循环性结石加深
Cirquent calculus deepened
摘要：
循环演算是一种新的证明理论和语义框架，其主要区别特征是基于循环，而不是更传统的方法，处理树状对象，如公式或序列。其优点包括更高的效率、灵活性和表现力。本文提出了一个详细的阐述了深推理事件逻辑，这是自然和内在的资源意识。它表明，经典逻辑，无论是在句法上还是在语义上，都只是这种更一般的、在某种意义上更基本的逻辑--以循环演算形式出现的资源逻辑--的一个特殊的、保守的片段。读者会发现各种有利于切换到新框架的论点，例如显示线性逻辑或其他基于公式的方法开发资源逻辑的表达能力不足的论点，在Cirquent演算提供的表示和证明复杂性方面，传统方法的指数改进等等。本文的主要目的之一是提供一个介绍性的起点，正如作者所希望的那样，可能有机会成为证明理论研究的一个新方向-基于电路而不是公式的证明理论。
英文摘要：
Cirquent calculus is a new proof-theoretic and semantic framework, whose main distinguishing feature is being based on circuits, as opposed to the more traditional approaches that deal with tree-like objects such as formulas or sequents. Among its advantages are greater efficiency, flexibility and expressiveness. This paper presents a detailed elaboration of a deep-inference cirquent logic, which is naturally and inherently resource conscious. It shows that classical logic, both syntactically and semantically, is just a special, conservative fragment of this more general and, in a sense, more basic logic -- the logic of resources in the form of cirquent calculus. The reader will find various arguments in favor of switching to the new framework, such as arguments showing the insufficiency of the expressive power of linear logic or other formula-based approaches to developing resource logics, exponential improvements over the traditional approaches in both representational and proof complexities offered by cirquent calculus, and more. Among the main purposes of this paper is to provide an introductory-style starting point for what, as the author wishes to hope, might have a chance to become a new line of research in proof theory -- a proof theory based on circuits instead of formulas.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
