Robert Stalnaker recently proposed a simple theory of propositions using the notion of a set of propositions being consistent, and conjectured that this theory is equivalent to the claim that propositions form a complete atomic Boolean algebra. This paper clarifies and confirms this conjecture. Stalnaker also noted that some of the principles of his theory may be given up, depending on the intended notion of proposition. This paper therefore also investigates weakened constraints on consistency and the corresponding classes of Boolean algebras.

中文翻译：

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论斯达纳克的简单命题理论

Robert Stalnaker 最近提出了一个简单的命题理论，使用一组命题一致的概念，并推测该理论等价于命题形成完整的原子布尔代数的主张。本文澄清并证实了这一猜想。Stalnaker 还指出，他的理论的一些原则可能会被放弃，这取决于命题的预期概念。因此，本文还研究了对一致性和布尔代数的相应类的弱化约束。