Generating Solution Candidates For Matching People in Clingo/ASP

person(a;b;c;d).
{match(A,B) : person(A), person(B), A < B}.
:- person(A), 1 < {match(A,B); match(B,A)}.

You exclude solutions that have more than 1 match for a single person.

It is not possible to simply choose a correct set of atoms without additional constraints. As match(a,b) and match(b,c) can occur in different answer sets, both variables need to be created. Only a constraint can rule out that both do not occur in the same answer set.

Also note that your generator rule

{match(X, Y): person(Y)}1 :- person(X) .

already is a shortcut writing for

{match(X, Y): person(Y)} :- person(X).
:- person(X), 2 {match(X, Y): person(Y)}.

And therefore you are already using a constraint whenever your generator choice rule has non-trivial bounds.

PS: Check the different versions using --stats=2 for constraint count and --text for a rough approximation of what kind of constraints are generated.

I'd go for Max Ostrowskis answer.

One of the difficulties is to handle the order of the attributes for the match predicate: this is a tuple, there is a difference if your value shows up on first or second position. Adding a rule to make the predicate commutative should do the trick since you don't need to distinguish for a value to be on first or second position. This method does not use a constraint (on first sight), but it duplicates the generated values so the output differs from your desired solution. Also it adds a line to the code.

person(a;b;c;d).
{match(X,Y): person(Y), X!=Y}1 :- person(X).
match(Y,X) :- match(X,Y).
#show match/2.

Output

Answer: 1

Answer: 2
match(c,a) match(a,c)
Answer: 3
match(b,a) match(a,b)
Answer: 4
match(c,d) match(d,c)
Answer: 5
match(b,a) match(a,b) match(c,d) match(d,c)
Answer: 6
match(b,d) match(d,b)
Answer: 7
match(c,a) match(a,c) match(b,d) match(d,b)
Answer: 8
match(b,c) match(c,b)
Answer: 9
match(d,a) match(a,d)
Answer: 10
match(d,a) match(a,d) match(b,c) match(c,b)
SATISFIABLE