Matthews, S. A Theory and its Metatheory in FS 0 . In Dov M Gabbay (Ed), What is a logic system?, 329--354. Oxford University Press, 1994. Home/Search Document Details and Download
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A New Machine-checked Proof of Strong Normalisation for.. - Dawson, Goré (2002) (Correct)
....to obtain certain structural rules like exchange, weakening and contraction for free . The associated weak normalisation results are therefore not as modular as in 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 possible to formalise weak normalisation for cut elimination in this implementation since Matthews outlines how it might be done using pencil and paper , and suggests ....
Matthews, S. A Theory and its Metatheory in FS 0 . In Dov M Gabbay (Ed), What is a logic system?, 329--354. Oxford University Press, 1994.
Formalization of the Development Process - Basin, Krieg-Brückner (1998) (Correct)
.... z (14.4) Fig. 14.1. Defining axioms and properties of use formal in a strong and restrictive sense: A development (or assertion) is formal when it is carried out (or stated) in an explicitly formalized calculus and is informal otherwise. Formal mathematics, as pioneered by the project of Automath [dB80], has been taken up with considerable enthusiasm by computer scientists. However, most arguments about program correctness and, in general, mathematics are informal in our strong sense. Before we consider what extra effort is required to formalize developments, let us first motivate why it might ....
....object logic are also defined in FS 0 by inductively defined classes. This allows the development of rules that are admissible but not necessarily derivable (for the distinction, see [HS86,Tro82] Furthermore, this facilitates a formal development of proof transformations such as cut elimination [Mat94] 14.3.3 Generalized unification and matching The advantage of schematic rules over rules specified using arbitrary programs is that the former may be directly applied using matching or unification. With the latter, a development step requires the user to provide appropriate instances, execute ....
Sean Matthews. A theory and its metatheory in FS0 . In Gabbay and Guenthner [GG94].
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