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.
Kripke Completeness of Strictly Positive Modal Logics over Meet-semilattices with Operators
University of Oxford（牛津大学）；Birkbeck, University of London（伦敦大学伯贝克学院）；Institute for Information Transmission Problems（信息传输问题研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；King’s College London（伦敦国王学院）；Kyushu Sangyo University（九州产业大学）；University of Liverpool（利物浦大学）
