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.

中文翻译：

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涉及条件聚合的约束的 ASP 语义

我们详细阐述了混合答案集编程 (ASP) 的正式基础，并使用约束值和变量上的聚合函数扩展了其底层逻辑框架。这是通过引入条件表达式的构造来实现的，该构造允许在评估约束时考虑两种选择。考虑哪种替代方案取决于解释并根据相关条件进行选择。我们将重点放在具有线性约束的逻辑程序上，并展示了如何将常见的 ASP 聚合视为所谓的条件线性约束的特殊情况。最后，我们引入了一个多项式大小、模块化和忠实的从我们的框架到常规（无条件）约束 ASP 的转换，概述了在现有混合 ASP 求解器之上的条件聚合的实现。