Traditional conformance checking tasks assume that event data provide a
faithful and complete representation of the actual process executions. This
assumption has been recently questioned: more and more often events are not
traced explicitly, but are instead indirectly obtained as the result of event
recognition pipelines, and thus inherently come with uncertainty. In this work,
differently from the typical probabilistic interpretation of uncertainty, we
consider the relevant case where uncertainty refers to which activity is
actually conducted, under a fuzzy semantics. In this novel setting, we consider
the problem of checking whether fuzzy event data conform with declarative
temporal rules specified as Declare patterns or, more generally, as formulae of
linear temporal logic over finite traces (LTLf). This requires to relax the
assumption that at each instant only one activity is executed, and to
correspondingly redefine boolean operators of the logic with a fuzzy semantics.
Specifically, we provide a threefold contribution. First, we define a fuzzy
counterpart of LTLf tailored to our purpose. Second, we cast conformance
checking over fuzzy logs as a verification problem in this logic. Third, we
provide a proof-of-concept, efficient implementation based on the PyTorch
Python library, suited to check conformance of multiple fuzzy traces at once.

传统的一致性检查任务假设事件数据提供了实际流程执行的准确和完整的表示。然而，由于日益普遍的事件识别管道所导致的不确定性，事件不再以明确的方式被跟踪，而是间接地得到。本文提出了一个新的模糊语义的模型，用于检查模糊事件数据是否符合声明模式或线性时间逻辑的要求。通过放宽假设并重新定义模糊语义的布尔运算符，我们能够检查多个模糊跟踪的一致性，以解决这一问题。

模糊日志的一致性检查与声明性时间规范

Conformance Checking of Fuzzy Logs against Declarative Temporal  Specifications

Order-Sorted Feature (OSF) logic is a knowledge representation and reasoning
language based on function-denoting feature symbols and set-denoting sort
symbols ordered in a subsumption lattice. OSF logic allows the construction of
record-like terms that represent classes of entities and that are themselves
ordered in a subsumption relation. The unification algorithm for such
structures provides an efficient calculus of type subsumption, which has been
applied in computational linguistics and implemented in constraint logic
programming languages such as LOGIN and LIFE and automated reasoners such as
CEDAR. This work generalizes OSF logic to a fuzzy setting. We give a flexible
definition of a fuzzy subsumption relation which generalizes Zadeh's inclusion
between fuzzy sets. Based on this definition we define a fuzzy semantics of OSF
logic where sort symbols and OSF terms denote fuzzy sets. We extend the
subsumption relation to OSF terms and prove that it constitutes a fuzzy partial
order with the property that two OSF terms are subsumed by one another in the
crisp sense if and only if their subsumption degree is greater than 0. We show
how to find the greatest lower bound of two OSF terms by unifying them and how
to compute the subsumption degree between two OSF terms, and we provide the
complexity of these operations.

在这项研究中，我们将 OSF 逻辑推广到模糊环境下，并给出了模糊子包含关系的灵活定义，建立了 OSF 逻辑的模糊语义，讨论了 OSF 术语之间的模糊子包含关系，并证明其构成了模糊偏序，同时介绍了如何通过统一操作找到两个 OSF 术语的最大下界以及计算两个 OSF 术语之间的子包含度，并给出了这些操作的复杂度。