The present paper establishes systematic connections among the first-order correspondents of Sahlqvist modal reduction principles in various relational semantic settings which include crisp and many-valued Kripke frames, and crisp and many-valued polarity-based frames (aka enriched formal contexts). Building on unified correspondence theory, we aim at introducing a theoretical environment which makes it possible to: (a) compare and inter-relate the various frame correspondents (in different relational settings) of any given Sahlqvist modal reduction principle; (b) recognize when first-order sentences in the frame-correspondence languages of different types of relational structures encode the same "modal content"; (c) meaningfully transfer and represent well known relational properties such as reflexivity, transitivity, symmetry, seriality, confluence, density, across different semantic contexts. These results can be understood as a first step in a research program aimed at making correspondence theory not just (methodologically) unified, but also (effectively) parametric.

翻译：本文系统性地建立了Sahlqvist模态归约原理在不同关系语义框架（包括清晰与多值Kripke框架、清晰与多值极性化框架，亦称扩充形式语境）中一阶对应物之间的联系。基于统一对应理论，我们旨在引入一个理论环境，使得能够：（a）比较并关联任意给定Sahlqvist模态归约原理在不同关系设定下的多种框架对应物；（b）识别不同类型关系结构框架对应语言中的一阶句子何时编码相同的“模态内容”；（c）将自反性、传递性、对称性、序列性、合流性、稠密性等已知关系属性有意义地转移并呈现在不同语义语境中。这些结果可被视为一个研究计划的第一步，该计划旨在使对应理论不仅（方法论上）统一，而且（有效地）参数化。