Answer set programming (ASP) is a popular declarative programming paradigm with various applications. Programs can easily have many answer sets that cannot be enumerated in practice, but counting still allows quantifying solution spaces. If one counts under assumptions on literals, one obtains a tool to comprehend parts of the solution space, so-called answer set navigation. However, navigating through parts of the solution space requires counting many times, which is expensive in theory. Knowledge compilation compiles instances into representations on which counting works in polynomial time. However, these techniques exist only for conjunctive normal form (CNF) formulas, and compiling ASP programs into CNF formulas can introduce an exponential overhead. This paper introduces a technique to iteratively count answer sets under assumptions on knowledge compilations of CNFs that encode supported models. Our anytime technique uses the inclusion–exclusion principle to improve bounds by over- and undercounting systematically. In a preliminary empirical analysis, we demonstrate promising results. After compiling the input (offline phase), our approach quickly (re)counts.

中文翻译：

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IASCAR：通过随时细化进行增量答案集计数

答案集编程 (ASP) 是一种流行的声明式编程范例，具有各种应用程序。程序可以很容易地拥有许多在实践中无法枚举的答案集，但计数仍然可以量化解决方案空间。如果人们在文字假设下进行计算，人们就获得了一种理解部分解空间的工具，即所谓的答案集导航。然而，浏览部分解决方案空间需要进行多次计数，这在理论上是昂贵的。知识汇编将实例编译成可在多项式时间内进行计数的表示形式。然而，这些技术仅适用于合取范式 (CNF) 公式，并且将 ASP 程序编译为 CNF 公式可能会带来指数级开销。本文介绍了一种在对编码支持模型的 CNF 知识编译的假设下迭代计算答案集的技术。我们的随时技术使用包含-排除原则，通过系统地多计数和少计数来改善界限。在初步的实证分析中，我们展示了有希望的结果。编译输入（离线阶段）后，我们的方法快速（重新）计数。