Undefinability in Inquisitive Logic with Tensor

Ivano Ciardelli, Fausto Barbero

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

Abstract

Logics based on team semantics, such as inquisitive logic and dependence logic, are not closed under uniform substitution. This leads to an interesting separation between expressive power and definability: it may be that an operator O can be added to a language without a gain in expressive power, yet O is not definable in that language. For instance, even though propositional inquisitive logic and propositional dependence logic have the same expressive power, inquisitive disjunction and implication are not definable in propositional dependence logic. A question that has been open for some time in this area is whether the tensor disjunction used in propositional dependence logic is definable in inquisitive logic. We settle this question in the negative. In fact, we show that extending the logical repertoire of inquisitive logic by means of tensor disjunction leads to an independent set of connectives; that is, no connective in the resulting logic is definable in terms of the others.
Original languageEnglish
Title of host publicationLogic, Rationality and Interaction : 7th International Workshop, LORI 2019, Chongqing, China, October 18–21, 2019, Proceedings
EditorsPatrick Blackburn, Emiliano Lorini, Meiyun Guo
Number of pages14
Volume11813
PublisherSpringer
Publication date2019
EditionLecture Notes in Computer Science
Pages29-42
ISBN (Print)9783662602911
ISBN (Electronic)9783662602928
DOIs
Publication statusPublished - 2019
MoE publication typeA4 Article in conference proceedings
Event7th International Workshop, LORI 2019 - Chongqing, China
Duration: 18 Oct 201921 Oct 2019
Conference number: 7

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume11813
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Fields of Science

  • 111 Mathematics
  • 611 Philosophy

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