From what the OP wrote, I think he wants:
If there are circuits or devices A,B,C and D and a target device T, he wants T to get AC when one or more of A,B,C or D get AC. However, un-powered devices remain un-powered.
Solution is to use four AC relays, connected across each device. All the relay contacts(normal open) are paralleled to power up device T.
But, messing with central heating is not something which one should just do without understanding the consequence.