According to the patent law, " applicant may use terms in a manner contrary to or inconsistent with one or more of their ordinary meanings if the written description clearly redefines the terms." This has to be done by expressing such intentions in the patent application and providing custom definitions with reasonable clarity and precision. One way of achieving this is to include all definitions in the patent application, and ensuring that such terms are used while drafting claims as well. If I want to use highly abstract terms, invented by and unused in the field that my application relates to, how exactly should I technically do it in my application? How should I include all definitions in the patent application and where? And if I will do that and I will use these terms in my claims, are there any restrictions or risks associated with that? Is the right to be my own lexicographer recognized internationally in patent laws or just in U.S.?
Precise definitions are a risk. Real words have nuance and interpretation. If you have a concisely worded formal definition you have little leeway to argue later and can give an infringer a blueprint for designing around your claims. Something less than a formal definition might be a better approach.
The definition of special terms belongs in your Written Description. Then your Claims (which aren’t required for a provisional patent by the way) will be interpreted in view of the definitions in the description, as long as those definitions are clear to a PHOSITA (“person having ordinary skill in the art”).
If you litigate, there will be a claims construction phase. The only way I could imagine your custom definitions will not hold up is if they are contradictory or unclear, such that a PHOSITA would not understand them.
This will suffice internationally.
UPDATE: If you do define your own terms, or even if you use standard terms with some nuance, explicit definitions will be valuable to you in the event of infringement or invalidity litigation. You will save legal expense and increase the chance of a successful outcome in a Markman hearing (the courtroom proceeding that settles claim constructions). Explicit definitions will make it much harder for the opposing side to construe claim terms in a different way that may harm your position.
Disclaimer: I am not a lawyer.