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arXiv · 1707.08754

Arbitrary Arrow Update Logic with Common Knowledge is neither RE nor co-RE

Louwe B. Kuijer
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Abstract

Arbitrary Arrow Update Logic with Common Knowledge (AAULC) is a dynamic epistemic logic with (i) an arrow update operator, which represents a particular type of information change and (ii) an arbitrary arrow update operator, which quantifies over arrow updates. By encoding the execution of a Turing machine in AAULC, we show that neither the valid formulas nor the satisfiable formulas of AAULC are recursively enumerable. In particular, it follows that AAULC does not have a recursive axiomatization.

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Louwe B. Kuijer. 2017-07-27. Arbitrary Arrow Update Logic with Common Knowledge is neither RE nor co-RE. https://doi.org/10.4204/eptcs.251.27

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