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Models for Substructural Arithmetics

“Models for Substructural Arithmetics,’ Miscellanea Logica, 1–20 (2009), edited by Marta Bílková.

This paper explores models for arithmetics in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK (C plus weakening). The eventual goal is to find negation complete models for arithmetic in R.

This paper is dedicated to Professor Robert K. Meyer.

Details

Author: Greg Restall
Status: Published in 2009

Local file: mfsa.pdf (233KB)

Subjects: mathematics relevant logic substructural 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.

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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 2010-02-16 at 11:03PM.

Thought

Since we are in the main not sceptics, we might go on and frankly confess to each other the motives for our several faiths. I frankly confess mine – I cannot but think that at bottom they are of an aesthetic and not of a logical sort. — William James Essays in Radical Empiricism.