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Labelled Natural Deduction for Public Announcement Logic with Common Knowledge

Author

Listed:
  • Muhammad Farhan Mohd Nasir

    (Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia)

  • Wan Ainun Mior Othman

    (Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia)

  • Kok Bin Wong

    (Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia)

Abstract

Public announcement logic is a logic that studies epistemic updates. In this paper, we propose a sound and complete labelled natural deduction system for public announcement logic with the common knowledge operator (PAC). The completeness of the proposed system is proved indirectly through a Hilbert calculus for PAC known to be complete and sound. We conclude with several discussions regarding the system including some problems of the system in attaining normalisation and subformula property.

Suggested Citation

  • Muhammad Farhan Mohd Nasir & Wan Ainun Mior Othman & Kok Bin Wong, 2020. "Labelled Natural Deduction for Public Announcement Logic with Common Knowledge," Mathematics, MDPI, vol. 8(4), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:626-:d:347234
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