Valid Extensions of Introspective Systems: A Foundation for Reflective Theorem Provers

Introspective systems have been proved useful 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). Contents 1 Introduction 2 2 Basic notions 3 3 Introspective systems and their extensions 7 4 Application to reflective reasoning systems 11 5 Related Work 15 6 Conclusion 18 This work was supported by the Deutsche For..