In this paper we develop a novel propositional semantics based on the framework of branching time. The basic idea is to replace the moment-history pairs employed as parameters of truth in the standard Ockhamist semantics by pairs consisting of a moment and a consistent, downward closed set of so-called transitions. Whereas histories represent complete possible courses of events, sets of transitions can represent incomplete parts thereof as well. Each transition captures one of the alternative immediate future possibilities open at a branching point. The transition semantics exploits the structural resources a branching time structure has to offer and provides a fine-grained picture of the interrelation of modality and time. In addition to temporal and modal operators, a so-called stability operator becomes interpretable as a universal quantifier over the possible future extensions of a given transition set. The stability operator allows us to specify how and how far time has to unfold for the truth value of a sentence at a moment to become settled and enables a perspicuous treatment of future contingents. We show that the semantics developed along those lines generalizes and extends extant approaches: both Peirceanism and Ockhamism can be viewed as limiting cases of the transition approach that build on restricted resources only, and on both accounts, stability collapses into truth.

中文翻译：

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分支时间的转换语义

在本文中，我们基于分支时间框架开发了一种新颖的命题语义。基本思想是将标准奥卡姆主义语义中用作真理参数的矩-历史对替换为由矩和一致的、向下封闭的所谓转换集组成的对。历史代表事件的完整可能过程，而转换集也可以代表其中不完整的部分。每个转换都捕获了在分支点打开的替代的近期未来可能性之一。转换语义利用分支时间结构必须提供的结构资源，并提供模态和时间相互关系的细粒度图。除了时间和模态运算符，所谓的稳定性算子变得可以解释为对给定转换集的未来可能扩展的全称量词。稳定性算子允许我们指定时间必须如何展开以及多远才能使某个时刻的句子的真值变得稳定，并且可以清楚地处理未来的偶然性。我们表明，沿着这些路线发展的语义概括和扩展了现存的方法：皮尔斯主义和奥卡姆主义都可以被视为仅建立在有限资源上的过渡方法的限制案例，并且在这两种情况下，稳定性都崩溃了。稳定性算子允许我们指定时间必须如何展开以及多远才能使某个时刻的句子的真值变得稳定，并且可以清楚地处理未来的偶然性。我们表明，沿着这些路线发展的语义概括和扩展了现存的方法：皮尔斯主义和奥卡姆主义都可以被视为仅建立在有限资源上的过渡方法的限制案例，并且在这两种情况下，稳定性都崩溃了。稳定性算子允许我们指定时间必须如何展开以及多远才能使某个时刻的句子的真值变得稳定，并且可以清楚地处理未来的偶然性。我们表明，沿着这些路线发展的语义概括和扩展了现存的方法：皮尔斯主义和奥卡姆主义都可以被视为仅建立在有限资源上的过渡方法的限制案例，并且在这两种情况下，稳定性都崩溃了。