An ASP semantics for Constraints involving Conditional Aggregates
This work incrementally advances the formal foundations of hybrid ASP for logic programming applications.
The paper extends Answer Set Programming (ASP) with conditional aggregates to handle constraints involving two alternatives based on interpretation-dependent conditions, and provides a polynomial-size translation to regular Constraint ASP for implementation on existing solvers.
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.