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The Learning Brick Sorter • Masterpiece 2 93

combination of bins and colors.Thus, we need a logic based on three values, usually
called a trivalent logic, and we define three constants with these meanings:
#define KB_YES 1
#define KB_NO -1
#define KB_UNKNOWN 0

Bricks & Chips…

Trivalent Logic
Jan Lukasiewicz, the Polish mathematician and philosopher, is considered the
founder of the non-classical logical calculus. At the beginning of the 1900s, he
demonstrated that trivalent logic has the same solid formal foundation that clas-
sical bivalent logic has. Quoting his work: “I maintain that there are propositions
which are neither true nor false but indeterminate. All sentences about future
facts which are not yet decided belong to this category.” As many other great
thinkers he was largely ahead of his time, and many years later multi-valued logic
became a common tool of AI researchers.
For more information on Jan Lukasiewicz and his work, please refer to
www.fmag.unict.it/PolPhil/Lukas/Lukas.html

Our knowledge base is simply a matrix that represents all the possible combinations
of colors (ranges) and bins, where each cell contains what the program knows about that
particular combination. Initially, all the cells are in KB_UNKNOWN status.The initial
knowledge base can be seen in Table 2.1.

Table 2.1 Initial Knowledge Base

Bin 1 Bin 2 Bin 3

Range 1 kb_unknown kb_unknown kb_unknown
Range 2 kb_unknown kb_unknown kb_unknown
Range 3 kb_unknown kb_unknown kb_unknown

Let’s simulate what happens during a possible training session of the Brick Sorter.The
user gives the Learning Brick Sorter a black brick.The Brick Sorter knows nothing about
that color, but assigns the brick to the color “black” (actually its reading) to the first range,
and places the brick in Bin 1. Bin 1 happens to be incorrect, so the user presses the red
lever and passes a negative feedback to the Learning Brick Sorter. Now the program can
update the knowledge base with this information.The updated knowledge base is shown
in Table 2.2.