A multi-type calculus for inquisitive logic

G. Greco, Sabine Frittella, Alessandra Palmigiano, Fan Yang

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


In this paper, we define a multi-type calculus for inquisitive logic, which is sound, complete and enjoys Belnap-style cut-elimination and subformula property. Inquisitive logic is the logic of inquisitive semantics, a semantic framework developed by Groenendijk, Roelofsen and Ciardelli which captures both assertions and questions in natural language. Inquisitive logic adopts the so-called support semantics (also known as team semantics). The Hilbert-style presentation of inquisitive logic is not closed under uniform substitution, and some axioms are sound only for a certain subclass of formulas, called flat formulas. This and other features make the quest for analytic calculi for this logic not straightforward. We develop a certain algebraic and order-theoretic analysis of the team semantics, which provides the guidelines for the design of a multi-type environment accounting for two domains of interpretation, for flat and for general formulas, as well as for their interaction. This multi-type environment in its turn provides the semantic environment for the multi-type calculus for inquisitive logic we introduce in this paper.
Original languageEnglish
Title of host publicationLogic, Language, Information, and Computation - 23rd Workshop, WoLLIC 2016, Puebla, Mexico, August 16-19th, 2016. Proceedings
EditorsJ. Väänänen, Å. Hirvonen , R. de Queiroz
ISBN (Electronic)978-3-662-52921-8
ISBN (Print)978-3-662-52920-1
Publication statusPublished - 2016


  • Multi-type calculi
  • inquisitive logic
  • algebraic proof theory


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