I'm starting this thread upon Fivejedjon's request. The problem to be discussed is whether 'should' is a subjunctive form or not when it's used in a construction like "Should you change your mind, let me know". To decide whether A belongs to class B, we need: 1)To describe the characteristics of class B; 2) To prove that A has or doesn't have those characteristics. Since Fivejedjon initiated this discussion, I think, it would be fair to let him/her be the first to speak. You are welcome, Dr.Fivejedjon.
This is the impression that an amateur (corum) managed to gain from his English self-studies, using books and the Internet plus the experience he gained in one year that he spent in an English speaking country.
To me, subjunctive is a type of mood, a purely morphological category, a set of inflected verb forms used to denote, express, certain types of modality. Modality, a purely semantic category, is the taxonomic system of propositions created on the basis of whether they express possibility, contingency, necessity and many more things. As far as I know, the concepts that I directly named (possibility, contingency, necessity) are those -- no more, no less -- for which we use the subjunctive conjugational system of verb phrases.
Now let us examine this sentence:
Should you change your mind, let me know.
The concept of contingency comes up in my mind. Why? In the first clause, in the subordinate clause, or if you so like, in the protasis, is expressed the condition upon which the fulfillment of letting someone know hinges. In other words, the act of "letting me know" is contingent upon one condition: you change your mind. You will either change your mind or not. The speaker does not know. As contingency is expressed, resort can/should be made to the subjunctive inflectional system. What is the verb (phrase) in the protasis? It is "should change". "Should" is a modal auxiliary verb. In this sentence, its auxiliary function unfolds in its putative meaning.
The meaning of the protasis determines its mood. The type of mood determines whether resort can/should be made to the subjunctive inflectional system. Since 'should' is used putatively: subjunctive! In a complex verb phrase, it is always the operator whose form may change. In present subjunctive, the unmarked base form of the modal is called for.