On Three-Valued Modal Logics: from a Four-Valued Perspective
Abstract
This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical usage. Based on an existing line of work concerned with investigating three-valued logic out of innovative angles of view, we adopt a detour approach to interpret three-valued logic from a four-valued perspective, which results in the invention of an universal and systematic methodology for developing, explaining as well as utilizing three-valued modal logic. We illustrate our method through two concrete cases, one deontic and another epistemic, for both of which a sound and strongly complete natural deduction proof system is also presented in detail. We perceive our three-valued modal logic as a lightweight candidate to merge deontic or epistemic notion into temporal logic, without heavier burden of multiple modalities.
Keywords
Cite
@article{arxiv.2209.13079,
title = {On Three-Valued Modal Logics: from a Four-Valued Perspective},
author = {Xinyu Wang and Yang Song and Satoshi Tojo},
journal= {arXiv preprint arXiv:2209.13079},
year = {2022}
}