Although much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to an argument when it contributes to the validity of that argument. I then argue that the sequents which best embody this ideal of relevance are the so-called perfect sequents—that is, sequents which are valid but have no proper subsequents that are valid. Church’s theorem entails that there is no recursively axiomatizable proof-system that proves all and only the perfect sequents, so the project that emerges from studying perfection in classical logic is not one of finding a perfect subsystem of classical logic, but is rather a comparative study of classifying subsystems of classical logic according to how well they approximate the ideal of perfection.

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古典逻辑学家的相关性

尽管已经对相关性逻辑给予了很多技术和哲学上的关注，但相关性本身的概念通常停留在直观的层面。很难在文献中找到对形式推理相关性的明确说明。在这篇文章中，我对演绎逻辑中的相关性概念进行了形式化的解释，并认为这个概念在经典逻辑的研究中占有一席之地。主要思想是，当前提有助于论证的有效性时，前提与论证相关。然后，我认为最能体现这种相关性理想的后继词是所谓的完美后继词——即有效但没有正确后继有效的后继词。