可计算性逻辑中的并行递归与分支递归
The parallel versus branching recurrences in computability logic
摘要：
本文证明了可计算性逻辑的并行递归导出的基本逻辑是分支递归导出的基本逻辑的真超集。后者被称为精确捕获的cirquent演算系统CL 15，由Japaridze保持健全--但不完整--与平行递归，而不是分支递归。目前的结果是通过积极验证该猜想。第二个结果的文件表明，平行递归是严格弱于分支递归的意义上说，而后者在逻辑上意味着前者，反之亦然不成立。
英文摘要：
This paper shows that the basic logic induced by the parallel recurrence of Computability Logic is a proper superset of the basic logic induced by the branching recurrence. The latter is known to be precisely captured by the cirquent calculus system CL15, conjectured by Japaridze to remain sound---but not complete---with parallel recurrence instead of branching recurrence. The present result is obtained by positively verifying that conjecture. A secondary result of the paper is showing that parallel recurrence is strictly weaker than branching recurrence in the sense that, while the latter logically implies the former, vice versa does not hold.
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