Mares and Goldblatt (The Journal of Symbolic Logic, 71(01), 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the relevant logic R. In this paper, I show how to extend the Mares-Goldblatt frames to accommodate identity. Simpler frames are provided for two zero-order logics en route to the full logic in order to clarify what is needed for identity and substitution, as opposed to quantification. I close with a comparison of this work with the Fine-Mares models for relevant logics with identity and a discussion of constant and variable domains.

中文翻译：

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量化相关逻辑的Mares-Goldblatt模型中的身份

Mares和Goldblatt（Journal of Symbolic Logic，71（01），163-187，2006）为相关逻辑R的两个量化扩展提供了一种替代的框架语义。在本文中，我将展示如何扩展Mares-Goldblatt框架以适应身份。为两个零阶逻辑提供了更简单的框架，该逻辑在到达完整逻辑的过程中是为了阐明与量化相对应的标识和替换所需要的内容。最后，我将这项工作与Fine-Mares模型进行了比较，以了解具有身份的相关逻辑，并讨论了恒定域和可变域。