Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article ‘Elementary-base cirquent calculus I: Parallel and choice connectives’ built the sound and complete axiomatization |$\textbf{CL16}$| of a propositional fragment of computability logic. The atoms of the language of |$\textbf{CL16}$| represent elementary, i.e. moveless, games and the logical vocabulary consists of negation, parallel connectives and choice connectives. The present paper constructs the first-order version |$\textbf{CL17}$| of |$\textbf{CL16}$|⁠, also enjoying soundness and completeness. The language of |$\textbf{CL17}$| augments that of |$\textbf{CL16}$| by including choice quantifiers. Unlike classical predicate calculus, |$\textbf{CL17}$| turns out to be decidable.

中文翻译：

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初等基础微积分II：选择量词

连续演算是一种新颖的证明理论，允许在逻辑表达式之间共享组件。前一篇文章“基于基本的演算I：并行和选择连接词”使用它构建了声音，并完成了公理化| $ \ textbf {CL16} $ | 可计算性逻辑的命题片段。| $ \ textbf {CL16} $ |语言的原子 代表基本游戏，即一动不动的游戏，逻辑词汇由否定，并行连接词和选择连接词组成。本文构造了一阶版本| $ \ textbf {CL17} $ | 的| $ \ textbf {CL16} $ |⁠，还享受可靠性和完备性。语言| $ \ textbf {CL17} $ | 扩大了| $ \ textbf {CL16} $ | 通过包括选择量词。与经典谓词演算不同，| $ \ textbf {CL17} $ | 事实证明是可以决定的。