New Territories for Modal Logic

• Applicant: Dr. Ivano Alessandro Ciardelli
• Subject Area: Theoretical Philosophy ; General and Comparative Linguistics, Experimental Linguistics, Typology, Non-European Languages ; Mathematics ; Theoretical Computer Science
• Term: from 2021 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 446711878

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.

• DFG Programme: Independent Junior Research Groups