Modal logics for reasoning about infinite unions and intersections of binary relations

Natasha Alechina, Philippe Balbiani*, Dmitry Shkatov

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We consider multi-modal logic Kw(with countably infinite number of basic modalities) extended with additional modalities ∪ and ∩ corresponding to the union and intersection of all basic modalities. We present complete and sound axiomatic systems and polynomial-space terminating tableau-based decision procedures for the basic logic in this language, and its deterministic counterpart. We also show that admits filtration, which can be used independently of our tableaux to establish its decidability.

Original languageEnglish
Pages (from-to)275-294
Number of pages20
JournalJournal of Applied Non-Classical Logics
Volume22
Issue number4
DOIs
Publication statusPublished - 1 Dec 2012
Externally publishedYes

Keywords

  • axiomatic systems
  • filtration
  • infinite intersections and unions
  • modal logic
  • tableau-based decision procedures

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