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ON DEFINABILITY IN MULTIMODAL LOGIC

  • JOSEPH Y. HALPERN (a1), DOV SAMET (a2) and ELLA SEGEV (a3)
  • DOI: http://dx.doi.org/10.1017/S175502030999013X
  • Published online: 01 September 2009
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.

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Corresponding author
*COMPUTER SCIENCE DEPARTMENT, CORNELL UNIVERSITY, ITHACA, NY 14853 E-mail:halpern@cs.cornell.edu
THE FACULTY OF MANAGEMENT, TEL AVIV UNIVERSITY, TEL AVIV, 69978, ISRAEL E-mail:samet@post.tau.ac.il
FACULTY OF INDUSTRIAL ENGINEERING AND MANAGEMENT, TECHNION—ISRAEL INSTITUTE OF TECHNOLOGY, ISRAEL E-mail:esegev@ie.technion.ac.il
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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