New Territories for Modal Logic

模态逻辑的新领域

• 批准号: 446711878
• 负责人: Dr. Ivano Alessandro Ciardelli
• 金额: --
• 依托单位: Munich Center for Mathematical Philosophy (MCMP)
• 依托单位国家: 德国
• 项目类别: Independent Junior Research Groups
• 财政年份: 2021
• 资助国家: 德国
• 起止时间: 2020-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/446711878?language=en
• 关键词: New; Territories; Modal; Logic

Modal logic is at the heart of an incredibly fruitful interdisciplinary enterprise: it is used to analyze notions which are constitutive of our lives as rational social agents, such as knowledge, communication, obligation, action, and outcome; it finds important applications in computer science, and is a key tool in natural language semantics. In its existing form, modal logic builds on truth-conditional semantics, which models meaning in terms of truth conditions. This limits the applicability of modal logic in two ways. First, since questions are not true or false, we cannot analyze question-directed modal notions. Second, much recent work indicates that natural language modals are sensitive not only to the truth conditions of their argument, but also to the alternatives it evokes. In recent years, the applicant and his collaborators have developed an alternative to truth-conditional semantics, called inquisitive semantics. This theory provides a uniform foundation for the analysis of statements and questions. Moreover, it associates to each sentence a corresponding set of alternatives. Thus, inquisitive semantics provides just the ingredients needed to overcome the two limitations mentioned above. The project aims to explore a new framework for modal logic based on inquisitive semantics. This opens up new territories for modal logic in two ways. First, we can now define question-directed modalities, i.e., modalities that can be applied to a question such as "who will get elected?". This brings within the scope of modal logic a range of notions which are of philosophical as well as technical interest: examples are control/responsibility (e.g., “agent x controls who will get elected”), interest/indifference (e.g., “x is interested in/indifferent to who will get elected”), and dependency/determination (e.g., “who will get elected is determined by how many votes each candidate gets”). Second, we can now define and investigate alternative-sensitive modalities. In this way, the goal of a general theory of the alternative-sensitivity of natural language modals comes within reach.

模态逻辑是一个极其富有成效的跨学科事业的核心：它被用来分析构成我们作为理性社会主体的生活的概念，如知识、交流、义务、行动和结果；它在计算机科学中找到了重要的应用，并且是自然语言语义的关键工具。在现有的形式中，模态逻辑建立在真值条件语义的基础上，该语义学根据真值条件对意义进行建模。这从两个方面限制了模态逻辑的适用性。首先，由于问题不是真的或假的，我们不能分析问题导向的情态概念。其次，最近的研究表明，自然语言情态词不仅对其论据的真值条件敏感，而且对它所引起的选择也敏感。近年来，申请者和他的合作者开发了一种替代真值条件语义学的方法，称为探究性语义学。这一理论为分析陈述句和疑问句提供了统一的基础。此外，它还为每个句子关联了一组相应的备选方案。因此，探究性语义学正好提供了克服上述两个限制所需的成分。该项目旨在探索一种基于探究性语义的新的模态逻辑框架。这在两个方面为模态逻辑开辟了新的领域。首先，我们现在可以定义以问题为导向的模式，即可以应用于诸如“谁将当选？”之类的问题的模式。这在模态逻辑的范围内带来了一系列具有哲学和技术意义的概念：例如，控制/责任(例如，“代理x控制谁将当选”)、兴趣/冷漠(例如，“x对谁将当选感兴趣/无关”)，以及依赖/决定(例如，“谁将当选取决于每个候选人获得多少选票”)。其次，我们现在可以定义和研究替代敏感型模式。这样，自然语言情态的另类敏感度一般理论的目标就近在咫尺了。