Modal reduction principles across relational semantics

Willem Conradie; Andrea De Domenico; Krishna Manoorkar; Alessandra Palmigiano; Mattia Panettiere; Daira Pinto Prieto; Apostolos Tzimoulis

arXiv · 2202.00899

Modal reduction principles across relational semantics

Willem Conradie·Andrea De Domenico·Krishna Manoorkar·Alessandra Palmigiano·Mattia Panettiere·Daira Pinto Prieto·Apostolos Tzimoulis

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Abstract

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.

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Willem Conradie, Andrea De Domenico, Krishna Manoorkar, Alessandra Palmigiano, Mattia Panettiere, Daira Pinto Prieto, Apostolos Tzimoulis. 2022-02-02. Modal reduction principles across relational semantics. https://arxiv.org/abs/2202.00899

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