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Structuring metatheory on inductive definitions

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Basin,  David A.
Programming Logics, MPI for Informatics, Max Planck Society;

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Matthews,  Seán
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Basin, D. A., & Matthews, S. (1996). Structuring metatheory on inductive definitions. In M. A. McRobbie, & J. K. Slaney (Eds.), Proceedings of the 13th International Conference on Automated Deduction (CADE-13) (pp. 171-185). Berlin, Germany: Springer.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-AC17-2
Abstract
We examine a problem in formal metatheory: if theories are structured hierarchically, there are metatheorems which hold in only some extensions. We illustrate this using modal logics and the deduction theorem. We show how statements of metatheorems in such hierarchies can take account of possible theory extensions; i.e., a metatheorem formalizes not only the theory in which it holds, but also under what extensions, both to the language and proof system, it remains valid. We show that FS/sub 0/, a system for formal metamathematics, provides a basis for organizing theories this way, and we report on our practical experience