非同余模态逻辑的高内涵模型

Pub Date : 2023-09-21 DOI:10.1093/jigpal/jzad018
Matteo Pascucci, Igor Sedlár
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引用次数: 0

摘要

在这项工作中,我们说明了基于高内涵模型的非同余模态逻辑的语义框架的应用。我们首先讨论这种方法背后的一些哲学思想;特别是,公式为真的可能世界集(其强度)与公式的语义内容(其高强度)之间的差异,后者在高强度模型中以严格的方式捕获。接下来,我们严格地说明了这种方法,并提供了一个基本的完备性定理。此外,我们分析了非同余系统的例子,这些系统可以在这个框架内以优雅和模块化的方式进行语义表征。最后,我们将提出的框架与文献中可用的一些替代方案进行比较。根据所获得的结果,我们认为高内涵模型构成了(非同余)模态逻辑的基本、一般和统一的语义框架。
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Hyperintensional models for non-congruential modal logics
Abstract In this work, we illustrate applications of a semantic framework for non-congruential modal logic based on hyperintensional models. We start by discussing some philosophical ideas behind the approach; in particular, the difference between the set of possible worlds in which a formula is true (its intension) and the semantic content of a formula (its hyperintension), which is captured in a rigorous way in hyperintensional models. Next, we rigorously specify the approach and provide a fundamental completeness theorem. Moreover, we analyse examples of non-congruential systems that can be semantically characterized within this framework in an elegant and modular way. Finally, we compare the proposed framework with some alternatives available in the literature. In the light of the results obtained, we argue that hyperintensional models constitute a basic, general and unifying semantic framework for (non-congruential) modal logic.
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