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The Geometry of Non-Distributive Logics

(with Francesco Paoli) “The Geometry of Non-Distributive Logics”, Journal of Symbolic Logic 70:4 (2005) 1108–1126.

In this paper, we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness. We show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic, and we indicate how proofs in this system may be labelled with terms exhibiting a kind of Curry-Howard isomorphism. This natural deduction system is inspired both by Shoesmith and Smiley’s multiple conclusion systems for classical logic and Girard’s proofnets for linear logic.

This paper is joint work with Francesco Paoli.

Details

Author: Greg Restall
Status: Published in 2005

Local file: gndl.pdf (185KB)

DOI: 10.2178/jsl/1129642117

Subjects: non-classical logic proofs sequents

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 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.

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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 2009-05-25 at 03:19PM.

Thought

I haven’t a clue what it is to give a sense to a notion; the notion of giving sense to a notion hasn’t been given a sense, either in this context or, as far as I know, in any other. (I’ve been told that sense are sometimes given to concepts at Oxford after the gates close to visitors; but that may be a leg-pull.)
— Jerry Fodor, in The London Review of Books July 2000.