Introspective systems have been proved ueful in several
applications, especially in the area of automated reasoning.
In this paper we propose to use structured algebraic
specifications to describe the embedded account of introspective
systems. Our main result is that extending such an introspective
system in a valid manner can be reduced to development of correct
software. Since sound extension of automated reasoning systems
again can be reduced to valid extension of introspective systems,
our work can be seen as a foundation for extensible
introspective reasoning systems, and in particular for
reflective provers. We prove correctness of our mechanism and
report on first experiences we have made with its realization in
the KIV system (Karlsruhe Interactive Verifier).