Levesque's Axiomatization of only Knowing is Incomplete
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Abstract We show that the axiomatization given by Levesque for his logic of “only knowing” [2], which he showed to be sound and complete for the unquantified version of the logic and conjectured to be complete for the full logic, is in fact incomplete.
[1] Jr. Hartley Rogers. Theory of Recursive Functions and Effective Computability , 1969 .
[2] Hector J. Levesque,et al. Foundations of a Functional Approach to Knowledge Representation , 1984, Artif. Intell..
[3] Hector J. Levesque,et al. All I Know: A Study in Autoepistemic Logic , 1990, Artif. Intell..