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Journal of Logic and Computation Advance Access published online on January 8, 2008
Journal of Logic and Computation, doi:10.1093/logcom/exm077
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original papers

General Models and Completeness of First-Order Modal µ-calculus

Ryo Kashima

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology. Ookayama, Meguro, Tokyo 152-8552, Japan. E-mail: kashima{at}is.titech.ac.jp

Keishi Okamoto

Research Center for Verification and Semantics, National Institute of Advanced Industrial Science and Technology, 1-2-14 Shin-Senri Nishi, Toyonaka, Osaka 560-0083, Japan. E-mail: keishi-okamoto{at}aist.go.jp

Received 16 April 2007.


  Abstract

There is no recursive axiomatization of first-order modal µ-calculus that is complete with respect to usual Kripke models. Then we introduce `general' models, and we prove that the natural axiom system of first-order modal µ-calculus is complete with respect to general models.

Keywords: First-order modal µ-calculus; modal logic; Kripke model; general model; completeness


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