On displaying negative modalities

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Abstract

We extend Takuro Onishi's result on displaying substructural negations by formulating display calculi for non-normal versions of impos- sibility and unnecessity operators, called regular and co-regular negations, respectively, by Dimiter Vakarelov. We make a number of connections be- tween Onishi's work and Vakarelov's study of negation. We also prove a decidability result for our display calculus, which can be naturally extended to obtain decidability results for a large number of display calculi for logics with negative modal operators.

Original languageEnglish
Pages (from-to)161-192
Number of pages32
JournalLogic and Logical Philosophy
Volume27
Issue number2
DOIs
Publication statusPublished - Jun 2018

Keywords

  • Bi-intuitionistic logic
  • Decidability
  • Display calculus
  • Distributive logic
  • Impossibility
  • Negative modalities
  • Un-necessity
  • impossibility
  • unnecessity
  • negative modalities
  • bi-intuitionistic logic
  • distributive logic
  • decidability
  • display calculus

OECD FOS+WOS

  • 6.03.UA PHILOSOPHY
  • 1.01.QL LOGIC

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