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

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.

In Proceedings TARK 2017, arXiv:1707.08250

References in corpus (1)

• The Undecidability of Arbitrary Arrow Update Logic