HISTORY:

In 1881, Princeton Professor Allan Marquand constructed a machine capable of solving simple problems in formal logic. It was made from the wood of a red cedar post from Princeton's oldest homestead. The machine displays all valid implications of a simple logical proposition by using an arrangement of rods, levers, catgut strings, and spiral springs. Later, Marquand diagrammed an electrical circuit for his machine that became known as the first design for an electric logic machine.

THEORY:

In effect, the machine displays a truth table in accordance with the logical premises entered into it. An interesting aspect of the machine is that the premises must be input in the negative form. In this way, the machine eliminates any conclusions which contradict the premises. The machine can handle up to four terms labeled A, B, C, & D. The negation of these terms are represented by the corresponding lowercase letters a, b, c, & d. The sixteen possible combinations of these four terms are represented by the sixteen rotating pointers. The labeling on the top and right sides indicate the term associated with the pointer. Starting from the top left and moving right, the terms are ABCD, AbCD, and aBcD. The lower right corner corresponds to abcd. A left pointing pointer indicates that the corresponding term is 'true', whereas a downward pointing pointer indicates 'false'. When the machine is reset, all pointers initially point left indicating that all terms start out being assumed true.

OPERATION:

There are ten keys near the bottom face of the machine. Pressing the '1' key resets the machine by setting all pointers to 'true' (pointing left). Each premise contains two terms, for example consider the premise 'A IMPLIES B'. This can be restated in a negative form by saying that a true A cannot combine with a false B. In other words, all combinations containing Ab must be eliminated. This can easily be entered into the machine by first pressing A, then pressing b, followed by pressing the '0' key (the 'destruction' key). Once this is done, all pointers corresponding to a term containing Ab will point down indicating that these terms are false. This process is continued until all premises have been entered. When complete, the final state of the pointers reflect the remaining combinations which are consistent with the premises. The following example best illustrates this process.

EXAMPLE:

Marquand stated the following problem:
Let us suppose there are four girls at school, Anna, Bertha, Cora, and Dora, and that someone had observed that:
(1) Whenever either Anna or Bertha (or both) remained at home, Cora was at home; and
(2) When Bertha was out, Anna was out; and
(3) Whenever Cora was at home, Anna was at home.
What information is conveyed here concerning Dora?

Let the A, B, C, & D terms stand for the four girls, where each term corresponds to the first letter of a girl's name.
A capital letter indicates 'at home', a lowercase letter indicates the negation, 'not at home'. Putting the above into logical form we have:

1. ( A OR B ) IMPLIES C
2. NOT B IMPLIES NOT A
3. C IMPLIES A

Putting these into the negative form using Marquand's notation yields:

1.1 Ac = 0
1.2 Bc = 0
2. bA = 0
3. Ca = 0

After entering these premises into the machine, we examine the pointers to see what can be inferred about Dora.

The following left facing (true) pointers which include the D term are ABCD and abcD. In other words, when Dora is at home, the other girls are either all at home or either all out.

Also the following left facing (true) pointers which include the d term are ABCd and abcd. A similar conclusion can be drawn as before. In other words, when Dora is out, the other girls are either all at home or either all out.

REFERENCES:

Logic Machines and Diagrams - Martin Gardner http://www-03.ibm.com/ibm/history/exhibits/attic2/attic2_087.html

NOTE:

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