We propose the identification of feedback mechanisms in biological systems by learning logical rules in R. Thomas’ Kinetic Logic (Thomas and D’Ari in Biological feedback. CRC Press, 1990). The principal advantages claimed for Kinetic Logic are that it captures an important class of regulatory networks at an appropriate level of precision, and that the representation is close to that used routinely by biologists, with a well-understood relationship to a differential description. In this paper we present a formalisation of Kinetic Logic as a labelled transition system and provide a provably correct implementation in a modified form of the Event Calculus. The behaviour of a system is then a logical consequence of the core-axioms of a (modified) Event Calculus C, the axioms K implementing Kinetic Logic and the axioms H describing the system. This formulation allows us to specify system identification in the manner adopted in Inductive Logic Programming (ILP), namely, given C, K, system behaviour S and possibly some additional domain-knowledge B, find H s.t. \(B \wedge C \wedge K \wedge H \models S\). Identifying a suitable Kinetic Logic hypothesis requires the simultaneous identification of definite clauses for: (a) logical definitions relating the occurrence of events to values of fluents; (b) delays in changes of the values of fluents arising from the occurrence of events; and possibly (c) exceptions to changes in fluent values, arising from asynchronous behaviour inherent to the system. We use a standard ILP engine for (a), and special-purpose abduction procedures for (b) and (c). We demonstrate this combination of induction and abduction on several canonical feedback patterns described by Thomas, and to identify the regulatory mechanism in two well-known biological problems (immune-response and phage-infection).

我们建议通过学习 R. Thomas 的 Kinetic Logic（Thomas 和 D'Ari in Biological feedback.CRC Press, 1990）中的逻辑规则来识别生物系统中的反馈机制。Kinetic Logic 声称的主要优势在于，它以适当的精度捕获一类重要的调节网络，并且表示与生物学家常规使用的表示接近，与差异描述之间具有易于理解的关系。在本文中，我们将 Kinetic Logic 形式化为标记的转换系统，并以事件微积分的修改形式提供可证明正确的实现。系统的行为则是（修改后的）事件演算C的核心公理的逻辑结果，公理K实现动力学逻辑和描述系统的公理H。这个公式允许我们以归纳逻辑编程 (ILP) 中采用的方式指定系统识别，即，给定C、  K、系统行为S和可能的一些附加领域知识B，找到H st \(B \wedge C \wedge K \楔形 H \模型 S\). 确定合适的动力学逻辑假设需要同时确定以下方面的明确条款： (a) 将事件的发生与流的值相关联的逻辑定义；(b) 因事件发生而导致的流体值变化的延迟；以及可能的 (c) 流畅值变化的异常，由系统固有的异步行为引起。我们对 (a) 使用标准 ILP 引擎，对 (b) 和 (c) 使用特殊目的诱拐程序。我们在 Thomas 描述的几种典型反馈模式上展示了这种诱导和诱导的组合，并确定了两个众所周知的生物学问题（免疫反应和噬菌体感染）中的调节机制。