Labelled Natural Deduction for Public Announcement Logic with Common Knowledge

Muhammad Farhan Mohd Nasir, Wan Ainun Mior Othman and Kok Bin Wong
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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

Mathematics, 2020, vol. 8, issue 4, 1-17

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.

Keywords: public announcement logic; common knowledge; labelled natural deduction; dynamic logic; epistemic logic; proof theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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