Logical Approach to Scientific Theories/Laws

I think we may be saying the same thing.

The simpler form proposed for scientific testing is:

H -> I (if H, then I)
I or ~I (either the implications the hypothesis stipulates occur or don't occur)
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In the case of ~I, it is deductively valid to say ~H is the case, but as I expressed later on in my initial post, it isn't just H, but various other auxiliary hypothesis and the circumstances
In the case of I, it is deductively invalid to affirm H, possibly inductively, which I comment about towards the end of my post.

And what is the point? That what you claimed is anything more than common sense? Perhaps something "scientific"?
A conclusion is arrived at logically through what is known. An alligator will sprout flowers if all is known about it is that it is green (and all green things sprout).
Whether or not the hypothesis is true is another problem. Our curve of hypothesis and the curve of "ultimate truth" barely touch each other as we move closer to the truth via gaining more and more knowledge/information. There is no absolute denying that we're all just dreamers and a God is laughing at our science and truth some place under a tree, but this is as far as we can get, with what we are given. I would call that pretty damned logical.