I have a feeling Logback doesn't have a SyslogAppender that can send data using TLS.  I say that because I don't see a mention of "syslog" on http://logback.qos.ch/manual/usingSSL.html and I see http://jira.qos.ch/browse/LOGBACK-890 that mentions TLSSyslogAppender, but it looks like this never ended up in Logback.  I've only found it committed here: https://github.com/balabit/logback/commit/e0d89de2536e0925a6c816a50793f6a74e6a8dad