Falsity conditions for if-sentences

Francien Dechesne

pp. 305-322

in: Gerhard Heinzmann, Manuel Rebuschi (eds), Aperçus philosophiques en logique et en mathématiques, Philosophia Scientiae 9 (2), 2005.

Abstract

We give a procedure to obtain falsity conditions for IF-sentences, using Skolemization. The expressive power of an IF-sentence can then be strongly captured by a pair of Σ11-sentences1. A result from [Burgess 2003] shows that, conversely, any pair of incompatible Σ11-sentences corresponds with an IF-sentence.In the second part, we reflect on the influence of the order of the steps (inside-out versus outside-in) in the Skolemization procedures for IF-logic. We also reflect on the nature of game theoretical negation.