In the first part of this paper we analyzed finite non-deterministic matrix semantics for propositional non-normal modal logics as an alternative to the standard Kripke possible world semantics. This kind of modal system characterized by finite non-deterministic matrices was originally proposed by Ju. Ivlev in the 70s. The aim of this second paper is to introduce a formal non-deterministic semantical framework for the quantified versions of some Ivlev-like non-normal modal logics. It will be shown that several well-known controversial issues of quantified modal logics, relative to the identity predicate, Barcan’s formulas and de re and de dicto modalities, can be tackled from a new angle within the present framework.

中文翻译：

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具有非确定性语义的模态逻辑：第二部分——量化案例

在本文的第一部分，我们分析了命题非正规模态逻辑的有限非确定矩阵语义，作为标准 Kripke 可能世界语义的替代方案。这种以有限非确定矩阵为特征的模态系统最初是由 Ju 提出的。70 年代的伊夫列夫。第二篇论文的目的是为一些类似 Ivlev 的非正规模态逻辑的量化版本引入一个正式的非确定性语义框架。它将表明，量化模态逻辑的几个众所周知的有争议的问题，与恒等谓词、Barcan 公式以及 de re 和 de dicto 模态有关，可以在当前框架内从一个新的角度解决。