New Territories for Modal Logic

模态逻辑是一项卓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；它在计算机科学中有重要的应用，是自然语言语义研究的关键工具。模态逻辑的现有形式是建立在真条件语义的基础上的，它根据真条件对意义进行建模。这在两个方面限制了模态逻辑的适用性。首先，由于问题不是真或假，我们不能分析问题导向的模态概念。其次，最近的许多研究表明，自然语言情态不仅对其论点的真值条件敏感，而且对它所唤起的替代选项也敏感。近年来，申请人和他的合作者开发了一种替代真条件语义，称为好奇语义。这一理论为分析陈述和问题提供了统一的基础。此外，它还为每个句子关联了一组相应的替代词。因此，探究性语义提供了克服上述两个限制所需的要素。该项目旨在探索基于探究语义的模态逻辑的新框架。这从两个方面为模态逻辑开辟了新的领域。首先，我们现在可以定义问题导向的模态，即可以应用于诸如“谁将当选？”这样的问题的模态。这将模态逻辑的范围引入了一系列哲学和技术上感兴趣的概念：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/漠不关心”），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模式。这样，自然语言情态的替代敏感性的一般理论的目标就可以实现了。

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.