将LPMLN与弱约束、P-log关联，实现概率推理的统一求解。
LPMLN, Weak Constraints, and P-log
- 通过弱约束重写LPMLN，用标准ASP求解器计算最可能模型
- 将P-log转化为LPMLN，支持概率非单调性建模与计算
- 兼容多种形式化系统，提升可扩展性与求解效率
LPMLN是一种新提出的逻辑编程形式化，通过采用马尔可夫逻辑的对数线性权重机制扩展答案集程序。本文研究了LPMLN与另外两种答案集程序扩展——用于表达答案集间定量偏好的弱约束，以及用于处理概率不确定性的P-log——之间的关系。我们提出了将LPMLN翻译为带弱约束的程序的方法，以及将P-log翻译为LPMLN的方法，补全了现有反向翻译。前者使标准ASP求解器能计算LPMLN程序的最可能稳定模型（即MAP估计）；该结果可推广至其他可翻译为LPMLN的形式化系统，如马尔可夫逻辑、ProbLog和佩尔的因果模型。后者揭示了如何在LPMLN中表示P-log的概率非单调性，从而可借助标准ASP和MLN求解器进行求解。
原文摘要 · Abstract (English)
LPMLN is a recently introduced formalism that extends answer set programs by adopting the log-linear weight scheme of Markov Logic. This paper investigates the relationships between LPMLN and two other extensions of answer set programs: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. We present a translation of LPMLN into programs with weak constraints and a translation of P-log into LPMLN, which complement the existing translations in the opposite directions. The first translation allows us to compute the most probable stable models (i.e., MAP estimates) of LPMLN programs using standard ASP solvers. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl's Causal Models, that are shown to be translatable into LPMLN. The second translation tells us how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers and MLN solvers.
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