一句话:通过扩展素事件结构并引入等价关系,构造一般事件结构的因果展开,证明其为伪右伴随。
一般事件结构能刻画事件由多组原因(析取原因)使能的情形,包括互斥原因和可共存并行的原因;但当需要把概率与共同事件的不同、可能共存的因果历史精确关联时,它过于粗略。论文尝试让一般事件结构的因果历史对应到其到素事件结构的因果展开的构型,并希望因果展开是素事件结构嵌入一般事件结构的右伴随,但该伴随不存在。作者扩展素事件结构,引入等价关系分离事件与其使能,使素原因由析取事件(等价类)标记;并以极值因果实现为核心,证明因果展开是伪右伴随的普适构造。最后研究支持并行原因的子范畴及构建概率分布式策略所需操作。
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.