标题： 模态逻辑 -- RN矩阵 vs. N矩阵 显示英文标题

标题： Modal Logics -- RNmatrices vs. Nmatrices

摘要： 在本文中，我们将讨论两种模态逻辑的语义方法之间的相似之处和不同之处——非确定性语义和限制性非确定性语义。 一般来说，这两种语义在某种程度上是相似的，因为它们都以非确定性矩阵作为起点，但在构建最小模态逻辑 M 的扩展方式上存在显著差异。 这两种语义都是多值的，真值通常用 0 和 1 的元组来表示，其中元组的每个维度代表真/假、可能/不可能、必然/不必然等。 虽然模态逻辑的非确定性语义提供了对真值和模态概念的直观解释，但限制性非确定性语义在以统一的方式提供 M 的扩展（包括正常的扩展）方面更为普遍。 通过三个模态逻辑 MK、MKT 和 MKT4 的例子，我们将展示这两种方法的差异和相似之处。 此外，我们将简要讨论这两种方法（目前）的限制。 显示英文摘要

摘要： In this short paper we will discuss the similarities and differences between two semantic approaches to modal logics - non-deterministic semantics and restricted non-deterministic semantics. Generally speaking, both kinds of semantics are similar in the sense that they employ non-deterministic matrices as a starting point but differ significantly in the way extensions of the minimal modal logic M are constructed. Both kinds of semantics are many-valued and truth-values are typically expressed in terms of tuples of 0s and 1s, where each dimension of the tuple represents either truth/falsity, possibility/non-possibility, necessity/non-necessity etc. And while non-deterministic semantics for modal logic offers an intuitive interpretation of the truth-values and the concept of modality, with restricted non-deterministic semantics are more general in terms of providing extensions of M, including normal ones, in an uniform way. On the example of three modal logics, MK, MKT and MKT4, we will show the differences and similarities of those two approaches. Additionally, we will briefly discuss (current) restrictions of both approaches.