PositiveDependencyGraph negative aggregates

[MaxOstrowski]

Currently the pdg just takes all predicates inside the body that are not directly preceeded with "not". so a :- b(X), not X = #sum {1: a}. creates a positive dependency. Is this true ?

[MaxOstrowski]

a :- b(X), not X = #sum {1: a}. seems to be equivalent to: a :- b(X), not a. while a :- b(X), not X = #sum {1: not a}. is more like: a :- b(X), not not a. ? @wanko can you help me out here ? When exactly do i have a positive dependency to the head.

[MaxOstrowski]

@rkaminsk Can you give me a quick tip without challenging me mentally ;)

[rkaminsk]

We have a dependency graph for aggregates in Section 5 of https://www.cs.uni-potsdam.de/wv/publications/DBLP_journals/corr/abs-2108-04769.pdf. It is inspired by the translation of aggregates into propositional formulas.

The gist is:

• monotone aggregates induce positive depnedencies
• antimonotone aggregates induce negative dependencies
• other kinds of aggregates do both

It is sometimes possible to drop a double negation or turn a negated antimonotone aggregate into a positive one. An easy scenario is if there is no recursion through the negated parts.

[MaxOstrowski]

Example to deal with later: #false :- S = #count { (X,Y): bend(X,Y,_,1) }; not S = #sum { N,(X,Y): hint(X,Y,N) }.

With a more complicated head like hint/3 would this be a positive or negative dependency ?