In the simplest form of event structure, a prime event structure, an event is associated with a unique causal history, its prime cause. However, it is quite common for an event to have disjunctive causes in that it can be enabled by any one of multiple sets of causes. Sometimes the sets of causes may be mutually exclusive, inconsistent one with another, and sometimes not, in which case they coexist consistently and constitute parallel causes of the event. The established model of general event structures can model parallel causes. On occasion however such a model abstracts too far away from the precise causal histories of events to be directly useful. For example, sometimes one needs to associate probabilities with different, possibly coexisting, causal histories of a common event. Ideally, the causal histories of a general event structure would correspond to the configurations of its causal unfolding to a prime event structure; and the causal unfolding would arise as a right adjoint to the embedding of prime in general event structures. But there is no such adjunction. However, a slight extension of prime event structures remedies this defect and provides a causal unfolding as a universal construction. Prime event structures are extended with an equivalence relation in order to dissociate the two roles, that of an event and its enabling; in effect, prime causes are labelled by a disjunctive event, an equivalence class of its prime causes. With this enrichment a suitable causal unfolding appears as a pseudo right adjoint. The adjunction relies critically on the central and subtle notion of extremal causal realisation as an embodiment of causal history. Finally, we explore subcategories which support parallel causes as well the key operations needed in developing probabilistic distributed strategies with parallel causes.

中文翻译：

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因果展开和分离原因

在事件结构的最简单形式中，主要事件结构中，事件与独特的因果历史相关联，这是其主要原因。然而，一个事件具有分离原因是很常见的，因为它可以被多组原因中的任何一组启用。有时，这组原因可能是相互排斥的，彼此不一致，有时则不是，在这种情况下，它们始终共存并构成事件的平行原因。建立的一般事件结构模型可以模拟平行原因。然而，有时这样的模型离事件的精确因果历史太远而不能直接有用。例如，有时需要将概率与同一事件的不同的、可能共存的因果历史联系起来。理想情况下，一般事件结构的因果历史将对应于其因果展开到主要事件结构的配置；因果展开将作为素数嵌入一般事件结构的正确伴随出现。但是没有这样的附加条件。然而，素事件结构的轻微扩展弥补了这一缺陷，并提供了作为普遍结构的因果展开。主要事件结构通过等价关系进行扩展，以分离事件及其使能的两种角色；实际上，主要原因被标记为析取事件，即其主要原因的等价类。通过这种丰富，合适的因果展开表现为伪右伴随。附加词批判地依赖于作为因果历史体现的极值因果实现的核心和微妙的概念。最后，我们探索支持并行原因的子类别以及开发具有并行原因的概率分布式策略所需的关键操作。