On Definability in multimodal logic

Joseph Y. Halpern, Dov Samet, Ella Segev

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth's theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, reducibility, is introduced; it is shown that in multimodal logics, explicit definability is equivalent to the combination of implicit definability and reducibility. The three notions of definability are characterized semantically using (modal) algebras. The use of algebras, rather than frames, is shown to be necessary for these characterizations.

Original languageEnglish
Pages (from-to)451-468
Number of pages18
JournalReview of Symbolic Logic
Volume2
Issue number3
DOIs
StatePublished - 1 Sep 2009
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Philosophy
  • Logic

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