The Collaborative International Dictionary of English v.0.48:

exposit \exposit\ v.
   1. to set forth reasons; to explain or expound.
      [WordNet 1.5]

   2. to make external.

   Syn: externalize, externalise.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

exposit
    v 1: state; "set forth one's reasons" [syn: set forth,
         expound, exposit]
    2: add details, as to an account or idea; clarify the meaning of
       and discourse in a learned way, usually in writing; "She
       elaborated on the main ideas in her dissertation" [syn:
       elaborate, lucubrate, expatiate, exposit, enlarge,
       flesh out, expand, expound, dilate] [ant:
       abbreviate, abridge, contract, cut, foreshorten,
       reduce, shorten]