Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like Machine-Learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation. We propose MV-Datalog and MV-Datalog+- as extensions of Datalog and Datalog+-, respectively, to the fuzzy semantics of infinite-valued Lukasiewicz logic L as languages for effectively reasoning in scenarios where such uncertain observations occur. We show that the semantics of MV-Datalog exhibits similar model-theoretic properties as Datalog. in particular, we show that (fuzzy) entailment can be defined in terms of an analogue of minimal models and give a characterisation, and proof of the uniqueness of such minimal models. On the basis of this characterisation, we propose similar many-valued semantics for rules with existential quantification in the head, extending Datalog+-.
翻译:现代应用将来自多种来源的信息结合起来。 通常,其中一些来源,如机器学习系统,并非纯粹是二进制的,而是与某种程度(缺乏)对观测缺乏信心相关联。 我们建议将MV-Datalog和MV-Datalog+-分别作为数据log和Datalog+-的延伸,作为无限价值Lukasiewicz逻辑L的模糊的语义,作为在出现这种不确定的观察的情况下有效推理的语言。我们表明,MV-Datalog的语义与Datalog相似,其模型理论特征与Datalog相似。我们特别表明,(模糊的)要求可以用最起码模型的模拟来界定,并给出特征,并证明这种最起码模型的独特性。根据这种特征,我们提出了类似的多种价值的语义,在头部对存在性进行量化,扩展Datalog+-。