question about AGPLv3, OSLv3, the keyword 'communicate'

[Finjon Kiang]

Dear All,

I know both AGPLv3 and OSLv3 try to solve the 'ASP loophole' problem.
But the keywords 'communicate' in OSLv3 and 'communication' in AGPLv3
make me feel confused.

If I modify one application which licensed under AGPLv3 or OSLv3. And
I just use it as my own website, without offering services like ASP
vendors does. Is it possible anyone who visiting my website also grant
the right to ask the source code from me? Because they must
'communicate' the application through browser.

Or maybe somebody could point me to something like FAQ about this
issue. It's a little bit hard to find the answer. Thanks. :)

-- 
Finjon Kiang