In this paper we present a methodology for introducing customizable metalogic features in logic-based knowledge representation and reasoning languages. The proposed approach is based on concepts of introspection and reflection previously introduced and discussed by various authors in relevant literature. This allows a knowledge engineer to specify enhanced reasoning engines by defining properties and meta-properties of relations as expressible for instance in OWL. We employ meta-level axiom schemata based upon a naming (reification) device. We propose general principles for extending the semantics of “host” formalisms accordingly. Consequently, suitable pre-defined libraries of properties can be made available, while user-defined new schemata are also allowed. We make the specific cases of Answer Set Programming (ASP) and Datalog±, where such features may be part of software engineering toolkits for these programming paradigms. On the one hand, concerning ASP, we extend the programming principles and practice to accommodate the proposed methodology, so as to perform meta-reasoning within the plain ASP semantics. The computational complexity of the resulting framework does not change. On the other hand, we show how metalogic features can significantly enrich Datalog± with minor changes to its operational semantics (provided in terms of “chase”) and, also in this case, no additional complexity burden.

中文翻译：

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向知识表示语言添加元逻辑特征

在本文中，我们提出了一种在基于逻辑的知识表示和推理语言中引入可定制元逻辑特征的方法。所提出的方法基于相关文献中不同作者先前介绍和讨论的内省和反思概念。这允许知识工程师通过将关系的属性和元属性定义为可表达的（例如在 OWL 中）来指定增强的推理引擎。我们采用基于命名（具体化）设备的元级公理模式。我们提出了相应地扩展“宿主”形式主义语义的一般原则。因此，可以提供合适的预定义属性库，同时还允许用户定义新模式。我们制作了答案集编程（ASP）和Datalog±的具体案例，这些功能可能是这些编程范式的软件工程工具包的一部分。一方面，关于 ASP，我们扩展了编程原则和实践以适应所提出的方法，以便在普通的 ASP 语义中执行元推理。生成的框架的计算复杂度不会改变。另一方面，我们展示了元逻辑特征如何通过对其操作语义（以“chase”的形式提供）进行微小更改来显着丰富 Datalog±，并且在这种情况下，也没有额外的复杂性负担。生成的框架的计算复杂度不会改变。另一方面，我们展示了元逻辑特征如何通过对其操作语义（以“chase”的形式提供）进行微小更改来显着丰富 Datalog±，并且在这种情况下，也没有额外的复杂性负担。生成的框架的计算复杂度不会改变。另一方面，我们展示了元逻辑特征如何通过对其操作语义（以“chase”的形式提供）进行微小更改来显着丰富 Datalog±，并且在这种情况下，也没有额外的复杂性负担。