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/Conference proceedings/Edited volumeConference contributionScientificpeer-review

24 Citations (Scopus)


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 publicationProceedings of Logic, Language, Information, and Computation - 23rd International Workshop, WoLLIC 2016
Number of pages19
ISBN (Print)9783662529201
Publication statusPublished - 2016
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)
ISSN (Print)03029743
ISSN (Electronic)16113349


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


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