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Journal Article

Structuring Metatheory on Inductive Definitions

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

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

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Citation

Matthews, S., & Basin, D. A. (2000). Structuring Metatheory on Inductive Definitions. Information and Computation, 162(1/2), 80-95.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-346F-B
Abstract
We examine a problem for machine supported metatheory. There are statements true about a theory that are true of some (but only some) extensions; however standard theory-structuring facilities do not support selective inheritance. We use the example of the deduction theorem for modal logic and show how a statement about a theory can explicitly formalize the closure conditions extensions should satisfy for it to remain true. We show how metatheories based on inductive definitions allow theories and general metatheorems to be organized hierarchically this way, and report on a case study using the theory FS0.