Example of Hypothesis Selection in Discovering

Example 0   Suppose you are working with matrices $a,b,c$ etc. If an NCProcess command discovers that and, at that point, you realize that it is reasonable to assume that no eigenvalue of $a$ is an eigenvalue of $c$, then $b$ must be zero from an analytic argument.¹ Therefore, one can add the polynomial equation to the collection of polynomial equations and continue. As research progressed, one would add more and more analytic observations at the points where it became clear what those observations were.

The syllogism corresponding to the above type of argument would go as follow.

Fact 0   If whatever hypothesis , then .

Fact 0   If $a$, $b$ and $c$ are matrices, no eigenvalue of $a$ is an eigenvalue of $c$ and , then .

Fact 0   If whatever hypothesis and , then desired conclusion .

Conclusion 0   If whatever hypothesis , then desired conclusion .

Fact 41.2 would be seen by using the algorithms in this paper. Fact 41.3 is an observation from analysis. Fact 41.4 would be seen by using the algorithms in this paper. Conclusion 41.5 is a tautological conclusion of the Facts 41.2, 41.3 and 41.4.