I was kindly granted permission by the Wiley-VCH Verlag GmbH & Co. KGaA to post here the pre-peer reviewed version of the article. I was asked to include this text: "Proof interpretations with truth", Jaime Gaspar and Paulo Oliva, Mathematical Logic Quarterly, volume 56, number 6, Copyright (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. I was also asked to include this text: This is the pre-peer reviewed version of the following article: Jaime Gaspar and Paulo Oliva, "Proof interpretations with truth", Mathematical Logic Quarterly, volume 56, number 6, pages 591-610, 2010, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/malq.200910112/abstract.