Note that all of the Shard's Intents are verbs or actions. Based on this, I would say that Logic wouldn't be possible as an Intent. However, Reason, Revelation, or Obfuscation are possible.
Brandon has said that if Alcatraz were Cosmere, the Shard would have been the Shard of Self-Contradiction or Self-Betrayal. Based on that, there might still be a Shard with that intent somewhere. But... I doubt that he would use it since he already used some of those ideas in Alcatraz.