A note on distributive normal forms

Dana Scott

pp. 75-90

in: Esa Saarinen, Risto Hilpinen, Ilkka Niiniluoto, Merrill Provence Hintikka (eds), Essays in honour of Jaakko Hintikka, Berlin, Springer, 1979

Abstract

This note should perhaps be called just a "footnote', since my concern here is in a reformulation of the definition. In a long sequence of papers Hintikka and his coworkers (see the bibliography, which I hope is reasonably complete) have introduced, developed, and applied the idea of this normal form and its constituents which are the main ingredient. Usually the description is quite syntactical — since after all these are normal forms of formulae written out in first-order predicate calculus. In the reformulation here the definition will be purely set theoretical: the constituents will correspond to certain sets of finite rank ("types' of finite depth) that could be considered quite apart from the usual formal language. However, the translation back to first-order logic is very quick, so not all that much is gained. The exercise of seeing the connection might nevertheless help the reader understand what exactly is being expressed in these normal forms.