澄清剂II简介
Introduction to clarithmetic II
摘要：
早期的论文“Introduction to clarithmetic I”构建了一个基于可计算性逻辑的算术公理系统（见http：//www.cis.upenn.edu/linggiorgi/cl.html），并证明了它在多项式时间可计算性方面的可靠性和扩展完备性。本文阐述了三个额外的声音和完整的系统在相同的风格和意义：一个多项式空间可计算性，一个基本的递归时间（和/或空间）可计算性，和一个原始递归时间（和/或空间）可计算性。
英文摘要：
The earlier paper "Introduction to clarithmetic I" constructed an axiomatic system of arithmetic based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and extensional completeness with respect to polynomial time computability. The present paper elaborates three additional sound and complete systems in the same style and sense: one for polynomial space computability, one for elementary recursive time (and/or space) computability, and one for primitive recursive time (and/or space) computability.
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。
