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

 download pdf

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.

Do you like this, or do you have a comment? Then please  share or reply on Twitter, or  email me.

← Logical Laws | Writing Archive | Displaying and Deciding Substructural Logics 1: Logics with Contraposition →


I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.



To receive updates from this site, you can subscribe to the  RSS feed of all updates to the site in an RSS feed reader, or follow me on Twitter at  @consequently, where I’ll update you if anything is posted.