have prior knowledge
of a small set of counting principles that constrains counting behavior.
HS can duplicate the acquisition of this skill, given the same knowledge
that children start out with. HS was programmed with the basic competence
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of pointing to objects and saying numbers. In addition, we gave HS the actions
that are specific to the counting domain, primarily to select an object, point to
an object, retrieve a number, speak a number and declare the answer. HS was
given an initial competence that consisted of six rules, one to control the appli-
cation of each of the six key cognitive operations; see Table 7.2. These rules
were overly general and hence error prone. The prior declarative knowledge
consisted of constraints that represented a version of the Gelman and Gallistel
counting principles. The five constraints are stated conceptually in Table 7.3.