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ON DEFINABILITY IN MULTIMODAL LOGIC

Published online by Cambridge University Press:  05 October 2009

JOSEPH Y. HALPERN ,
DOV SAMET  and
ELLA SEGEV
JOSEPH Y. HALPERN*
Affiliation:
Computer Science Department, Cornell University
DOV SAMET*
Affiliation:
The Faculty of Management, Tel Aviv University
ELLA SEGEV*
Affiliation:
Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology
*
*COMPUTER SCIENCE DEPARTMENT, CORNELL UNIVERSITY, ITHACA, NY 14853 E-mail:[email protected]
†THE FACULTY OF MANAGEMENT, TEL AVIV UNIVERSITY, TEL AVIV, 69978, ISRAEL E-mail:[email protected]
‡FACULTY OF INDUSTRIAL ENGINEERING AND MANAGEMENT, TECHNION—ISRAEL INSTITUTE OF TECHNOLOGY, ISRAEL E-mail:[email protected]
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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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 3 , September 2009 , pp. 451 - 468
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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