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首页> 外文期刊>Journal of web semantics: >Implicit quantification made explicit: How to interpret blank nodes and universal variables in Notation3 Logic
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Implicit quantification made explicit: How to interpret blank nodes and universal variables in Notation3 Logic

机译：隐式量化明确：如何在符号中解释空白节点和通用变量3逻辑

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Since the invention of Notation3 Logic, several years have passed in which the theory has been refined and applied in different reasoning engines like Cwm, EYE, and FuXi. But despite these developments, a clear formal definition of Notation3's semantics is still missing. This does not only form an obstacle for the formal investigation of that logic and its relations to other formalisms, it has also practical consequences: in many cases the interpretations of the same formula differ between reasoning engines. In this paper we tackle one of the main sources of that problem, namely the uncertainty about implicit quantification. This refers to Notation3's ability to use bound variables for which the universal or existential quantifiers are not explicitly stated, but implicitly assumed. We provide a tool for clarification through the definition of a core logic for Notation3 that only supports explicit quantification. We specify an attribute grammar which maps Notation3 formulas to that logic according to the different interpretations and thereby define the semantics of Notation3. This grammar is then implemented and used to test the impact of the differences between interpretations on practical cases. Our dataset includes Notation3 implementations from former research projects and test cases developed for the reasoner EYE. We find that 31% of these files are understood differently by different reasoners. We further analyse these cases and categorise them in different classes of which we consider one most harmful: if a file is manually written by a user and no specific built-in predicates are used (13% of our critical files), it is unlikely that this user is aware of possible differences. We therefore argue the need to come to an agreement on implicit quantification, and discuss the different possibilities. (C) 2019 Elsevier B.V. All rights reserved.
机译：由于符号3逻辑的发明，已经通过了几年，其中该理论已被精制和应用于CWM，Eye和Fuxi等不同的推理发动机。但尽管有这些发展，但仍然缺少了一个明确的正式定义。这不仅形成了这种逻辑的正式调查及其关系等形式主义的障碍，它也有着实际的后果：在许多情况下，同一个公式的解释推理引擎之间的差异。在本文中，我们解决了这个问题的主要来源之一，即隐含量化的不确定性。这是指Notation3使用不明确说明通用或存在量子的绑定变量的能力，而是隐含地假设。我们提供了一种工具，以澄清核心逻辑的核心逻辑，仅支持显式量化。我们指定一个属性语法，根据不同的解释，将Notate3公式映射到该逻辑，从而定义了Notation3的语义。然后实施该语法并用于测试解释与实际情况之间的差异的影响。我们的数据集包括来自前研究项目的注释3实现和为推理眼睛开发的测试用例。我们发现31％的文件由不同的推理员差别被视为不同。我们进一步分析这些案件中，我们考虑一个最有害的不同类别加以分类：如果文件是手工编写的用户和没有内置谓词具体使用（我们的重要文件13％），这是不可能的此用户了解可能的差异。因此，我们认为需要就隐含量化达成协议，并讨论不同的可能性。 （c）2019 Elsevier B.v.保留所有权利。

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