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Journal of Logic and Computation Advance Access published online on June 16, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp031
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

A Complete Deductive System for Probability Logic1

Chunlai Zhou

State Key Lab of Intelligent Systems and Technology, Tsinghua National Lab for Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China.
E-mail: czhou{at}tsinghua.edu.cn

Received 4 December 2007.


  Abstract

In this article, we provide a complete deductive system {Sigma}+ for probability logic that is different from the systems by Fagin and Halpern and by Heifetz and Mongin in the literature. The most important principle of the axiomatization is an infinitary Archimedean rule (ARCH). Our proof of the completeness of {Sigma}+ is in keeping with the Kripke-style proof of completeness in modal logic. With the Fourier–Motzkin elimination method, we show both the decidability and Moss's conjecture that the rule (ARCH) is essentially finitary. The perspective of this article is mainly logical. At the end, we point to some further research continuing this piece of work from a coalgebraic perspective.

Keywords: Knowledge and belief; probability logic; modal logic; coalgebras

1This research is partially supported by NSF of China (Grant No: 60736011) and by the Chinese Postdoctoral Foundation (Grant No: 023220030).


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