The calculus of Natural Calculation is introduced as an extension of Natural Deduction by proper term rules. Such term rules provide the capacity of dealing directly with terms in the calculus instead of the usual reasoning based on equations, and therefore the capacity of a natural representation of informal mathematical calculations. Basic proof theoretic results are communicated, in particular completeness and soundness of the calculus; normalisation is briefly investigated. The philosophical impact on a proof theoretic account of the notion of meaning is considered.

中文翻译：

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自然计算的演算

自然计算的演算是通过适当的术语规则作为自然演绎的扩展引入的。这样的术语规则提供了直接处理微积分中的术语的能力，而不是基于方程的通常推理，因此提供了非正式数学计算的自然表示的能力。传达基本的证明理论结果，特别是微积分的完整性和可靠性；规范化进行了简要研究。考虑了对意义概念的证明理论解释的哲学影响。