This is Greg Restall’s website, with news, writings, pictures, and links. For background see below.

On Permutation in Simplified Semantics

Greg Restall and Tony Roy “On Permutation in Simplified Semantics,” Journal of Philosophical Logic, 38:3 (2009) 333–341.

This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Journal of Philosophical Logic 1993) concerning the modelling conditions for the axioms of assertion A → ((A → B) → B) and permutation (A → (B → C)) → (B → (A → C)). We show that the modelling conditions for assertion and permutation proposed in ‘Simplified Semantics’ overgenerate. In fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism. The semantics provides for no models of R in which the “base point” is inconsistent.

In this note, we explain this result, diagnose the mistake in ‘Simplified Semantics’ and propose a correction.

Details

Author: Greg Restall and Tony Roy
Status: Published in 2009

Local file: permutation.pdf (230KB)

DOI: 10.1007/s10992-009-9104-z

Subjects: models negation relevant logic

About

I’m Greg Restall, and this is my website. I work in Philosophy at the University of Melbourne. Email: greg at consequently.org; Post: School of of Philosophy, Anthropology and Social Inquiry, University of Melbourne, Parkville 3010, Australia.

Start at the home page—a summary of the site. The left column is news, archived on the news archive page. The central column is for photos, archived on the occasional photos page. The right column contains recent items from the writing page, which lists my publications. These are also categorised by topic. You can follow my links at my account on delicious and occasional short snarky remarks at @consequently on twitter.

Current CO2 concentration in the atmosphere

To subscribe to this site, either read the full feed  of everything, the feed of news items only , or the feed of writing items only , which is also great for podcasting pdfs automatically.

This site is handcoded: I write text in Textmate, and Webby files things in the right place and uploads them to the server. This page was last modified on 2009-05-25 at 03:12PM.

Thought

The Glory of God is a human being fully alive. —St. Irenaeus.