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A proof-theoretic approach to knowledge

We speculate on logical aspects of the so-called three wise men puzzle with proof-theoretic methods. We propose and study the following. (1) Logical ability of each player of a puzzle is equivalent to a logical system KL, which is based on classical propositional calculus augmented with inferences of knowledge operators. (2) Enriched pieces of knowledge of players are obtained as results of meta-theorems of KL. (3) Solvability of a puzzle is guaranteed by automated theorem proving. All this is attained by means of the cut elimination theorem for KL and its corollaries.