非现实可能世界的逻辑

Logics of Non-actual Possible Worlds

在陈佳(2020)中,强可能性与弱必然性的逻辑被提出,并在许多框架类上被公理化。本文将称该逻辑为“非现实可能世界的逻辑”。然而,那里的完全性证明非常复杂,其中涉及到在典范模型的构造中极大一致集副本的使用,以及其他的考虑。在本文中,我们证明陈佳(2020)中某些系统的完全性可以通过翻译归约为文献中一些熟悉系统的完全性,从而在这些系统之间架起一座桥梁。我们也将探讨该逻辑的框架可定义性问题。

In Jia Chen(2020),a logic of strong possibility and weak necessity,which we call‘logic of non-actual possible worlds’here,is proposed and axiomatized over various frames.However,the completeness proof therein is quite complicated,which involves the use of copies of maximal consistent sets in the construction of the canonical model,among other considerations.In this paper,we demonstrate that the completeness of some systems thereof can be reduced to those of the familiar systems in the literature via translations,which builds a bridge among these systems.We also explore the frame definability of such a logic.