New Territories for Modal Logic

模态逻辑是一个令人难以置信的富有成效的跨学科事业的核心：它被用来分析构成我们生活的理性社会代理的概念，如知识，沟通，义务，行动和结果;它在计算机科学中找到重要的应用，是自然语言语义学的关键工具。 模态逻辑以其现有的形式建立在真值条件语义学的基础上，它根据真值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的，我们不能分析问题导向的模态概念。其次，最近的研究表明，自然语言模态不仅对它们的论点的真值条件敏感，而且对它所唤起的替代品也敏感。 近年来，申请人和他的合作者已经开发了一种替代真值条件语义学的方法，称为探究语义学。这一理论为分析陈述句和疑问句提供了统一的基础。此外，它还将每个句子与一组相应的备选方案相关联。因此，探究语义学提供了克服上述两个限制所需的成分。 该项目旨在探索一个新的框架，模态逻辑的基础上探究语义。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模态，即，可适用于“谁将当选？".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控制谁将被选举”），兴趣/无差别（例如，“X对谁将当选感兴趣/不关心”），以及依赖性/确定性（例如，“谁当选取决于每个候选人得到多少选票”）。其次，我们现在可以定义和研究替代敏感模态。这样，自然语言情态动词的选择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.