New Territories for Modal Logic

• Applicant: Professor 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

• Final Report Year: 2024

Final Report Abstract

The aim of the project was to establish a new and more general framework for modal logic based on inquisitive semantics. The working hypothesis, substantiated in the proposal, is that such a framework would allow us to bring within the scope of modal logic a range of interesting modal notions that were simply out of reach for the standard modal logic framework: the reason is that such notions are naturally analyzed as modal properties of (or relations between) questions, rather than propositions. As such, they are naturally regimented in a modal logic where modalities can be applied to questions. In addition, certain applications to the semantics of modals in natural language were envisaged; in particular, the new framework should allow us to systematize some important ideas that have appeared in the recent linguistics literature concerning the way modals interact with disjunction and other disjunction-like items. Given the short duration of the funding period, significant results have been achieved on multiple fronts, in particular with respect to: • the establishment of a general framework of inquisitive modal logic • the investigation of the mathematical properties of inquisitive logics • the application of the framework to the analysis of interesting (philosophical) notions • the investigation of certain topics at the interface between logic and philosophy of language. These results will be very important in the further development of this research program, to which I remain fully committed and around which a significant research community is gathering, as witnessed also by a recent workshop I organized at the University of Padua.

Publications

• Coherence in inquisitive first-order logic. Annals of Pure and Applied Logic, 173(9), 103155.
  Ciardelli, Ivano & Grilletti, Gianluca
  
• Describing neighborhoods in inquisitive modal logic. In S. Pinchinat, D. Fernandez-Duque, and A. Palmigiano, editors, Advances in Modal Logic (AiML), 217–236, London. College Publications. ISBN-13: 978-1-84890-413-2
  Ciardelli, I.
  
• Medvedev logic is the logic of finite distributive lattices without top element. In S. Pinchinat, D. Fernandez-Duque, and A. Palmigiano, editors, Advances in Modal Logic (AiML), 451–466, London. College Publications. ISBN-13: 978-1-84890-413-2
  Grilletti, G.
  
• Probabilities of conditionals: Updating Adams. Noûs, 58(1), 26-53.
  Ciardelli, Ivano & Ommundsen, Adrian
  
• Complexity of the model checking problem for inquisitive propositional and modal logic
  Ciardelli, I. & Grilletti, G.