A multi-type calculus for inquisitive logic

Sabine Frittella*, Giuseppe Greco, Alessandra Palmigiano, Fan Yang

*Corresponding author for this work

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 International Workshop, WoLLIC 2016, Proceedings
EditorsJouko Väänänen, Åsa Hirvonen, Ruy de Queiroz
PublisherSpringer Verlag
Number of pages19
ISBN (Print)9783662529201
Publication statusPublished - 1 Jan 2016
Externally publishedYes
Event23rd International Workshop on Logic, Language, Information, and Computation, WoLLIC 2016 - Puebla, Mexico
Duration: 16 Aug 201619 Aug 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9803 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Workshop on Logic, Language, Information, and Computation, WoLLIC 2016


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