Modal Semantics without Possible Worlds:A Study of Hierarchical Non-deterministic Many-valuedSemantics

没有可能世界的模态语义:分层非确定性多值语义研究

• 批准号: 438073380
• 负责人: Dr. Daniel Skurt
• 金额: --
• 依托单位: Institut für Philosophie I
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/438073380?language=en
• 关键词: Modal; Semantics; without; Possible; Worlds

The aim of this project is the systematical investigation and development of non-deterministic many-valued hierarchical semantics, or Kearns' semantics, for various normal and non-normal modal logics. We will aim at answering the questions whether such semantics can be a suitable alternative to the established Kripke semantics for modal logics. Whereas for a long time presenting modal logics as many-valued logics seemed to be a dead research programme, the rediscovery of non-deterministic matrices has now changed the picture. As was to be expected, the non-deterministic many-valued semantics for modal logics is considerably more complex than the ordinary matrix semantics. However, as has been shown very recently, the non-deterministic many-valued semantics is significantly more expressive than Kripke's possible worlds semantics when it comes to axiomatizing a primitive possibility operator. The many-valued approach thus not only avoids any commitment to possible worlds or similar indices of semantic evaluation, but also promises to offer some formal advantage over the standard approach. In particular, we aim at a correspondence theory, similar to the correspondence theory of Kripke's possible worlds semantics, between different axiomatizations and, languages and their respective non-deterministic semantics. Furthermore, we will extend the modal language with additional modal operators, such as an actuality operator and plan on investigating constructive variants of modal logics in terms of Kearns’ semantics. Finally, we will discuss the philosophical implications of a concept of modality, which is not expressed in terms of possible worlds.

这个项目的目的是系统的调查和发展的非确定性多值层次语义，或卡恩斯的语义，为各种正常和非正常模态逻辑。我们的目标是回答这样的语义是否可以是一个合适的替代已建立的Kripke语义模态逻辑的问题。虽然在很长一段时间里，将模态逻辑作为多值逻辑来呈现似乎是一个死的研究计划，但非确定性矩阵的重新发现现在改变了这一局面。正如预期的那样，模态逻辑的非确定性多值语义比普通的矩阵语义复杂得多。然而，正如最近所示，非确定性多值语义在公理化原始可能性运算符时比克里普克的可能世界语义更具表达力。因此，多值方法不仅避免了对可能世界或类似的语义评估指标的任何承诺，而且还承诺提供一些比标准方法更正式的优势。特别是，我们的目标是在对应理论，类似于克里普克的可能世界语义的对应理论，不同的公理化和，语言和它们各自的非确定性语义之间。此外，我们将扩展模态语言与额外的模态操作符，如现实操作符，并计划调查建设性变体的模态逻辑在卡恩斯的语义。最后，我们将讨论模态概念的哲学含义，该概念不是用可能世界来表达的。