A Detailed Examination of Methods for Unifying, Simplifying and   Extending Several Results About Self-Justifying Logics
  This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps single most surprising new result will be its exploration of a viable alternative to conventional reflection principles. 
Dan E. Willard
math.LO