Linear Arithmetic Desecsed

March 1998

(with John K. Slaney and Robert K. Meyer) “Linear Arithmetic Desecsed,” Logique et Analyse, 39 (1996) 379–388 (published in 1998).

In classical and intuitionistic arithmetics, any formula implies a true equation, and a false equation implies anything. In weaker logics fewer implications hold. In this paper we rehearse known results about the relevant arithmetic R#, and we show that in linear arithmetic LL# by contrast false equations never imply true ones. As a result, linear arithmetic is desecsed. A formula A which entails 0=0 is a secondary equation; one entailed by 0≠0 is a secondary unequation. A system of formal arithmetic is secsed if every extensional formula is either a secondary equation or a secondary unequation. We are indebted to the program MaGIC for the simple countermodel SZ7, on which 0=1 is not a secondary formula. This is a small but significant success for automated reasoning.


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I’m Greg Restall, and this is my personal website. I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.

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