Representing "if and only if" concisely

Question

Suppose you happen to know that $P is true if and only if $Q is true. You can write a pair of integrity constraints to enforce this:

:- $P, not $Q.
:- $Q, not $P.

However, sometimes $P and $Q are fairly long expressions; e.g., :- truth(martin, 2), house_assign(turner, H1), animal_assign(P2, whales), house_assign(P2, H2), not opposite(H1, H2). and it would be preferable to only have to write them once. Is there a way to concisely specify this in clingo?

(Related: Q4 in https://stackoverflow.com/a/28319815/23845 ; the suggestion there is explicitly represent the truthiness of P/Q in the predicate, so you can do a comparison on it. Is this really the only way?)

Answer 1

I would write it like this:

:- {$P; $Q}==1.

However it does not seem to work for conjuctions within $P and $Q.

So my fix would look something like this ((a(N) and b(N)) iff c(N)):

{a(1);a(2);b(1);b(2);c(1);c(2)}.    
num(1;2)

x(N):-a(N),b(N).
:- {x(N);c(N)}==1, num(N).