Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are a suitable framework to handle uncertain information, and in the last decade many probabilistic logical languages have been proposed, as well as inference and learning systems for them. In the realm of Abductive Logic Programming (ALP), a variety of proof procedures have been defined as well. In this paper, we consider a richer logic language, coping with probabilistic abduction with variables. In particular, we consider an ALP program enriched with integrity constraints `a la IFF, possibly annotated with a probability value. We first present the overall abductive language, and its semantics according to the Distribution Semantics. We then introduce a proof procedure, obtained by extending one previously presented, and prove its soundness and completeness.

翻译：在越来越多的应用领域考虑到不确定的信息,与此同时,绑架被证明是处理假设推理和不完全知识的有力工具,概率逻辑模型是处理不确定信息的适当框架,在过去十年中,提出了许多概率逻辑语言,并为这些语言提出了许多概率逻辑语言以及推论和学习系统,在虚拟逻辑编程领域,也界定了各种证明程序。在本文件中,我们考虑了一种更丰富的逻辑语言,应对各种变量的概率绑架。特别是,我们考虑了一个具有完整性限制的ALP程序,`a la IFF, 可能带有概率值的注释。我们首先根据发行语的语义介绍整个诱拐语言及其语义。我们随后采用了一种证据程序,通过扩展先前的语义,并证明其合理性和完整性。