  We elaborate upon the formal foundations of hybrid Answer Set Programming
(ASP) and extend its underlying logical framework with aggregate functions over
constraint values and variables. This is achieved by introducing the construct
of conditional expressions, which allow for considering two alternatives while
evaluating constraints. Which alternative is considered is
interpretation-dependent and chosen according to an associated condition. We
put some emphasis on logic programs with linear constraints and show how common
ASP aggregates can be regarded as particular cases of so-called conditional
linear constraints. Finally, we introduce a polynomial-size, modular and
faithful translation from our framework into regular (condition-free)
Constraint ASP, outlining an implementation of conditional aggregates on top of
existing hybrid ASP solvers.
