Relational concept analysis (RCA) is an extension of formal concept analysis allowing to deal with several related contexts simultaneously. It has been designed for learning description logic theories from data and used within various applications. A puzzling observation about RCA is that it returns a single family of concept lattices although, when the data feature circular dependencies, other solutions may be considered acceptable. The semantics of RCA, provided in an operational way, does not shed light on this issue. In this report, we define these acceptable solutions as those families of concept lattices which belong to the space determined by the initial contexts (well-formed), cannot scale new attributes (saturated), and refer only to concepts of the family (self-supported). We adopt a functional view on the RCA process by defining the space of well-formed solutions and two functions on that space: one expansive and the other contractive. We show that the acceptable solutions are the common fixed points of both functions. This is achieved step-by-step by starting from a minimal version of RCA that considers only one single context defined on a space of contexts and a space of lattices. These spaces are then joined into a single space of context-lattice pairs, which is further extended to a space of indexed families of context-lattice pairs representing the objects manip

翻译：关系概念分析（RCA）是形式概念分析的一种扩展，允许同时处理多个相关上下文。它旨在从数据中学习描述逻辑理论，并已在各种应用中使用。关于RCA的一个令人困惑的观察是，它返回单一的概念格族，尽管当数据具有循环依赖关系时，其他解可能也被认为可接受。RCA的语义以操作方式给出，并未阐明这一问题。在本报告中，我们将这些可接受解定义为属于初始上下文确定的空间（良构）、无法扩展新属性（饱和）、且仅引用该族中的概念（自支撑）的概念格族。我们通过定义良构解空间以及该空间上的两个函数（一个扩张函数，一个收缩函数），采用函数视角看待RCA过程。我们证明可接受解是这两个函数的公共不动点。这是通过逐步实现得到的：从RCA的最小版本开始，该版本仅考虑定义在上下文空间和格空间上的单一上下文；然后将这些空间合并为上下文-格对的单一空间，进一步扩展为表示所操作对象的上下文-格对索引族空间。