The difference between object-language and metalanguage is crucial for logical analysis, but has yet not been examined for the field of computer science. In this paper the difference is examined with regard to inferential relations. It is argued that inferential relations in a metalanguage (like a calculus for propositional logic) cannot represent conceptual relations of natural language. Inferential relations govern our concept use and understanding. Several approaches in the field of Natural Language Understanding (NLU) and Natural Language Inference (NLI) take this insight in account, but do not consider, how an inference can be assessed as a good inference. I present a logical analysis that can assesss the normative dimension of inferences, which is a crucial part of logical understanding and goes beyond formal understanding of metalanguages.

中文翻译：

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逻辑、语言和微积分

对象语言和元语言之间的差异对于逻辑分析至关重要，但尚未在计算机科学领域进行过研究。在本文中，关于推理关系的差异进行了研究。有人认为，元语言中的推理关系（如命题逻辑的演算）不能表示自然语言的概念关系。推论关系支配着我们对概念的使用和理解。自然语言理解 (NLU) 和自然语言推理 (NLI) 领域的几种方法考虑了这种见解，但没有考虑如何将推理评估为良好的推理。我提出了一个逻辑分析，可以评估推理的规范维度，这是逻辑理解的关键部分，超越了对元语言的正式理解。