@MISC{_minimalfrom, author = {}, title = {Minimal from Classical Proofs}, year = {} }

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Abstract

It is well known that any proof can be transformed into a unique normal form with respect to fi-conversion. Using j-expansion we can then construct the long normal form, where all minimal formulas are atomic. We are interested in the problem of how to find proofs in minimal logic, from a somewhat practical point of view. * In particular we want to make use of existing theorem provers based on classical logic. So our problem is to review under what circumstances a classical proof can be converted into a proof in minimal logic, and moreover to describe reasonable algorithms which do this conversion. A good survey of the subject can be found in [3, Chapter 2.3]. Here we add a new result. Note first that a convenient way to represent classical logic in our setting is to add stability assumptions of the form stabP: 8~x:::P ~x! P ~x for all predicate symbols P. For then we can easily derive:: ' ! ' for an arbitrary formula ', using