Mind, Body, World- Foundations of Cognitive Science, 2013a

The decision tree provided in Table 4-4 is a classical theory of how mushrooms can
be classified. It is not surprising, then, that one can translate this decision tree into
the lingua franca: Dawson et al. (2000) rewrote the decision tree as an equivalent
set of production rules. They did so by using the features of mushrooms that must
be true at each terminal branch of the decision tree as the conditions for a production.
The action of this production is to classify the mushroom (i.e., to assert that a
mushroom is either edible or poisonous). For instance, at the Rule 1 Edible decision
point in Table 4-4, one could create the following production rule: “If the odour is
anise or almond, then the mushroom is edible.” Similar productions can be created
for later decision points in the algorithm; these productions will involve a longer list
of mushroom features. The complete set of productions that were created for the
decision tree algorithm is provided in Table 4-5.
Dawson et al. (2000) trained a network of value units to solve the mushroom
classification problem and to determine whether a classical model (such as the decision
tree from Table 4-4 or the production system from Table 4-5) could be translated
into a network. To encode mushroom features, their network used 21 input
units, 5 hidden value units, and 10 output value units. One output unit encoded the
edible/poisonous classification—if a mushroom was edible, this unit was trained to
turn on; otherwise this unit was trained to turn off.
Decision Point
From Table 4-4
Equivalent Production
Network
Cluster
Rule 1 Edible P1: if (odor = anise) (odor = almond) edible 2 or 3
Rule 1 Poisonous
P2: if (odor anise) (odor almond) (odor none)
not edible
1
Rule 2 Edible
P3: if (odor = none) (spore print colour green)
(spore print colour purple) (spore print colour ¹
white) edible
9
Rule 2 Poisonous
P4: if (odor = none) ((spore print colour = green)
(spore print colour = purple)) not edible
6
Rule 3 Edible
P5: if (odor = none) (spore print colour = white) (gill
size = broad) edible
4
Rule 4 Edible
P6: if (odor = none) (spore print colour = white) (gill
size = narrow) (stalk surface above ring = fibrous)
edible
7 or 11
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