Weakly complete axiomatization of exogenous quantum propositional logic

Authors:
P. Mateus;A. Sernadas
Affiliations:
CLC, Department of Mathematics, IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;CLC, Department of Mathematics, IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Venue:
Information and Computation
Year:
2006

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Abstract

A finitary axiomatization for EQPL (exogenous quantum propositional logic) is presented. The axiomatization is shown to be weakly complete relative to an oracle for analytical reasoning. The proof is carried out using a non-trivial extension of the Fagin-Halpern-Megiddo technique together with three Henkin style completions.