Models for Substructural Arithmetics

Australasian Journal of Logic 8:82-99 (2011)
  Copy   BIBTEX

Abstract

This paper explores models for arithmetic 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.

Categories

Keywords

Reprint years

2010

DOI

10.26686/ajl.v8i0.1814

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Models for substructural arithmetics.Greg Restall - 2010
An Algebraic Approach to the Disjunction Property of Substructural Logics.Daisuke Souma - 2007 - Notre Dame Journal of Formal Logic 48 (4):489-495.
Substructural epistemic logics.Igor Sedlár - 2015 - Journal of Applied Non-Classical Logics 25 (3):256-285.
Relevant and substructural logics.Greg Restall - unknown
Normal modal substructural logics with strong negation.Norihiro Kamide - 2003 - Journal of Philosophical Logic 32 (6):589-612.
Current Trends in Substructural Logics.Katalin Bimbó - 2015 - Journal of Philosophical Logic 44 (6):609-624.
Synthesized substructural logics.Norihiro Kamide - 2007 - Mathematical Logic Quarterly 53 (3):219-225.
Informational interpretation of substructural propositional logics.Heinrich Wansing - 1993 - Journal of Logic, Language and Information 2 (4):285-308.
Displaying and deciding substructural logics 1: Logics with contraposition.Greg Restall - 1998 - Journal of Philosophical Logic 27 (2):179-216.
A Canonical Model Construction For Substructural Logics With Strong Negation.N. Kamide - 2002 - Reports on Mathematical Logic:95-116.
Inter-model connectives and substructural logics.Igor Sedlár - 2014 - In Roberto Ciuni, Heinrich Wansing & Caroline Willkommen (eds.), Recent Trends in Philosophical Logic (Proceedings of Trends in Logic XI). Cham, Switzerland: Springer. pp. 195-209.
Kripke semantics for modal substructural logics.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (4):453-470.
Glivenko theorems revisited.Hiroakira Ono - 2010 - Annals of Pure and Applied Logic 161 (2):246-250.
Metacompleteness of Substructural Logics.Takahiro Seki - 2012 - Studia Logica 100 (6):1175-1199.
Cut Elimination In Noncommutative Substructural Logics.Bayu Surarso & Hiroakira Ono - 1996 - Reports on Mathematical Logic:13-29.

Analytics

Added to PP
2017-02-14

Downloads
7 (#1,356,784)

6 months
1 (#1,510,037)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Greg Restall
University of Melbourne

Citations of this work

Assertion, denial and non-classical theories.Greg Restall - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 81--99.
Wittgenstein on Incompleteness Makes Paraconsistent Sense.Francesco Berto - 2008 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 257--276.
From Hilbert proofs to consecutions and back.Tore Fjetland Øgaard - 2021 - Australasian Journal of Logic 18 (2):51-72.
Substitution in relevant logics.Tore Fjetland Øgaard - 2019 - Review of Symbolic Logic (3):1-26.

Add more citations

References found in this work

Add more references