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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 de nitions allow... (Update)
Context of citations to this paper: More
.... display calculi since omitting one or more of these rules is then not possible (trivially) The second is the work of Matthews et al. [16,4,17,15] which implements Feferman s FS 0 in Isabelle, and uses it to formalise and extend various metatheoretical systems. It should be...
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BibTeX entry: (Update)
Basin, D A and S Matthews. Structuring metatheory on inductive definitions. Information and Computation, 162 (2000), 80--95. http://citeseer.ist.psu.edu/article/basin00structuring.html More
@inproceedings{ basin96structuring,
author = "David Basin and Se{\'a}n Matthews",
title = "Structuring Metatheory on Inductive Definitions",
booktitle = "Proceedings of the 13th International Conference on Automated Deduction ({CADE}-13)",
publisher = "Springer-Verlag LNAI 1104",
address = "New Brunswick, New Jersey",
editor = "M. A. McRobbie and J. K. Slaney",
pages = "171--185",
year = "1996",
url = "citeseer.ist.psu.edu/article/basin00structuring.html" }
Citations (may not include all citations):592 Introduction to HOL: A Theorem Proving Environment for Highe.. (context) - Gordon, Melham - 1993
505 Implementing Mathematics with the Nuprl Proof Development Sy.. - Constable - 1986
311 Abstract types have existential type (context) - Mitchell, Plotkin - 1985
294 Isabelle: A Generic Theorem Prover (context) - Paulson - 1994
150 Edinburgh LCF: A Mechanized Logic of Computation (context) - Gordon, Milner et al. - 1979
104 Metamathematical Investigation of Intuitionistic Arithmetic .. (context) - Troelstra - 1982
98 Using dependent types to express modular structure - MacQueen - 1986
75 Using typed lambda calculus to implement formal systems on a.. - Avron, Honsell et al. - 1992
38 Metalogical frameworks - Basin, Constable - 1993
38 Little theories - Farmer, Guttman et al. - 1992
14 Introduction to Combinators and -Calculus (context) - Hindley, Seldin - 1986
14 Almqvist and Wiksell (context) - Prawitz - 1965
13 A xedpoint approach to implementing (context) - Paulson - 1994
7 Implementing FS 0 in Isabelle: adding structure at the metal.. (context) - Matthews - 1996
6 Finitary inductive systems (context) - Feferman - 1990
5 Set theory for verication: II (context) - Paulson - 1995
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A Modular Presentation of Modal Logics in a Logical.. - Basin, Matthews.. (Correct)
A Recursion Planning Analysis of Inductive Completion - Barnett, Basin, Hesketh (1994) (Correct)
Program Development Schemata as Derived Rules - Anderson, Basin (1998) (Correct)
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