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Labelled Natural Deduction for Public Announcement Logic with Common Knowledge

Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia
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Mathematics 2020, 8(4), 626; https://doi.org/10.3390/math8040626
Received: 1 April 2020 / Revised: 14 April 2020 / Accepted: 15 April 2020 / Published: 18 April 2020
(This article belongs to the Section Mathematics and Computer Science)
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. View Full-Text
Keywords: public announcement logic; common knowledge; labelled natural deduction; dynamic logic; epistemic logic; proof theory public announcement logic; common knowledge; labelled natural deduction; dynamic logic; epistemic logic; proof theory
MDPI and ACS Style

Mohd Nasir, M.F.; Mior Othman, W.A.; Wong, K.B. Labelled Natural Deduction for Public Announcement Logic with Common Knowledge. Mathematics 2020, 8, 626.

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