论文标题
通过简短公式解释性：实施的命题逻辑的情况
Explainability via Short Formulas: the Case of Propositional Logic with Implementation
论文作者
论文摘要
我们从逻辑和公式大小方面概念化了解释性，在非常一般的环境中给出了许多相关的解释性定义。我们的主要兴趣是所谓的特殊解释问题，旨在在输入模型中解释输入公式的真实价值。解释是一个最小尺寸的公式，（1）与输入模型上的输入公式一致，（2）将所涉及的真实价值传输到全球输入公式，即每个模型上。作为一个重要的例子，我们在这种情况下研究了命题逻辑，并表明在多项式层次结构的第二级中，特殊的解释性问题是完整的。我们还将在答案集编程中提供了此问题的实施，并研究了其与解释N-Queens和主导集合问题的答案有关的能力。
We conceptualize explainability in terms of logic and formula size, giving a number of related definitions of explainability in a very general setting. Our main interest is the so-called special explanation problem which aims to explain the truth value of an input formula in an input model. The explanation is a formula of minimal size that (1) agrees with the input formula on the input model and (2) transmits the involved truth value to the input formula globally, i.e., on every model. As an important example case, we study propositional logic in this setting and show that the special explainability problem is complete for the second level of the polynomial hierarchy. We also provide an implementation of this problem in answer set programming and investigate its capacity in relation to explaining answers to the n-queens and dominating set problems.
