Detection and Exploitation of Functional Dependencies for Model Generation published in Theory and Practice of Logic Programming BROES DE CAT AND MAURICE BRUYNOOGHE

Aggregates. For aggregates, we build on ideas in (Pelov 2004). We only consider decomposable aggregate functions, i.e., aggregates for which agg(S) = agg({agg(S′), agg(S \S′)}), for sets of domain elements S and S′ ⊂ S. Our transformation of agg({x ∈ T : φ : t}) is based on the decomposability of the considered aggregates and the fact that there is a total order on all domain elements, with a function MIN (minimum) and a (partial) function PRED (predecessor) and that this order can be extended to a total order over tuples of domain elements. Assuming neutralagg is the neutral element of agg, we de ne an accumulator function acc(T ) : N as:  acc(MIN(T )) = t[x/MIN(T )] ←φ[x/MIN(T )] acc(MIN(T )) = neutralagg ←¬φ[x/MIN(T )] ∀x ∈ T : acc(x) = agg(acc(PRED(x)), t)←φ ∧ ¬(x = MIN(T )) ∀x ∈ T : acc(x) = acc(PRED(x)) ←¬φ ∧ ¬(x = MIN(T )) 