基数极小条件推理的复杂性
Complexity of Reasoning with Cardinality Minimality Conditions
摘要：
许多与人工智能相关的推理问题都是基于命题公式在某种基数极小条件下的可满足性问题。虽然可满足性问题（SAT）的复杂性在系统地考虑Schaefer框架（STOC 1978）内的所有命题逻辑片段时得到了很好的理解，但当添加这种极小条件时情况并非如此。我们考虑CardMinSat问题，它问，给定一个公式F和一个原子x，x是否在F的某个基数最小模型中为真。我们完全分类的计算复杂性的CardMinSat问题的Schaefer的框架内，从而铺平了道路，更好地理解许多人工智能相关的推理问题的易处理性前沿。为此，我们使用由（Schnoor & Schnoor 2008）和（Lagerkvist 2014）开发的高级代数工具。
英文摘要：
Many AI-related reasoning problems are based on the problem of satisfiability of propositional formulas with some cardinality-minimality condition. While the complexity of the satisfiability problem (SAT) is well understood when considering systematically all fragments of propositional logic within Schaefer's framework (STOC 1978) this is not the case when such minimality condition is added. We consider the CardMinSat problem, which asks, given a formula F and an atom x, whether x is true in some cardinality-minimal model of F. We completely classify the computational complexity of the CardMinSat problem within Schaefer's framework, thus paving the way for a better understanding of the tractability frontier of many AI-related reasoning problems. To this end we use advanced algebraic tools developed by (Schnoor & Schnoor 2008) and (Lagerkvist 2014).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
