Ah, I think that I understand what you're saying now. I think that people are getting caught up in the phrase 'logical construct', since science doesn't (obviously) demonstrate logical relationships, only empirical ones. Let me know if this is accurate.
Science 'works' means that science's methodology produces conclusions of a certain kind -- namely, conclusions that're consistent with each other and with other agreed upon norms like verifiability, simplicity, etc. In other words, science's methodology just does produce conclusions of a certain kind because producing conclusions of a certain kind because producing conclusions of a certain kind just is a significant part of that methodology.
Probably accurate. The scientific method is a logical construct. Science itself, may or may not demonstrate logical relationships, though in the context of the SM the relationships should still be logical.
Your second sentance is a bit obtuse though, at least I am having some difficulty parsing it. I think I agree with it, but I'm not quite sure 
It's not about 'Science' working, it's about the Scientific Method working. With that change I think I agree with you. Of course the SM is definitional, you do things a certain way, and if you get a certain result you claim that the hypothesis held, if you get another result you discard (or refine more often than not) the hypothesis and test a revised one again. You don't see me using the word 'conclusion' because many people will think it means the same thing as 'proof' or 'fact'. Science works when you can collect facts (which are, of course, still based in some set of underlying assumptions) and apply those facts to one or several hypotheses. The facts can never validate (meaning prove) the hypothesis, all they can really do is invalidate it, if you can find facts which contradict the hypothesis. 'Facts' can also be replaced by 'measurements' or 'observations'.
Again, this is an inductive process, but a process which has it's own consistant internal logic. Most bad science happens when researchers violate that logic. Intelligent Design is a 'theory' (though it's really not a scientific theory, but consider the word in the vernacular) which violates the SM because it is inherently untestable, and unfalsifiable. To be sure, there are interesting 'theories' which fall outside the bounds of the SM, but they are not nominally considered 'science' either. At least until technology or understanding has reached a point where they are able to be tested.
