Skip to main content
×
Home
    • Aa
    • Aa

ON DEFINABILITY IN MULTIMODAL LOGIC

  • JOSEPH Y. HALPERN (a1), DOV SAMET (a2) and ELLA SEGEV (a3)
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.

Copyright
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
References
Hide All
Andréka H., van Benthem J., & Németi I. (1998). Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic, 27(3), 217274.
Beth E. W. (1953). On Padoa’s method in the theory of definition. Indagationes Mathematicae, 15, 330339.
Blackburn P., de Rijke M., & Venema Y. (2001). Modal Logic. Cambridge Tracts in Theoretical Computer Science, Vol. 53. Cambridge, UK: Cambridge University Press.
Halpern J. Y., Samet D., & Segev E. (2008). Defining knowledge in terms of belief: the modal logic perspective. Review of Symbolic Logic, forthcoming. Available from: http://www.cs.cornell.edu/home/halpern/papers.
van der Hoek W. (1993). Systems for knowledge and belief. Journal of Logic and Computation, 3(2), 173195.
Jónsson B., & Tarski A. (1951). Boolean algebras with operators, Part I. American Journal of Mathematics, 73, 891939.
Jónsson B., & Tarski A. (1952). Boolean algebras with operators, Part II. American Journal of Mathematics, 74, 127162.
Kracht M. (1999). Tools and Techniques in Modal Logic. Studies in Logic and the Foundations of Mathematics, Vol. 142. Amsterdam, The Netherlands: Elsevier.
Lenzen W. (1979). Epistemoligische betrachtungen zu [S4, S5]. Erkenntnis, 14, 3356.
Maksimova L. L. (1992a). An analogue of Beth’s theorem in normal extensions of the model logic K4. Siberian Mathematical Journal, 33(6), 10521065.
Maksimova L. L. (1992b). Modal logics and varieties of modal algebras: The Beth properties, interpolation, and amalgamation. Algebra and Logic, 31(2), 90105.
Pelletier F. J., & Urquhart A. (2003). Synonymous logics. Journal of Philosophical Logic, 32(3), 259285.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 13 *
Loading metrics...

Abstract views

Total abstract views: 137 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd October 2017. This data will be updated every 24 hours.