They are two very different things. Logic as a word is related to the greek word Logos, and it has to do with deductive and inductrive reasoninng; true statement vs false statments, and proper vs fallacious argumentation, etc.
Psychics, on the other hand, deals with what's called Divination. Psychics are supposidly gifted with the power to see into the future. Historically, kings have used them to see whether they would win the battle (Oracle of Delphi), or to solve a vision or dream (Daniel 2:1-19), but most commonly, they're seen in small shops they've set for themselves.