There is a curious bifurcation in the literature on ground and its logic. On the one hand, there has been a great deal of work that presumes that logical complexity invariably yields grounding. So, for instance, it is widely presumed that any fact stated by a true conjunction is grounded in those stated by its conjuncts, that any fact stated by a true disjunction is grounded in that stated by any of its true disjuncts, and that any fact stated by a true double negation is grounded in that stated by the doubly-negated formula. This commitment is encapsulated in the system GG axiomatized and semantically characterized by [deRosset and Fine, 2023] (following [Fine, 2012]). On the other hand, there has been a great deal of important formal work on “flatter” theories of ground, yielding logics very different from GG [Correia, 2010] [Fine, 2016, 2017b]. For instance, these theories identify the fact stated by a self-conjunction \((\phi \wedge \phi )\) with that stated by its conjunct \(\phi \). Since, in these systems, no fact grounds itself, the “flatter” theories are inconsistent with the principles of GG. This bifurcation raises the question of whether there is a single notion of ground suited to fulfill the philosophical ambitions of grounding enthusiasts. There is, at present, no unified semantic framework employing a single conception of ground for simultaneously characterizing both GG and the “flatter” approaches. This paper fills this gap by specifying such a framework and demonstrating its adequacy.

关于地面及其逻辑的文献存在一个奇怪的分歧。一方面，已经有大量的工作假设逻辑复杂性总是会产生基础。因此，例如，人们普遍认为，真合取所陈述的任何事实都以它的合取所陈述的事实为基础，真析取所陈述的任何事实都以它的任何真析取所陈述的事实为基础，并且任何事实真正的双重否定所表述的内容是以双重否定公式所表述的内容为基础的。这一承诺被封装在由 [deRosset 和 Fine, 2023]（遵循 [Fine, 2012]）公理化和语义表征的系统 GG 中。另一方面，关于“平坦”地面理论已经有大量重要的正式工作，产生了与 GG 非常不同的逻辑 [Correia, 2010] [Fine, 2016, 2017b]。例如，这些理论将自结合\((\phi \wedge \phi )\)所陈述的事实与其结合\(\phi \)所陈述的事实识别出来。由于在这些系统中没有事实依据，“扁平化”理论与 GG 原则不一致。这种分歧提出了一个问题：是否存在单一的基础概念适合满足基础爱好者的哲学抱负。目前，还没有统一的语义框架采用单一的基础概念来同时表征 GG 和“扁平”方法。本文通过指定这样一个框架并证明其充分性来填补这一空白。