Yes, you have the possibility to recover the files with the help of a recovery application. For this operation, I would like to recommend installing Recuva. Recuva will scan the deleted files with the possibility to recover them. Access the application's page at Software Informer and download it. Start the application and use the built-in Wizard menu to initiate the scanning procedure. Select Other as file type and then choose the partition/folder where the logs were stored. For maximum accuracy, select the Deep Scan mode. It might take longer, but the accuracy is increased. Once you find the files, right click them and select Restore. Choose another partition other than the original location and that's it.