A Recursively Axiomatizable Subsystem of Levesque’s Logic of Only Knowing
Ho Ngoc Duc
Institute for Information Systems, University of Luebeck, Ratzeburger Allee 160, 23562 Luebeck, Germany
A complete, recursive axiomatization of a subsystem of Levesque’s only-knowing logic is given. The sublogic is obtained by relaxing some of Levesque’s semantic conditions while keeping the most important definitions unchanged. The axiom system is obtained by adding an axiom of Humberstone to a subset of the set of Levesque’s axioms. The completeness result is proved using the subordination method of Hughes and Cresswell.