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.
翻译:本文旨在为这个古老的开放问题提供一个全面的解决办法:如何用生动直观的图象、令人信服的哲学理由以及多种实用的用法来界定三重模型逻辑的语义;根据从创新角度从创新角度调查三重逻辑的现有工作方针,我们采取绕行法,从四重观的角度来解释三重逻辑,这导致发明了一种普遍和系统的方法来发展、解释和利用三重模型逻辑;我们通过两个具体案例来说明我们的方法,一个是虚构的,另一个是缩写性的,两者都详细介绍了一个健全和非常完整的自然扣减验证系统;我们认为,我们三重的模型逻辑是一个轻量级的候选,可以将脱俗或隐含的概念合并为时间逻辑,而不用多种方式的更重负担。