Probabilistic logical models deal effectively with uncertain relations and entities typical of many real world domains. In the field of probabilistic logic programming usually the aim is to learn these kinds of models to predict specific atoms or predicates of the domain, called target atoms/predicates. However, it might also be useful to learn classifiers for interpretations as a whole: to this end, we consider the models produced by the inductive constraint logic system, represented by sets of integrity constraints, and we propose a probabilistic version of them. Each integrity constraint is annotated with a probability, and the resulting probabilistic logical constraint model assigns a probability of being positive to interpretations. To learn both the structure and the parameters of such probabilistic models we propose the system PASCAL for “probabilistic inductive constraint logic”. Parameter learning can be performed using gradient descent or L-BFGS. PASCAL has been tested on 11 datasets and compared with a few statistical relational systems and a system that builds relational decision trees (TILDE): we demonstrate that this system achieves better or comparable results in terms of area under the precision–recall and receiver operating characteristic curves, in a comparable execution time.

中文翻译：

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概率归纳约束逻辑

概率逻辑模型有效地处理了许多现实世界领域中典型的不确定关系和实体。在概率逻辑编程领域，通常的目的是学习这些类型的模型来预测域的特定原子或谓词，称为目标原子/谓词。然而，从整体上学习用于解释的分类器也可能是有用的：为此，我们考虑由归纳约束逻辑系统产生的模型，由完整性约束集表示，我们提出了它们的概率版本。每个完整性约束都用概率进行注释，并且由此产生的概率逻辑约束模型为解释分配一个积极的概率。为了学习这种概率模型的结构和参数，我们提出了用于“概率归纳约束逻辑”的系统 PASCAL。可以使用梯度下降或 L-BFGS 进行参数学习。PASCAL 已在 11 个数据集上进行了测试，并与一些统计关系系统和构建关系决策树 (TILDE) 的系统进行了比较：我们证明该系统在精度-召回和接收器操作特性下的面积方面取得了更好或可比的结果曲线，在可比的执行时间内。